Pat'sBlog: January 2018

Wednesday, 31 January 2018

On This Day in Math - January 31

Joost Bürgi nich at Kepler monument

on the market-place in the city Weil der Stadt in Baden-Württemberg

*Zeugnisse zu Mathematikern

The capacity to blunder slightly is the real marvel of DNA.
Without this special attribute, we would still be anaerobic bacteria
and there would be no music.

~Antoine-Thomson d' Abbadie

The 31st day of the year; 31 = 2² + 3³, i.e., The eleventh prime, and third Mersenne prime, it is also the sum of the first two primes raised to themselves. *Number Gossip (Is there another prime which is the sum of consecutive primes raised to themselves? A note from Andy Pepperdine of Bath who informed me that $2^2 + 3^3 +5^5 + 7^7 = 826699 $, a prime.)

There are exactly 31 positive integers which cannot be written as the sum of two distinct squares; and one of them is the number 31. Finding the 31 is not so hard, they all occur in the first six months of the year. Proving there are no more is a little tougher.

Jim Wilder ‏@wilderlab offered, The sum of digits of the 31st Fibonacci number (1346269) is 31.

If you like unusual speed limits, the speed limit in downtown Trenton, a small city in northwestern Tennessee, is 31 miles per hour.
And the little teapot on the sign? Well, Trenton also bills itself as the teapot capital of the nation. The 31 mph road sign seems to come from a conflict between Trenton and a neighboring town which I will not name ,...but I will tell you they think of themselves as the white squirrel capital.

31 is also the smallest integer that can be written as the sum of four positive squares in two ways 1+1+4+25; 4+9+9+9.

31 is an evil math teacher number. The sequence of the maximum number of regions obtained by joining n points around a circle by straight lines begins 2, 4, 8, 16... but for five points, it is 31.

And 31 is also the minimal number of moves to solve the Towers of Hanoi problem with five disks. (now wondering if there is a mathematical connection between these two ideas other than coincidence)

@JamesTanton posted a mathematical fact and query regarding 31. 31 =111(base 5) =11111(base 2) and 8191 =111(base 90) = 111111111111(base 2) are the only two integers known to be repunits at least 3 digits long in two different bases.
Is there an integer with representations 10101010..., ,at least three digits, in each of two different bases?

Which made me wonder, are there other pairs that are repdigits (all alike, but not all units) in two (or more) different bases?

EVENTS

1599 During an observation of the lunar eclipse, Tycho Brahe discovers that his predictive theory about the movement of the Moon is wrong since the eclipse started 24 minutes before his calculations predicted: he improves on his theory. On March 21 he sent a letter to Longomontanus, in which he reports his revised theory.*Wik

1802 Gauss elected a corresponding member of the St. Petersburg Academy of Science. *VFR

1834 Felix Klein declines to be the successor of J. J. Sylvester at John's Hopkins. Klein had been offered the position on December 13th of the previous year, but had demanded a salary equal to the departing Sylvester and some form of security for his family which Johns Hopkins did not meet. By October he would send notes to his family, "Gottingen is beginning to make noises." In the spring of 1836 he took over as Professor at Gottingen (he had been their second choice). *Constance Reid, The Road Not Taken, Mathematical Intelligencer, 1978

1839, Fox Talbot read a paper before the Royal Society, London, to describe his photographic process using solar light, with an exposure time of about 20 minutes: Some Account of the Art of Photogenic Drawing or the Process by which Natural Objects may be made to Delineate Themselves without the Aid of the Artist's Pencil. He had heard that Daguerre of Paris was working on a similar process. To establish his own priority, Fox Talbot had exhibited "such specimens of my process as I had with me in town," the previous week at a meeting of the Royal Institution, before he had this more detailed paper ready to present.*TIS

1939 Hewlett-Packard founded. Their calculators use the “reverse Polish notation” devised by Jan L Lukasiewicz (see here, 1878). *VFR

1939 Joseph Ehrenfried Hofmann began his academic career as a professor of the history of mathematics at the University of Berlin. He is noted for his work on Leibniz, especially the book Leibniz in Paris, 1672–1676: His Growth to Mathematical Maturity. *VFR Leibniz in Paris 1672-1676: His Growth to Mathematical Maturity

1958 Explorer 1 was launched on January 31, 1958 at 22:48 Eastern Time (equal to February 1, 03:48 UTC because the time change goes past midnight). It was the first spacecraft to detect the Van Allen radiation belt, returning data until its batteries were exhausted after nearly four months. It remained in orbit until 1970, and has been followed by more than 90 scientific spacecraft in the Explorer series. *Wik
Actually the Van Allen radiation was detectable by the Russian’s first satellite, Sputnik. Because the signals were sent in a secret code, it’s signal could not be received by the Russians when it was detecting the radiation of the belt. *Frederich Pohl, Chasing Science, pg 85

1995 AT&T Bell Laboratories and VLSI Technology announce plans to develop strategies for protecting communications devices from eavesdroppers. The goal would be to prevent problems such as insecure cellular phone lines and Internet transmissions by including security chips in devices. *CHM

2016, Since the year is a leap year beginning on a Friday, the typical calendar page for January takes six lines. Such months are called perverse months. (The same months will be perverse in a year starting on Saturday. 2016 has three such months, Jan, July and October. 2012 had only two. It is possible for there to be four in a single year. When will that year be? Is it possible for there to be a year with no perverse months?
There is an inverse relationship between Friday-the-thirteenths and perverse months; so what is good for the calendar makers is bad for the superstitious., so 2016 has only one Friday the 13th

Image credit: NASA/JPL-Caltech/MSSS/TAMU

2014 The Mars rover's view of its original home planet even includes our moon, just below Earth.
The images, taken about 80 minutes after sunset during the rover's 529th Martian day (Jan. 31, 2014) are available for a broad scene of the evening sky, and a zoomed-in view of Earth and the moon.
The distance between Earth and Mars when Curiosity took the photo was about 99 million miles (160 million kilometers). * NASA

2018 The rare combination of a blue moon (generally the second full moon of a month), a Supermoon (the full moon occurring nearest to perigee when moon is closer to earth), and a total lunar eclipse occurs early in the morning (8:37 am EST). Unfortunately it was only total in the western US. It is the first such triple treat in the US since 1866. *USA Today

BIRTHS

1715 Giovanni Francesco Fagnano dei Toschi (31 Jan 1715 in Sinigaglia, Italy - 14 May 1797 in Sinigaglia, Italy) He proved that the triangle which has as its vertices the bases of the altitudes of any triangle has those altitudes as its bisectors. *VFR Of all the triangles that could be inscribed in a given triangle, the one with the smallest perimeter is the orthic triangle. This has sometimes been called Fagnano's Problem since it was first posed and answered by Giovanni Francesco Fagnano dei Toschi. Fagnano also was the first to show that the altitudes of the original triangle are the angle bisectors of the orhtic triangle, so the incenter of the orthic triangle is the orthocenter of the original triangle.*pb
He was the son of the mathematician
Giulio Carlo Fagnano. He calculated the integral of the tangent and also proved the reduction formula $ \int x^n \sin {x} dx = -x^n \cos{x}+n\int x^{n-1} \cos{x} dx $

*VFR

1763 The Rt. Rev. John Mortimer Brinkley D.D. (ca. 1763 (Baptized 31 Jan,1763, Woodbridge, Suffolk – 14 September 1835, Dublin) was the first Royal Astronomer of Ireland and later Bishop of Cloyne.
He graduated B.A. in 1788 as senior wrangler and Smith's Prizeman, was elected a fellow of the college and was awarded M.A. in 1791. He was ordained at Lincoln Cathedral in the same year, and in 1792 became the second Andrews Professor of Astronomy in the University of Dublin, which carried the new title of Royal Astronomer of Ireland. Together with John Law, Bishop of Elphin, he drafted the chapter on "Astronomy" in William Paley's Natural Theology. His main work concerned stellar astronomy and he published his Elements of Plane Astronomy in 1808. In 1822 he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. He was awarded the Copley Medal by the Royal Society in 1824. Brinkley's observations that several stars shifted their apparent place in the sky in the course of a year were disproved at Greenwich by his contemporary John Pond, the Astronomer Royal. In 1826, he was appointed Bishop of Cloyne in County Cork, a position he held for the remaining nine years of his life. Brinkley was elected President of the Royal Astronomical Society in 1831, serving in that position for two years.
He died in 1835 at Leeson Street, Dublin and was buried in Trinity College chapel. He was succeeded at Dunsink Observatory by Sir William Rowan Hamilton. *Wik

1841 Samuel Loyd (31 Jan 1841 ; died 10 Apr 1911) was an American puzzlemaker who was best known for composing chess problems and games, including Parcheesi, in addition to other mathematically based games and puzzles. He studied engineering and intended to become a steam and mechanical engineer but he soon made his living from his puzzles and chess problems. Loyd's most famous puzzle was the 14-15 Puzzle which he produced in 1878. The craze swept America where employers put up notices prohibiting playing the puzzle during office hours. Loyd's 15 puzzle is the familiar 4x4 arrangement of 15 square numbered tiles in a tray that must be reordered by sliding one tile at a time into the vacant space. *TIS When he offered a cash prize to anyone who could solve the puzzle with 14&15 reversed, it swept the country. To show it impossible requires only a little group theory; see W. E. Story, “Note on the ‘15’ puzzle,” American Journal of Mathematics, 2, 399–404. For samples of Loyd’s many puzzles, see Mathematical Puzzles of Sam Loyd, edited by Martin Gardner, Dover 1959 [p. xi]. *VFR
Although Lloyd popularized the puzzle in his books and articles, he most certainly did not invent it. Loyd's first article about the puzzle was published in 1886 and it wasn't until 1891 that he first claimed to have been the inventor. The article mentioned by Story(1878) was dated prior to Loyd's first mention of the puzzle) Here is the history of the puzzle as related by Wikipedia:The puzzle was "invented" by Noyes Palmer Chapman, a postmaster in Canastota, New York, who is said to have shown friends, as early as 1874, a precursor puzzle consisting of 16 numbered blocks that were to be put together in rows of four, each summing to 34. Copies of the improved Fifteen Puzzle made their way to Syracuse, New York by way of Noyes' son, Frank, and from there, via sundry connections, to Watch Hill, RI, and finally to Hartford (Connecticut), where students in the American School for the Deaf started manufacturing the puzzle and, by December 1879, selling them both locally and in Boston, Massachusetts. Shown one of these, Matthias Rice, who ran a fancy woodworking business in Boston, started manufacturing the puzzle sometime in December 1879 and convinced a "Yankee Notions" fancy goods dealer to sell them under the name of "Gem Puzzle". In late-January 1880, Dr. Charles Pevey, a dentist in Worcester, Massachusetts, garnered some attention by offering a cash reward for a solution to the Fifteen Puzzle.
The game became a craze in the U.S. in February 1880, Canada in March, Europe in April, but that craze had pretty much dissipated by July. Apparently the puzzle was not introduced to Japan until 1889.
Noyes Chapman had applied for a patent on his "Block Solitaire Puzzle" on February 21, 1880. However, that patent was rejected, likely because it was not sufficiently different from the August 20, 1878 "Puzzle-Blocks" patent (US 207124) granted to Ernest U. Kinsey.*Wik
Play with an online version here.

1886 George Neville Watson (31 Jan 1886 in Westward Ho!, Devon, England - 2 Feb 1965 in Leamington Spa, Warwickshire, England) studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis. Titchmarsh wrote of Watson's books, "Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains." *SAU

1914 Lev Arkad'evich Kaluznin (31 Jan 1914 in Moscow, Russia - 6 Dec 1990 in Moscow, Russia) Kaluznin is best known for his work in group theory and in particular permutation groups. He studied the Sylow p-subgroups of symmetric groups and their generalisations. In the case of symmetric groups of degree pn, these subgroups were constructed from cyclic groups of order p by taking their wreath product. His work allowed computations in groups to be replaced by computations in certain polynomial algebras over the field of p elements. Despite the fact that the earliest applications of wreath products of permutation groups was due to C Jordan, W Specht and G Polya, it was Kaluznin who first developed special computational tools for this purpose. Using his techniques, he was able to describe the characteristic subgroups of the Sylow p-subgroups, their derived series, their upper and lower central series, and more. These results have been included in many textbooks on group theory. *SAU

1928 Heinz Bauer (31 January 1928 – 15 August 2002) was a German mathematician.
Bauer studied at the University of Erlangen-Nuremberg and received his PhD there in 1953 under the supervision of Otto Haupt and finished his habilitation in 1956, both for work with Otto Haupt. After a short time from 1961 to 1965 as professor at the University of Hamburg he stayed his whole career at the University of Erlangen-Nuremberg. His research focus was the Potential theory, Probability theory and Functional analysis
Bauer received the Chauvenet Prize in 1980 and became a member of the German Academy of Sciences Leopoldina in 1986. Bauer died in Erlangen. *Wik

1929 Rudolf Ludwig Mössbauer (31 Jan 1929 - 14 September 2011) German physicist and co-winner (with American Robert Hofstadter) of the Nobel Prize for Physics in 1961 for his researches concerning the resonance absorption of gamma-rays and his discovery in this connection of the Mössbauer effect. The Mössbauer effect occurs when gamma rays emitted from nuclei of radioactive isotopes have an unvarying wavelength and frequency. This occurs if the emitting nuclei are tightly held in a crystal. Normally, the energy of the gamma rays would be changed because of the recoil of the radiating nucleus. Mössbauer's discoveries helped to prove Einstein's general theory of relativity. His discoveries are also used to measure the magnetic field of atomic nuclei and to study other properties of solid materials. *TIS
Rudolf Mössbauer was an excellent teacher. He gave highly specialized lectures on numerous courses, including Neutrino Physics, Neutrino Oscillations, The Unification of the Electromagnetic and Weak Interactions and The Interaction of Photons and Neutrons With Matter. In 1984, he gave undergraduate lectures to 350 people taking the physics course. He told his students: “Explain it! The most important thing is, that you are able to explain it! You will have exams, there you have to explain it. Eventually, you pass them, you get your diploma and you think, that's it! – No, the whole life is an exam, you'll have to write applications, you'll have to discuss with peers... So learn to explain it! You can train this by explaining to another student, a colleague. If they are not available, explain it to your mother – or to your cat!” *Wik

1945 Persi Warren Diaconis (January 31, 1945; ) is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.
Diaconis left home at 14 to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, promising himself that he would return one day so that he could learn all of the math necessary to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He returned to school (City College of New York for his undergraduate work graduating in 1971 and then a Ph.D. in Mathematical Statistics from Harvard University in 1974), and became a mathematical probabilist.
According to Martin Gardner, at school Diaconis supported himself by playing poker on ships between New York and South America. Gardner recalls that Diaconis had "fantastic second deal and bottom deal".
Diaconis is married to Stanford statistics professor Susan Holmes. *Wik

DEATHS

1632 Joost Bürgi (28 Feb 1552, 31 Jan 1632) Swiss watchmaker and mathematician who invented logarithms independently of the Scottish mathematician John Napier. He was the most skilful, and the most famous, clockmaker of his day. He also made astronomical and practical geometry instruments (notably the proportional compass and a triangulation instrument useful in surveying). This led to becoming an assistant to the German astronomer Johannes Kepler. Bürgi was a major contributor to the development of decimal fractions and exponential notation, but his most notable contribution was published in 1620 as a table of antilogarithms. Napier published his table of logarithms in 1614, but Bürgi had already compiled his table of logarithms at least 10 years before that, and perhaps as early as 1588.
*TIS I posted about Burgi and his work w/ "proto" logarithms here if you would like more detail.

1903 Norman Macleod Ferrers; (11 Aug 1829 in Prinknash Park, Upton St Leonards, Gloucestershire, England - 31 Jan 1903 in Cambridge, England) John Venn wrote of him,.. ,

the Master, Dr Edwin Guest, invited Ferrers, who was by far the best mathematician amongst the fellows, to supply the place. His career was thus determined for the rest of his life. For many years head mathematical lecturer, he was one of the two tutors of the college from 1865. As lecturer he was extremely successful. Besides great natural powers in mathematics, he possessed an unusual capacity for vivid exposition. He was probably the best lecturer, in his subject, in the university of his day.

It was as a mathematician that Ferrers acquired fame outside the university. He made many contributions of importance to mathematical literature. His first book was "Solutions of the Cambridge Senate House Problems, 1848 - 51". In 1861 he published a treatise on "Trilinear Co-ordinates," of which subsequent editions appeared in 1866 and 1876. One of his early memoirs was on Sylvester's development of Poinsot's representation of the motion of a rigid body about a fixed point. The paper was read before the Royal Society in 1869, and published in their Transactions. In 1871 he edited at the request of the college the "Mathematical Writings of George Green" ... Ferrers's treatise on "Spherical Harmonics," published in 1877, presented many original features. His contributions to the "Quarterly Journal of Mathematics," of which he was an editor from 1855 to 1891, were numerous ... They range over such subjects as quadriplanar co-ordinates, Lagrange's equations and hydrodynamics. In 1881 he applied himself to study Kelvin's investigation of the law of distribution of electricity in equilibrium on an uninfluenced spherical bowl. In this he made the important addition of finding the potential at any point of space in zonal harmonics (1881).
Ferrers proved the proposition by Adams that "The number of modes of partitioning (n) into (m) parts is equal to the number of modes of partitioning (n) into parts, one of which is always m, and the others (m) or less than (m). " with a graphic transformation that is named for him. *SAU

1934 Duncan MacLaren Young Sommerville (24 Nov 1879 in Beawar, Rajasthan, India - 31 Jan 1934 in Wellington, New Zealand) Sommerville studied at St Andrews and then had a post as a lecturer there. He left to become Professor of Pure and Applied mathematics at Victoria College, Wellington New Zealand. He worked on non-Euclidean geometry and the History of Mathematics. He became President of the EMS in 1911. *SAU

1966 Dirk Brouwer (1 Sep 1902; 31 Jan 1966) Dutch-born U.S. astronomer and geophysicist known for his achievements in celestial mechanics, especially for his pioneering application of high-speed digital computers for astronomical computations. While still a student he determined the mass of Titan from its influence on other Saturnian moons. Brouwer developed general methods for finding orbits and computing errors and applied these methods to comets, asteroids, and planets. He computed the orbits of the first artificial satellites and from them obtained increased knowledge of the figure of the earth. His book, Methods of Celestial Mechanics, taught a generation of celestial mechanicians. He also redetermined astronomical constants.*TIS

1973 Noel Bryan Slater, often cited NB Slater, (29 July 1912 in Blackburn, Lancashire, England - January 31 1973 in Hull, England) was a British mathematician and physicist who worked on including statistical mechanics and physical chemistry, and probability theory.*Wik

1995 George Robert Stibitz (30 Apr 1904, 31 Jan 1995) U.S. mathematician who was regarded by many as the "father of the modern digital computer." While serving as a research mathematician at Bell Telephone Laboratories in New York City, Stibitz worked on relay switching equipment used in telephone networks. In 1937, Stibitz, a scientist at Bell Laboratories built a digital machine based on relays, flashlight bulbs, and metal strips cut from tin-cans. He called it the "Model K" because most of it was constructed on his kitchen table. It worked on the principle that if two relays were activated they caused a third relay to become active, where this third relay represented the sum of the operation. Also, in 1940, he gave a demonstration of the first remote operation of a computer.*TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Tuesday, 30 January 2018

On This Day in Math - January 30

God may not play dice with the universe,
but something strange is going on with the prime numbers.

~Paul Erdos **

(Not realy,Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes.")

The 30th day of the year; both the dodecahedron and the icosahedron have 30 edges. They may be positioned at a common center so that in the center of each of the 12 faces of the dodecahedron is one of the 12 vertices of the icosahedron, in the center of each of the 20 faces of the icosahedron is one of the 20 vertices of the dodecahedron, and the 30 edges of the dodecahedron and the 30 edges of the icosahedron cross each other at right angles at their midpoints. (I find this incredibly wonderful)

astounding to me, but 1¹+2²+3³...+30³⁰ = 208492413443704093346554910065262730566475781 is prime Republic of Math ‏@republicofmath If there is another prime of this type, it will have over 20025 digits.

7! hours is 30 weeks

and from *@MathYearRound
30 = 2*3*5 (first 3 primes).
30 =$ 1^2+2^2+3^2+4^2 $(first 4 perfect squares).
30 = 1*1*2*3*5 (first 5 Fibonacci #).

EVENTS

10 BCE Solar eclipse in Iran, as reported on a cuneiform tablet from the British Museum *History of Astronomy ‏@hist_astro (I have to admit that every time I look at this image it reminds me of the map of Michigan's lower peninsula, and that little chip up by the little finger is Grand Traverse Bay, which I see from my dining room)

1610 Galileo writes to Belisario Vinta, with notes on his long observation of the moon with a new twenty-power scope. A letter containing much of what was to appear about the Moon in Sidereus Nuncius, two months later. *Drake, Galileo at Work; 1978

1830 In a letter to Laplace, Gauss writes about a "curious problem" that he had been working on for twelve years. He gives the limiting value of the frequency of distribution of positive integers in the continued fraction of a random number (now called the Gauss-Kuzmin Distribution) as $ log_2(1+x) $ . He then asks if Laplace can offer help in finding the error term. *Math World

1897 Mary Frances Winston elected to membership in the American Mathematical Society. The previous year she received her PhD at G¨ottingen, being the ﬁrst American woman to receive a PhD in mathematics at a German university. *G. B. Price, History of the Department of Mathematics of the University of Kansas, 1866–1970, p. 70

1884 Sonja Kovelevskiaya gives her ﬁrst university lecturer. This was the ﬁrst regular lecture by a woman at a research institution in any ﬁeld in modern times. [The Mathematical Intelligencer, 6(1984), no. 1, p. 29] *VFR

1925 The U.S. History of Science Society was incorporated under the laws of the District of Columbia. The ﬁrst president was Lawrence Joseph Henderson (1878–1924). The movement to form the society was begun by David Eugene Smith and today is the most important historical society in the world. *VFR

1952 Two New Primes Found with SWAC. Using the Standards Western Automatic Computer (SWAC), researchers found two new prime numbers the first time they attempted a prime-searching program on the computer. Within the year, three other primes had been found. The National Bureau of Standards funded construction of the SWAC in Los Angeles in 1950 and it ran, in one form or another, until 1967.
*CHM {The first two primes found with SWAC were M521, M607. In 1951 Ferrier used a mechanical desk calculator to find the 44 digit prime (2¹⁴⁸+1)/17 = 20988936657440586486151264256610222593863921.
The first primes found with an electronic computer were by Miller and Wheeler (Nature, 168 (1951) 838) in 1951 when they found several new primes, including the 79 digit 180(2¹²⁷-1)²+1 }

1982 First computer virus, the Elk Cloner, written by 15-year old Rich Skrenta, is found in the wild. It infects Apple II computers via floppy disk. *Wik

1988 Science News reports that Noam D. Elkies, age 21, of Harvard found four fourth-powers whose sum is another fourth-power, thereby providing a counterexample to a conjecture of Euler in 1769. (Euler's conjecture was that the sum of the first n integers each raised to the nth power can not be an nth power.) The smallest number in his counterexample had eight digits. Later Roger Frye of Thinking Machines Corporation, Cambridge, MA, found the smallest counterexample:
95,800⁴ + 217,519⁴ + 414,560⁴ + 414 560⁴ = 422,418⁴ .
This took some 100 hours on a Connection Machine. Can you ﬁgure out how to verify this example using your calculator (which only displays 8 or 10 digits)? [Mathematics Magazine 61 (1988), p 130; Science 239 (1988), p 464]. *VFR
(Euler's general conjecture had been proven false by L. J. Lander and T. R. Parkin in 1966 when they found a counterexample for fifth powers. Elkies had suggested the computer approach that provided the minimal solution. It is still unknown if there are counterexamples above n=5)

1990 Ruth Lawrence sends a paper on homological representations of the Hecke algebra, introducing, among other things, certain novel linear representations of the braid group, the Lawrence–Krammer representation to the journal, Communications in Mathematical Physics
*Wik

1996 Yuji Hyakutake in Japan discovered a new comet using 25x150 binoculars. The comet was designated Comet C/1996 B2 (Hyakutake). As subsequent observations of the new comet were obtained, Brian Marsden from the IAU Central Bureau was able to compute the comet's orbital elements, and these computations indicated that the comet will pass as close as 0.10 AU (9.3 million miles) from the Earth on March 25, 1996! The comet has become a bright naked-eye object and remained so in March, April and May in 1996. The comet had exceeded expectations, becoming the brighest comet since Comet West in 1976. A long tail of up to 100 degrees was reported, and small fragments have been observed to break off the main nucleus. Comet Hyakutake is indeed the Great Comet of 1996. *jpl.nasa
Hyakutake discovered C/1996 B2 while looking for C/1995 Y1, a comet he had discovered a few weeks before. He died in Kokubu, Kagoshima, in 2002 at age 51 of an aneurysm which had led to internal bleeding. *Wik

BIRTHS

1619 Michelangelo Ricci (30 Jan 1619 in Rome, Italy - : 12 May 1682 in Rome) In 1666, he found the tangent lines to the parabolas of Fermat. *VFR Michelangelo Ricci was a friend of Torricelli; in fact both were taught by Benedetti Castelli. He studied theology and law in Rome and at this time he became friends with René de Sluze. It is clear that Sluze, Torricelli and Ricci had a considerable influence on each other in the mathematics which they studied.
Ricci made his career in the Church. His income came from the Church, certainly from 1650 he received such funds, but perhaps surprisingly he was never ordained. Ricci served the Pope in several different roles before being made a cardinal by Pope Innocent XI in 1681.
Ricci's main work was Exercitatio geometrica, De maximis et minimis (1666) which was later reprinted as an appendix to Nicolaus Mercator's Logarithmo-technia (1668). It only consisted of 19 pages and it is remarkable that his high reputation rests solely on such a short publication.
In this work Ricci finds the maximum of x^m(a - x)ⁿ and the tangents to y^m = kxⁿ. The methods are early examples of induction. He also studied spirals (1644), generalised cycloids (1674) and states explicitly that finding tangents and finding areas are inverse operations (1668). *SAU

1755 Nikolai Fuss (30 Jan 1755 in Basel, Switzerland - 4 Jan 1826 in St Petersburg, Russia) was a Swiss mathematician whose most important contribution was as amanuensis to Euler after he lost his sight. Most of Fuss's papers are solutions to problems posed by Euler on spherical geometry, trigonometry, series, differential geometry and differential equations. His best papers are in spherical trigonometry, a topic he worked on with A J Lexell and F T Schubert. Fuss also worked on geometrical problems of Apollonius and Pappus. He made contributions to differential geometry and won a prize from the French Academy in 1778 for a paper on the motion of comets near some planet Recherche sur le dérangement d'une comète qui passe près d'une planète. Fuss won other prizes from Sweden and Denmark. He contributed much in the field of education, writing many fine textbooks. *SAU

1805 Edward Sang,(30 Jan 1805 in Kirkcaldy, Fife, Scotland - 23 Dec 1890) A native of Fife, Sang wrote extensively on mathematical, mechanical, optical and actuarial topics. *SAU

1865 Georg Landsberg (30 Jan 1865 , 14 Sept 1912) studied the theory of functions of two variables and also the theory of higher dimensional curves. In particular he studied the role of these curves in the calculus of variations and in mechanics.
He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums. His most important work, however was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen (Leipzig, 1902) which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years. *SAU

1918 Heinz Rutishauser (30 January 1918 in Weinfelden, Switzerland; 10 November 1970 in Zürich) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science. *Wik

1925 Douglas Engelbart is Born, best known for inventing the computer mouse. Engelbart publically demonstrated the mouse at a computer conference in 1968, where he also showed off work his group had done in hypermedia and on-screen video teleconferencing. The founder of the Bootstrap Institute, Engelbart has 20 patents to his name.*CHM

DEATHS

1954 Gino Benedetto Loria (19 May 1862 in Mantua, Italy - 30 Jan 1954 in Genoa, Italy) In his day, Loria was arguably the pre-eminent historian of mathematics in Italy. A full professor of higher geometry at the University of Genoa beginning in 1891, Loria wrote the history of mathematics as a mathematician writing for other mathematicians. He emphasised this approach repeatedly in his works. For instance, in the introduction to his 'Storia delle matematiche dall'alba della civilità al tramonto del secolo XIX' (History of Mathematics from the Dawn of Civilisation to the End of the 19th Century), he stated that general history of mathematics was written "by a mathematician for mathematicians". *SAU

1977 Harry Clyde Carver (December 4, 1890 – January 30, 1977) was an American mathematician and academic, primarily associated with the University of Michigan. He was a major influence in the development of mathematical statistics as an academic discipline.
Born in Waterbury, Connecticut, Carver was educated at the University of Michigan, earning his B.S. degree in 1915, and the next year becoming an instructor in mathematics; he taught statistics in actuarial applications. At the time, the University of Michigan was only the second such institution in the United States to offer this type of course, after the pioneering Iowa State University. Carver was appointed assistant professor at Michigan in 1918, then associate professor (1921) and full professor (1936); during this period the University's program in mathematical statistics and probability underwent significant expansion.
In 1930 Carver founded the journal Annals of Mathematical Statistics, which over time became an important periodical in the field. Financial support, however, was lacking in the midst of the Great Depression; in January 1934 Carver undertook financial responsibility for the Annals and maintained the existence of the journal at his own expense. In 1935 he helped to start the Institute of Mathematical Statistics, which in 1938 assumed control over the journal; Samuel S. Wilks succeeded Carver as editor in the same year. The Institute has named its Harry C. Carver Medal after him.
With the coming of World War II, Carver devoted his energies to solving problems in aerial navigation, an interest he maintained for the remainder of his life. *Wik

1991 John Bardeen (23 May 1908, 30 Jan 1991) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

1992 Dom George Frederick James Temple FRS(born 2 December 1901, London; died 30 January 1992, Isle of Wight) was an English mathematician, recipient of the Sylvester Medal in 1969. He was President of the London Mathematical Society in the years 1951-1953.[2]
Temple took his first degree as an evening student at Birkbeck College, London, between 1918 and 1922, and also worked there as a research assistant. In 1924 he moved to Imperial College as a demonstrator, where he worked with Professor Sydney Chapman. After a period spent with Eddington at Cambridge, he returned to Imperial as reader in mathematics. He was appointed professor of mathematics at King's College London in 1932, where he returned after war service with the Royal Aircraft Establishment at Farnborough. In 1953 he was appointed Sedleian Professor of Natural Philosophy at the University of Oxford, a chair which he held until 1968, and in which he succeeded Chapman. He was also an honorary Fellow of Queen's College, Oxford.
After the death of his wife in 1980, Temple, a devout Christian, took monastic vows in the Benedictine order and entered Quarr Abbey on the Isle of Wight, where he remained until his death. *Wik

1998 Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish and American mathematician born in Warsaw, Russian Empire (now in Poland) and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.
He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor was Karol Borsuk. His main interest was algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (whose names the Eilenberg–Steenrod axioms bear), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.
Eilenberg was a member of Bourbaki and with Henri Cartan, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules.
Eilenberg also wrote an important book on automata theory. The X-machine, a form of automaton, was introduced by Eilenberg in 1974. *Wik

Monday, 29 January 2018

On This Day in Math - January 29

There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.
~Daniel Bernoulli

The 29th day of the year; 2²⁹ = 536870912 a nine-digit number with no digit repeated. Is it possible to create a power of a single digit number that has ten distinct digits?

The digits of 29 appear in one of the most unusual un-mistake I can imagine in numbers, if you inadvertently wrote the exponents of $2^5 9^2 $ on the same line as the bases you get 2592 which is = $2^5 9^2 $. It is believed that this is the only such example.

28 is a perfect number, and I think it is interesting that we have proven that if there is ever an odd perfect number it will have at least 29 prime factors, the largest will be greater than 10⁸

And I like this "Euler-like" function from Legendre in 1798, 2n² + 29 is prime for all n from 0 through 28.

EVENTS

1697 (o.s.) Newton received two challenge problems from Johann Bernoulli, one being the Brachistochrone problem published in Acta eruditorum the previous June and addressed “to the shrewdest mathematicians in the world.” The next day Newton posted his solution to the Royal Society. When Bernoulli saw the anonymous solution he recognized it as “ex ungue leonem” (as the lion is recognized by his paw). *Westfall, Never at Rest, pg 581

1769 "On the morning of the 29 January 1769, seven ‘transit’ astronomers went to Catherine the Great’s Winter Palace in St Petersburg because the Empress had requested to meet her astronomical army before they set out to their destinations across the Russian empire. The German Georg Moritz Lowitz and his assistant, the Russian Pjotr Inochodcev were going to Guryev, Russia (modern Atyrau, Kazakhstan), the Russian Stepan Rumovsky and the Swiss Jacques André Mallet and Jean-Louis Pictet were all travelling to different locations on the Kola peninsula, the Germans Christoph Euler was ordered to Orsk and Wolfgang Ludwig Krafft to Orenburg. *Andrea Wulf, Transit of Venus Web Site

1824 Even right at the end of his life, former President Thomas Jefferson was still reporting on the current news in mathematics. On this day he writes to Patrick K. Rogers concerning the abandonment of fluxional calculus at Cambridge in favour of the Leibnizian notation , "The English generally have been very stationary in later times, and the French, on the contrary, so active and successful, particularly in preparing elementary books, in mathematics and natural sciences, that those who wish for instruction without caring from what nation they get it, resort universally to the latter language. Besides the earlier and invaluable works of Euler and Bezout, we have latterly that of Lacroix in mathematics, of Legendre in geometry, . . . to say nothing of the many detached essays of Monge and others, and the transcendent labours of Laplace, and I am informed by a highly instructed person recently from Cambridge, that the mathematicians of that institution, sensible of being in the rear of those of the continent, and ascribing the cause much to their long-continued preference of the geometrical over the analytical methods, which the French have so long cultivated and improved, have now adopted the latter; and that they have also given up the fluxionary, for the differential calculus. " *John Fauval, Lecture at Univ of Va.

1939 J. Robert Oppenheimer hears about the discovery of fission. Within a few minutes, he realizes that excess neutrons must be emitted, and that it might be possible to build a bomb. Fission was discovered on December 17, 1938 by German Otto Hahn and his assistant Fritz Strassmann, but Oppenheimer probably hear about it through the publications which explained it (and named it) theoretically in January 1939 by Lise Meitner and her nephew Otto Robert Frisch. Frisch named the process by analogy with biological fission of living cells. *Wik

1957 SRI and GE Meet to Choose a Place for ERMA's MICR Encoding
ERMA (Electronic Recording Machine - Accounting), developed by SRI and General Electric for the Bank of America in California, employed Magnetic Ink Character Recognition (MICR) as a tool that captures data from checks. IBM was making a strong case to place the encoding at the top of a check. SRI and GE conducted a series of tests that clearly demonstrated the advantage of the bottom-of-the-check encoding. *CHM

1970 Yuri Matiyasevich presents proof of Hilbert's 10th Problem. Having been frustrated by the problem, he had given up hope of solving it. In December of the previous year after having been asked to review an article by Julia Robinson, he was inspired by the novelty of her approach and went back to work on H10. By Jan 3, 1970 he had a proof. He would present the proof on January 29, 1970

BIRTHS

1688 Emanuel Swedenborg (29 Jan 1688; 29 Mar 1772) Swedish scientist, philosopher and theologian. While young, he studied mathematics and the natural sciences in England and Europe. From Swedenborg's inventive and mechanical genius came his method of finding terrestrial longitude by the Moon, new methods of constructing docks and even tentative suggestions for the submarine and the airplane. Back in Sweden, he started (1715) that country's first scientific journal, Daedalus Hyperboreus. His book on algebra was the first in the Swedish language, and in 1721 he published a work on chemistry and physics. Swedenborg devoted 30 years to improving Sweden's metal-mining industries, while still publishing on cosmology, corpuscular philosophy, mathematics, and human sensory perceptions. *TIS

1700 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

1761 Josef (also José or Joseph) de Mendoza y Ríos (29 January 1761; Sevilla, Spain - 4 March 1816 Brighton, England) was a Spanish astronomer and mathematician of the 18th century, famous for his work on navigation. The first work of Mendoza y Ríos was published in 1787: his treatise, Tratado de Navegación, about the science and technique of navigation in two tomes. He also published several tables for facilitating the calculations of nautical astronomy and useful in navigation to calculate the latitude of a ship at sea from two altitudes of the sun, and the longitude from the distances of the moon from a celestial body.
In the field of the nautical instruments, he improved the reflecting circle.
In 1816, he was elected a foreign member of the Royal Swedish Academy of Sciences. @Wik

1810 Ernst Eduard Kummer (29 Jan 1810; 14 May 1893) He was professor at the University of Breslau(now Wroclaw, Poland) in 1842-1855 and developed his theory of ideals here. Kronecker studied with him. Later he replaced Dirichlet at The University of Berlin. He died at age 83, after a short attack of inﬂuenza. German mathematician whose introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic to complex number fields. He worked on Function theory, and extended Gauss's work on hypergeometric series, giving developments that are useful in the theory of differential equations. He was the first to compute the monodromy groups of these series. Later. Kummer devoted himself to the study of the ray systems, but treated these geometrical problems algebraically. He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent planes. *TIS and others An oft told, and almost certianly untrue anecdote is told about Kummer: Kummer was so inept at simple arithmetic that he often asked students to help him in class. On one occasion, Kummer sought the result of a simple multiplication. "Seven times nine," he began. "Seven times nine is er - ah - ah - seven times nine is..." "Sixty-one," a mischievous student suggested and Kummer wrote the "answer" on the blackboard. "Sir," another one interjected, "it should be sixty-seven." "Come, gentlemen, it can't be both," Kummer exclaimed. "It must be one or the other!" According to Erdos, Kumer reasoned out the answer as follows, -It can't be 61 as that is prime, as is 67, and 65 is a multiple of five, and 69 is too big, so it must be 63.

1817 William Ferrel (29 Jan 1817; 18 Sep 1891) American meteorologist who was an important contributor to the understanding of oceanic and atmospheric circulation. He was able to show the interrelation of the various forces upon the Earth's surface, such as gravity, rotation and friction. Ferrel was first to mathematically demonstrate the influence of the Earth's rotation on the presence of high and low pressure belts encircling the Earth, and on the deflection of air and water currents. The latter was a derivative of the effect theorized by Gustave de Coriolis in 1835, and became known as Ferrel's law. Ferrel also considered the effect that the gravitational pull of the Sun and Moon might have on the Earth's rotation and concluded (without proof, but correctly) that the Earth's axis wobbles a bit. *TIS (A more complete biography is here)

1838 Edward Williams Morley (29 Jan 1838; 24 Feb 1923) American chemist who is best known for his collaboration with the physicist A.A. Michelson in an attempt to measure the relative motion of the Earth through a hypothetical ether (1887). He also studied the variations of atmospheric oxygen content. He specialized in accurate quantitative measurements, such as those of the vapour tension of mercury, thermal expansion of gases, or the combining weights of hydrogen and oxygen. Morley assisted Michelson in the latter's persuit of measurements of the greatest possible accuracy to detect a difference in the speed of light through an omnipresent ether. Yet the ether could not be detected and the physicists had seriously to consider that the ether did not exist, even questioning much orthodox physical theory. *TIS

1888 Sydney Chapman (29 Jan 1888; 16 Jun 1970) English mathematician and physicist noted for his research in geophysics. After graduation (1910) he worked at the Greenwich Observatory, but returned to Cambridge upon the outbreak of WW I. Between 1915 and 1917 he completed a series of important papers on thermal diffusion and the fundamentals of gas dynamics. He developed systematic approximations to the Maxwell-Boltzmann formulation for the velocity distribution function for interacting particles under general force laws. During WW II he worked on military operational research and incendiary bomb problems. Chapman's main area of research was geomagnetism, beginning in 1913 and extending to terrestrial and interplanetary magnetism, the ionosphere and the aurora borealis.*TIS

1894 Miss Helen Almira Shaffer, A. M., LL. D., President of Welleslev College,
died of pneumonia at the college, on January 29, aged 54 years. She was chief teacher
of Mathematics for ten years in the St. Louis High School. In 1877 she accepted the
professorship of Mathematics in Wellesley, which she filled until 1888, when she became
president of that institution. *The American Mathematical Monthly Vol. 1, No. 2, Feb., 1894

1926 Abdus Salam (29 Jan 1926; 21 Nov 1996) Pakistani-British nuclear physicist who shared the 1979 Nobel Prize for Physics with Steven Weinberg and Sheldon Lee Glashow. Each had independently formulated a theory explaining the underlying unity of the weak nuclear force and the electromagnetic force. His hypothetical equations, which demonstrated an underlying relationship between the electromagnetic force and the weak nuclear force, postulated that the weak force must be transmitted by hitherto-undiscovered particles known as weak vector bosons, or W and Z bosons. Weinberg and Glashow reached a similar conclusion using a different line of reasoning. The existence of the W and Z bosons was eventually verified in 1983 by researchers using particle accelerators at CERN. *TIS

1928 O. Timothy O’Meara born in South Africa. This expert in quadratic forms is now Provost at the University of Notre Dame. *VFR On October 8, 2008, the Mathematics Library at Notre Dame was rededicated and named for Prof. O. Timothy O’Meara. Prof. O’Meara is a noted Mathematician, who has been on the faculty of the Mathematics Department since 1962, and twice served as its chairman. In 1976 he was named to the Kenna Endowed Chair in Mathematics. He is noted for serving as the first lay Provost of the University, 1978-1996. He is now an emeritus faculty member, but still very active and interested in the library *ND Web Site

1928 Joseph Bernard Kruskal, Jr. (January 29, 1928 – September 19, 2010) was an American mathematician, statistician, computer scientist and psychometrician. He was a student at the University of Chicago and at Princeton University, where he completed his Ph.D. in 1954, nominally under Albert W. Tucker and Roger Lyndon, but de facto under Paul Erdős with whom he had two very short conversations.Kruskal has worked on well-quasi-orderings and multidimensional scaling.
He was a Fellow of the American Statistical Association, former president of the Psychometric Society, and former president of the Classification Society of North America.
In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. In combinatorics, he is known for Kruskal's tree theorem (1960), which is also interesting from a mathematical logic perspective since it can only be proved nonconstructively. Kruskal also applied his work in linguistics, in an experimental lexicostatistical study of Indo-European languages, together with the linguists Isidore Dyen and Paul Black.
Kruskal was born in New York City to a successful fur wholesaler, Joseph B. Kruskal, Sr. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of Origami during the early era of television. He died in Princeton. *Wik

DEATHS

1707 Otto Mencke (22 March (OS) April 2, 1644 – 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1715 Bernard Lamy (15 June 1640, in Le Mans, France – 29 January 1715, in Rouen, France) was a French Oratorian mathematician and theologian. He wrote on geometry and mechanics and developed the idea of a parallelogram of forces at about the same time as Newton and Verignon. The Law of Sines as applied to three static forces in mechanics is sometimes called Lamy's Rule. (Would provide an interesting variation for Pre-calc classes)

1859 William Cranch Bond (9 Sep 1789, 29 Jan 1859) American astronomer who, with his son, George Phillips Bond (1825-65), discovered Hyperion, the eighth satellite of Saturn, and an inner ring called Ring C, or the Crepe Ring. While W.C. Bond was a young clockmaker in Boston, he spent his free time in the amateur observatory he built in part of his home. In 1815 he was sent by Harvard College to Europe to visit existing observatories and gather data preliminary to the building of an observatory at Harvard. In 1839 the observatory was founded. He supervised its construction, then became its first director. Together with his son he developed the chronograph for automatically recording the position of stars. They also took some of the first recognizable photographs of celestial objects.*TIS

1864 Benoît "Claudius" Crozet (December 31, 1789; Villefranche, France – January 29, 1864) was an educator and civil engineer.
After serving in the French military, in 1816, he immigrated to the United States. He taught at the U.S. Military Academy at West Point, New York, and helped found the Virginia Military Institute at Lexington, Virginia. He was Principal Engineer for the Virginia Board of Public Works and oversaw the planning and construction of canals, turnpikes, bridges and railroads in Virginia, including the area which is now West Virginia. He became widely known as the "Pathfinder of the Blue Ridge."
On June 7, 1816, in Paris, Crozet married Agathe Decamp.
Late in fall of 1816, Crozet and his bride headed for the United States. Almost immediately after arriving, Crozet began work as a professor of engineering at the U.S. Military Academy at West Point, New York.
While at West Point, Crozet is credited by some as being the first to use the chalkboard as an instructional tool. He also designed several of the buildings at West Point. Thomas Jefferson referred to Claudius Crozet as "by far the best mathematician in the United States." He also published A Treatise on Descriptive Geometry while at West Point, a copy of which was sent to Jefferson. Jefferson's response on Nov 23, 1821 began, "I thank you, Sir, for your kind attention in sending me a copy of your valuable treatise on Descriptive geometry." He continued the messsage with praise for the work, and the instructor both. The dining hall at the Virginia Military Institute is named in his honor. It has been affectionately nicknamed "Club Crozet" by the Cadets. * Wik & Natl. Archives

1905 Robert Tucker (26 April 1832 in Walworth, Surrey, England - 29 Jan 1905 in Worthing, England) A major mathematical contribution made by Tucker was his work as editor of William Kingdon Clifford's papers. Fifty-seven of Clifford's papers were collected and edited by Tucker and published in 1882 as Mathematical Papers. Tucker also wrote many biographies including those of Gauss, Sylvester, Chasles, Spottiswoode, and Hirst, all of which appeared in Nature. But, like a number of schoolmaster's at this time, he also made a contribution to research in geometry. He wrote over 40 research papers which were published in leading journals. These papers, although sometimes not of the highest quality, do contain a number of interesting ideas. Hill specially singles out for special mention his work on the Triplicate-Ratio Circle, the group of circles sometimes known as Tucker Circles, and the Harmonic Quadrilateral. *SAU

1984 John Macnaghten Whittaker I(7 March 1905 in Cambridge, England - 29 Jan 1984 in Sheffield, England) was the son of Edmund Whittaker. He studied at Edinburgh University and Cambridge. After posts at Edinburgh and Cambridge he became Professor at Liverpool though his tenure was interrupted by service in World War II. He left Liverpool to become Vice-Chancellor of Sheffield University. He worked in Quantum Mechanics and Complex Analysis. *SAU

1999 Viktor Aleksandrovich Gorbunov (17 Feb 1950 in Russia - 29 Jan 1999 in Novosibirsk, Russia) He published his first paper in 1973 being a joint work with A I Budkin entitled Implicative classes of algebras (Russian). The implicative class of algebras is a generalisation of quasivarieties. The structural characteristics of the implicative class are studied in this paper. A second join paper with Budkin On the theory of quasivarieties of algebraic systems (Russian) appeared in 1975. In the same year he published Filters of lattices of quasivarieties of algebraic systems (Russian), this time written with V P Belkin. In fact he had written six papers before his doctoral thesis On the Theory of Quasivarieties of Algebraic Systems was submitted. He received the degree in 1978. Gorbunov continued working at Novosibirsk State University, being promoted to professor. He also worked as a researcher in the Mathematics Institute of the Siberian Branch of the Russian Academy of Sciences. *SAU

Sunday, 28 January 2018

On This Day in Math - January 28

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.
~Janos Bolyai

The 28th day of the year; 28 is the second perfect number and the last year day that will be perfect; the sum of its proper factors. 28 = 1+2+4+7+14. Like all the perfect numbers after 6, it is the sum of the cubes of consecutive odd numbers, $28=1^3 + 3^3 $ And like all perfect numbers after 6, when expressed in base 6, it ends in 44.

28 is expressible as the sum of first five nonprime numbers, i.e., 1 + 4 + 6 + 8 + 9 = 28.

28 is the number of dominoes in the standard double-6 set. How many in a double-12 set

And a 28-sided polygon is called an icosikaioctagon.

EVENTS

1699 Leibniz becomes the ﬁrst elected foreign member of the French Academy. *VFR Huygens was a member at the origin.(1666)

1741 The first mention of the pentagonal theorem is in a letter from Daniel Bernoulli to Euler. Bernoulli is replying to a (lost) letter from Euler about the expansion, and he writes “The other problem, to transform (1 − x)(1 − x²)(. . .) into 1 − x − x² + x⁵ + . . ., follows easily by induction, if one multiplied many factors. The remainder of the series I do not see. This can be shown in a most pleasant investigation, together with tranquil pastime and the endurance of pertinacious labor, all three of which I lack.” *Dick Koch, The Pentagonal Theorem and All That

1790/91 imprimatur of An Essay on the Usefulness of Mathematical Learning by John Arbuthnot. He pointed out that mathematics was not on the syllabus of a single English grammar school. It was present by this time in most of Europe. Clavius introduced the mathematical sciences into the school and university curricula in the Catholic countries of Europe in the 17th century and Philipp Melanchthon had earlier performed the same for the mainland protestant countries in the 16th century. *RMAT

1902 "It is proposed to found in the city of Washington, an institution which...shall in the broadest and most liberal manner encourage investigation, research, and discovery [and] show the application of knowledge to the improvement of mankind..." — Andrew Carnegie, January 28, 1902
Established to support scientific research, today the Carnegie Institute of Washington directs its efforts in six main areas: plant molecular biology at the Department of Plant Biology (Stanford, California), developmental biology at the Department of Embryology (Baltimore, Maryland), global ecology at the Department of Global Ecology (Stanford, CA), Earth science, materials science, and astrobiology at the Geophysical Laboratory (Washington, DC); Earth and planetary sciences as well as astronomy at the Department of Terrestrial Magnetism (Washington, DC), and (at the Observatories of the Carnegie Institution of Washington (OCIW; Pasadena, CA and Las Campanas, Chile)).*Wik

1947 The patent request of R. T. James "Slinky" was approved. The name was thought up by his wife. *Priceonomics

1977 According to the Guinness Book of World Records, the most freakish rise in temperature ever recorded was on this date in Spearﬁsh, South Dakota. At 7:30 a.m. it was −4 degrees Fahrenheit; at 7:32 a.m. it was +45 degrees Fahrenheit. What was the average rate of change in temperature per minute? [NCTM Sourcebook of Applications of School Mathematics, p. 125] *VFR
Some other temp changes from around the net show:

1972 The greatest temperature change in 24 hours occurred in Loma, MT. on January 15. The temperature rose exactly 103 degrees, from -54 degrees Fahrenheit to 49 degrees. This is the world record for a 24—hour temperature change.
1911 Fastest temperature drop: 27.2 °C (49 °F) in 15 minutes on Jan 10 in Rapid City, South Dakota,

1986 The Space Shuttle Challenger (mission STS-51-L) broke apart 73 seconds into its flight, leading to the deaths of its seven crew members. One of them was Christa McAuliffe, the first member of the Teacher in Space Project and the (planned) first female teacher in space. Media coverage of the accident was extensive: one study reported that 85 percent of Americans surveyed had heard the news within an hour of the accident. The Challenger disaster has been used as a case study in many discussions of engineering safety and workplace ethics. *Wik

BIRTHS

1540 Ludolph van Ceulen, a German mathematician who is famed for his calculation of π to 35 places. In Germany π used to be called the Ludolphine number. Because van Ceulen could not read Greek, Jan Cornets de Groot, the burgomaster of Delft and father of the jurist, scholar, statesman and diplomat, Hugo Grotius, translated Archimedes' approximation to π for Van Ceulen. This proved a significant point in Van Ceulen's life for he spent the rest of his life obtaining better approximations to π using Archimedes' method with regular polygons with many sides.*SAU He has Pi on his memorial stone.

1608 Giovanni Alfonso Borelli (28 Jan 1608; 31 Dec 1679) Italian mathematician, physiologist and physicist sometimes called “father of biomechanics.” He was the first to apply the laws of mechanics to the muscular action of the human body. In De motu animalium (Concerning Animal Motion, 1680), he correctly described the skeleton and muscles as a system of levers, and explained the mechanism of bird flight. He calculated the forces required for equilibrium in various joints of the body well before the mechanics of Isaac Newton. In 1649, he published a work on malignant fevers. He repudiated astrological causes of diseases and believed in chemical cures. In 1658, he published Euclidus restitutus. He made anatomical dissections, drew a diver's rebreather, investiged volcanoes, was first to suggest a parabolic path for comets, and considered Jupiter had an attractive influence on its moons.*TIS

1611 Johannes Hevelius (28 Jan 1611; 28 Jan 1687) German astronomer, who studying in Leiden and

established his own observatory on the rooftops of several houses. From four years' telescopic study of the Moon, using telescopes of long focal power, Hevelius compiled Selenographia ("Pictures of the Moon", 1647), an atlas of the Moon with some of the earliest detailed maps. A few of his names for lunar mountains (e.g., the Alps) are still in use, and a lunar crater is named for him. Hevelius is today best remembered for his use of "aerial" telescopes of enormous focal length and his rejection of telescopic sights for stellar observation and positional measurement. He catalogued 1564 stars in Prodromus Astronomiae (1690), discovered four comets, and was one of the first to observe the transit of Mercury. He died on his birthday. *TIS You can find a nice blog about Hevelius, "The last great naked eye astronomer." You can find a nice blog about Hevelius, "The last great naked eye astronomer." by the Renaissance Mathematicus.

1622 Adrien Auzout (28 January 1622 – 23 May 1691) was a French astronomer. In 1664–1665 he made observations of comets, and argued in favor of their following elliptical or parabolic orbits. (In this he was opposed by his rival Johannes Hevelius.) Adrien was briefly a member of the Académie Royale des Sciences from 1666 to 1668, and a founding member of the French Royal Obseratory. (He may have left the academy due to a dispute.) He was elected a Fellow of the Royal Society of London in 1666. He then left for Italy and spent the next 20 years in that region, finally dying in Rome in 1691. Little is known about his activities during this last period.
Auzout made contributions in telescope observations, including perfecting the use of the micrometer. He made many observations with large aerial telescopes and he is noted for briefly considering the construction of a huge aerial telescope 1,000 feet in length that he would use to observe animals on the Moon. In 1647 he performed an experiment that demonstrated the role of air pressure in function of the mercury barometer. In 1667–68, Adrien and Jean Picard attached a telescopic sight to a 38-inch quadrant, and used it to accurately determine positions on the Earth. The crater Auzout on the Moon is named after him. *Wik

1701 Charles Marie de La Condamine (28 January 1701 – 13 February 1774) was a French explorer, geographer, and mathematician. He spent ten years in present-day Ecuador measuring the length of a degree latitude at the equator and preparing the first map of the Amazon region based on astronomical observations. *Wik

1794 Isidore Auguste Marie François Xavier Comte (28 January 1794 – 21 September 1859), better known as Auguste Comte (French: [oɡyst kɔ̃t]), was a French philosopher. He was a founder of the discipline of sociology and of the doctrine of positivism. He is sometimes regarded as the first philosopher of science in the modern sense of the term.
Strongly influenced by the utopian socialist Henri Saint-Simon, Comte developed the positive philosophy in an attempt to remedy the social malaise of the French Revolution, calling for a new social doctrine based on the sciences. Comte was a major influence on 19th-century thought, influencing the work of social thinkers such as Karl Marx, John Stuart Mill, and George Eliot.[3] His concept of sociologie and social evolutionism, though now outdated, set the tone for early social theorists and anthropologists such as Harriet Martineau and Herbert Spencer, evolving into modern academic sociology presented by Émile Durkheim as practical and objective social research.
Comte's social theories culminated in the "Religion of Humanity", which influenced the development of religious humanist and secular humanist organizations in the 19th century. Comte likewise coined the word altruisme (altruism)*Wik

1838 James Craig Watson (January 28, 1838 – November 22, 1880) was a Canadian-American astronomer born in the village of Fingal, Ontario Canada. His family relocated to Ann Arbor, Michigan in 1850.
At age 15 he was matriculated at the University of Michigan, where he studied the classical languages. He later was lectured in astronomy by professor Franz Brünnow.
He was the second director of Detroit Observatory (from 1863 to 1879), succeeding Brünnow. He wrote the textbook Theoretical Astronomy in 1868.
He discovered 22 asteroids, beginning with 79 Eurynome in 1863. One of his asteroid discoveries, 139 Juewa was made in Beijing when Watson was there to observe the 1874 transit of Venus. The name Juewa was chosen by Chinese officials (瑞華, or in modern pinyin, ruìhuá). Another was 121 Hermione in 1872, from Ann Arbor, Michigan, and this asteroid was found to have a small asteroid moon in 2002.
He was a strong believer in the existence of the planet Vulcan, a hypothetical planet closer to the Sun than Mercury, which is now known not to exist (however the existence of small Vulcanoid planetoids remains a possibility). He believed he had seen such two such planets during a July 1878 solar eclipse in Wyoming.
He died of peritonitis at the age of only 42. He had amassed a considerable amount of money through non-astronomical business activities. By bequest he established the James Craig Watson Medal, awarded every three years by the National Academy of Sciences for contributions to astronomy.
The asteroid 729 Watsonia is named in his honour, as is the lunar crater Watson. *Wik

1855 William Seward Burroughs (28 Jan 1855, 5 Sep 1898) American inventor who invented the world's

first commercially viable recording adding machine and pioneer of its manufacture. He was inspired by his experience in his beginning career as a bank clerk. On 10 Jan 1885 he submitted his first patent (issued 399,116 on 21 Aug 1888) for his mechanical “calculating machine.” Burroughs co-founded the American Arithmometer Co in 1886 to develop and market the machine. The manufacture of the first machines was contracted out, and their durability was unsatisfactory. He continued to refine his design for accuracy and reliability, receiving more patents in 1892, and began selling the much-improved model for $475 each. By 1895, 284 machines had been sold, mostly to banks, and 1500 by 1900. The company later became Burroughs Corporation (1905) and eventually Unisys. *TIS

1855 Karl Friedrich Wilhelm Rohn (January 25 1855 in Schwanheim - August 4 1920 in Leipzig ) was a German mathematician working mainly in geometry.
He studied under Alexander von Brill , who led him away from an initial engineering studies for mathematics; and in 1878 he received his doctorate in Munich under Felix Klein. His doctoral was on the Kummer surface of fourth Order and its relationship with hyperelliptic functions (with Riemann surfaces of genus 2). Besides his work on the Kummer surface, and other algebraic surfaces , he also examined algebraic space curves, and there completed the classification work of Georges Halphen and Max Noether. In 1913 he was president of the German Mathematical Society. *Wik His love of geometry is also illustrated by his beautiful thread models which were especially produced to excite the curiosity of the uninitiated. Rohn constructed models of surfaces and space curves that he was studying, particularly in the early part of his career. In 1884 the Jablonowski Society proposed as prize problem asking for essays on the general surface of order 4, extending the work of Schläfli, Klein and Zeuthen on cubic surfaces; they awarded the prize to Rohn for his essay in 1886. He made important contributions to the theory of quartic surfaces, in particular of ruled quartics and quartics with a triple point.*SAU

1884 Auguste Antoine Piccard (28 January 1884 – 24 March 1962) was a Swiss physicist, inventor and explorer. Piccard and his twin brother Jean Felix were born in Basel, Switzerland. Showing an intense interest in science as a child, he attended the Swiss Federal Institute of Technology (ETH) in Zurich, and became a professor of physics in Brussels at the Free University of Brussels in 1922, the same year his son Jacques Piccard was born. He was a member of the Solvay Congress of 1922, 1924, 1927, 1930 and 1933.
In 1930, an interest in ballooning, and a curiosity about the upper atmosphere led him to design a spherical, pressurized aluminum gondola that would allow ascent to great altitude without requiring a pressure suit. Supported by the Belgian Fonds National de la Recherche Scientifique (FNRS) Piccard constructed his gondola.
An important motivation for his research in the upper atmosphere were measurements of cosmic radiation, which were supposed to give experimental evidence for the theories of Albert Einstein, whom Piccard knew from the Solvay conferences and who was a fellow alumnus of ETH.
On May 27, 1931, Auguste Piccard and Paul Kipfer took off from Augsburg, Germany, and reached a record altitude of 15,781 m (51,775 ft). (FAI Record File Number 10634) During this flight, Piccard was able to gather substantial data on the upper atmosphere, as well as measure cosmic rays. On 18 August 1932, launched from Dübendorf, Switzerland, Piccard and Max Cosyns made a second record-breaking ascent to 16,201 m (53,153 ft). (FAI Record File Number 6590) He ultimately made a total of twenty-seven balloon flights, setting a final record of 23,000 m (75,459 ft).

In the mid-1930s, Piccard's interests shifted when he realized that a modification of his high altitude balloon cockpit would allow descent into the deep ocean. By 1937, he had designed the bathyscaphe, a small steel gondola built to withstand great external pressure. Construction began, but was interrupted by the outbreak of World War II. Resuming work in 1945, he completed the bubble-shaped cockpit that maintained normal air pressure for a person inside the capsule even as the water pressure outside increased to over 46 MPa (6,700 psi). Above the heavy steel capsule, a large flotation tank was attached and filled with a low density liquid for buoyancy. Liquids are relatively incompressible and can provide buoyancy that does not change as the pressure increases. And so, the huge tank was filled with gasoline, not as a fuel, but as flotation. To make the now floating craft sink, tons of iron were attached to the float with a release mechanism to allow resurfacing. This craft was named FNRS-2 and made a number of unmanned dives in 1948 before being given to the French Navy in 1950. There, it was redesigned, and in 1954, it took a man safely down 4,176 m (13,701 ft).
Piccard was the inspiration for Professor Cuthbert Calculus in The Adventures of Tintin by Belgian cartoonist Hergé. Piccard held a teaching appointment in Brussels where Hergé spotted his unmistakable figure in the street.
Gene Roddenberry named Captain Jean-Luc Picard in Star Trek after one or both of the twin brothers Auguste and Jean Felix Piccard, and derived Jean-Luc Picard from their names. *Wik

1888 Louis Joel Mordell (28 January 1888 – 12 March 1972) was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction. He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College, and was successful in gaining a place and support.Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation

y² = x² + k.

During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function. The proof was by means, in effect, of the Hecke operators, which had not yet been named after Erich Hecke; it was, in retrospect, one of the major advances in modular form theory, beyond its status as an odd corner of the theory of special functions.
In 1920 he took a teaching position in Manchester College of Technology, becoming the Fielden Reader in Pure Mathematics at the Victoria University of Manchester in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers. His basic work on Mordell's theorem is from 1921/2, as is the formulation of the Mordell conjecture.
In 1945 he returned to Cambridge as a Fellow of St. John's, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence of the Euler–Mascheroni constant was probably worth a doctorate. *Wik

1892 Carlo Emilio Bonferroni (28 Jan 1892 in Bergamo, Italy - 18 Aug 1960 in Florence, Italy) His articles are more of a contribution to probability theory than to simultaneous statistical inference. He also had interests in the foundations of probability. He developed a strongly frequentist view of probability denying that subjectivist views can even be the subject of mathematical probability. *SAU He is best known for the Bonferroni inequalities, and gives his name to (but did not devise) the Bonferroni correction in statistics. *Wik

1903 Dame Kathleen Lonsdale (28 Jan 1903; 1 Apr 1971) British crystallographer (née Yardley) who developed several X-ray techniques for the study of crystal structure. Her experimental determination of the structure of the benzene ring by x-ray diffraction, which showed that all the ring C-C bonds were of the same length and all the internal C-C-C bond angles were 120 degrees, had an enormous impact on organic chemistry. She was the first woman to be elected (1945) to the Royal Society of London. *TIS

1911 Robert Schatten (January 28, 1911 – August 26, 1977) principal mathematical achievement was that of initiating the study of tensor products of Banach spaces. The concepts of crossnorm, associate norm, greatest crossnorm, least crossnorm, and uniform crossnorm, all either originated with him or at least first received careful study in his papers. He was mainly interested in the applications of this subject to linear transformations on Hilbert space. In this subject, the Schatten Classes perpetuate his name. Schatten had his own way of making abstract concepts memorable to his elementary classes. Who could forget what a sequence was after hearing Schatten describe a long corridor, stretching as far as the eye could see, with hooks regularly spaced on the wall and numbered 1, 2, 3, ...? "Then," Schatten would say, "I come along with a big bag of numbers over my shoulder, and hang one number on each hook." This of course was accompanied by suitable gestures for emphasis. *SAU

1924 Wilhelm Paul Albert Klingenberg (28 January 1924 Rostock, Mecklenburg, Germany – 14 October 2010 Röttgen, Bonn) was a German mathematician who worked on differential geometry and in particular on closed geodesics. One of his major achievements is the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a simply connected manifold with sectional curvature between 1 and 4 is homeomorphic to the sphere. *Wik

DEATHS

1687 Johannes Hevelius (28 Jan 1611; 28 Jan 1687) German astronomer, who studying in Leiden and established his own observatory on the rooftops of several houses. From four years' telescopic study of the Moon, using telescopes of long focal power, Hevelius compiled Selenographia ("Pictures of the Moon", 1647), an atlas of the Moon with some of the earliest detailed maps. A few of his names for lunar mountains (e.g., the Alps) are still in use, and a lunar crater is named for him. Hevelius is today best remembered for his use of "aerial" telescopes of enormous focal length and his rejection of telescopic sights for stellar observation and positional measurement. He catalogued 1564 stars in Prodromus Astronomiae (1690), discovered four comets, and was one of the first to observe the transit of Mercury. He died on his birthday. *TIS

1864 Benoit Clapeyron (26 Feb 1799, 28 Jan 1864) French engineer who expressed Sadi Carnot's ideas on heat analytically, with the help of graphical representations. While investigating the operation of steam engines, Clapeyron found there was a relationship (1834) between the heat of vaporization of a fluid, its temperature and the increase in its volume upon vaporization. Made more general by Clausius, it is now known as the Clausius-Clapeyron formula. It provided the basis of the second law of thermodynamics. In engineering, Clayeyron designed and built locomotives and metal bridges. He also served on a committee investigating the construction of the Suez Canal and on a committee which considered how steam engines could be used in the navy.*TIS

1889 Joseph Émile Barbier (18 March 1839 in St Hilaire-Cottes, Pas-de-Calais, France - 28 Jan 1889 in St Genest, Loire, France)
He was offered a post at the Paris Observatory by Le Verrier and Barbier left Nice to begin work as an assistant astronomer. For a few years he applied his undoubted genius to problems of astronomy. He proved a skilled observer, a talented calculator and he used his brilliant ideas to devise a new type of thermometer. He made many contributions to astronomy while at the observatory but his talents in mathematics were also to the fore and he looked at problems in a wide range of mathematical topics in addition to his astronomy work.
As time went by, however, Barbier's behaviour became more and more peculiar. He was clearly becoming unstable and exhibited the fine line between genius and mental problems which are relatively common. He left the Paris Observatory in 1865 after only a few years of working there. He tried to join a religious order but then severed all contacts with his friends and associates. Nothing more was heard of him for the next fifteen years until he was discovered by Bertrand in an asylum in Charenton-St-Maurice in 1880.
Bertrand discovered that although Barbier was clearly unstable mentally, he was still able to make superb original contributions to mathematics. He encouraged Barbier to return to scientific writing and, although he never recovered his sanity, he wrote many excellent and original mathematical papers. Bertrand, as Secretary to the Académie des Sciences, was able to find a small source of income for Barbier from a foundation which was associated with the Académie. Barbier, although mentally unstable, was a gentle person and it was seen that, with his small income, it was possible for him to live in the community. This was arranged and Barbier spent his last few years in much more pleasant surroundings.
Barbier's early work, while at the Observatory, consists of over twenty memoirs and reports. These cover topics such as spherical geometry and spherical trigonometry. We mentioned above his work with devising a new type of thermometer and Barbier wrote on this as well as on other aspects of instruments. He also wrote on probability and calculus.
After he was encouraged to undertake research in mathematics again by Bertrand, Barbier wrote over ten articles between the years 1882 and 1887. These were entirely on mathematical topics and he made worthwhile contributions to the study of polyhedra, integral calculus and number theory. He is remembered for Barbier's theorem, nicely explained here by Alex Bogomolny.*SAU

1910 Alfredo Capelli (5 Aug 1855, Milan, Italy – 28 Jan 1910, Naples, Italy) was an Italian mathematician who discovered Capelli's identity.
Capelli graduated from the University of Rome in 1877, and moved to the University of Pavia where he worked as an assistant for Felice Casorati. In 1881 he became a professor at the University of Palermo, replacing Cesare Arzelà who had recently moved to Bologna. In 1886, he moved again to the University of Naples, where he held the chair in algebra. He remained at Naples until his death in 1910. As well as being a professor there, he was editor of the Giornale di Matematiche di Battaglini from 1894 to 1910, and was elected to the Accademia dei Lincei.*Wik

1946 Dmitrii Matveevich Sintsov (21 November 1867 – 28 January 1946) was a Russian mathematician known for his work in the theory of conic sections and non-holonomic geometry.
He took a leading role in the development of mathematics at Kharkov University, serving as chairman of the Kharkov Mathematical Society for forty years, from 1906 until his death at the age of 78.*Wik

1954 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician.
Born in Mison, Alpes-de-Haute-Provence, in 1895 he started to study mathematics at the École Normale Supérieure, graduating in 1898. Looking for some means of financial support while he completed his doctorate on quasi-periodic functions, he took a post at the Bordeaux Observatory, teaching some mathematics at the university.
During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939.
Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France.
The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik

1988 (Emil) Klaus (Julius) Fuchs (29 Dec 1911; 28 Jan 1988) was a German-born physicist who was convicted as a spy on 1 Mar 1950, for passing nuclear research secrets to Russia. He fled from Nazi Germany to Britain. He was interned on the outbreak of WW II, but Prof. Max Born intervened on his behalf. Fuchs was released in 1942, naturalized in 1942 and joined the British atomic bomb research project. From 1943 he worked on the atom bomb with the Manhattan Project at Los Alamos, U.S. By 1945, he was sending secrets to Russia. In 1946, he became head of theoretical physics at Harwell, UK. He was caught, confessed, tried, imprisoned for nine of a 14 year sentence, released on 23 Jun 1959, and moved to East Germany and resumed nuclear research until 1979. *TIS

1993 Helen Battles (Sawyer) Hogg (1 Aug 1905, 28 Jan 1993) was a Canadian astronomer who located, cataloged and measured the distances to variable stars in globular clusters (stars with cyclical changes of brightness found within huge, dense conglomerations of stars located in the outer halo of the Milky Way galaxy). Her interest in astronomy was spurred when she witnessed a total eclipse of the sun in 1925. Alongside her career work, she was also foremost in Canada in popularizing astronomy, about which she wrote a column in the Toronto Star for thirty years. She was the first woman to become president of the Royal Canadian Institute. In 1989, the observatory at the National Museum of Science and Technology in Ottawa was dedicated in her name.*TIS

2009 William Moser (5 Sep 1927;28 Jan 2009) My mathematical interests are: presentations for finite groups; combinatorial enumerations (e.g., counting restricted permutations and combinations); problems in discrete and combinatorial geometry. *From his page at McGill Univ.
In March 2003 Moser was interviewed by Siobhan Roberts who was working on her major work on Coxeter King of Infinite space. He recounted the following story

"Donald made many great contributions to mathematics. I made one great contribution," recounted Moser. Moser's opportunity came at the end of Coxeter's 1955 summer of roving lectures, after his session in Stillwater, at Oklahoma State University. Moser drove down to meet Coxeter and serve as his assistant, taking detailed notes of the well-polished lectures. "At the end of the summer we drove north, to civilisation," said Moser wryly. "We were in my car and Donald asked me if he could drive. It was a new car. Indeed it was the first car I had ever purchased, a green 1955 Plymouth 2-door. I paid $2,000 for it and drove it to Oklahoma. But I agreed. I was surprised to see that he was an aggressive driver. At one point he was trying to pass a car while driving up a hill on a 2-lane highway. I immediately perceived that this was not a prudent thing to do. He tried to coax the car to go faster but it wouldn't respond. At the last moment I shrieked at him, 'Pull back, pull back'. I was probably his only student to shriek at him. He began to pull back and at that moment a truck came over the hill. He managed to get back in the right lane just in time. I HAD SAVED HIS LIFE! And mine. But saving Coxeter's life was my greatest contribution to mathematics." *SAU

2012 Roman Juszkiewicz (born 8 August 1952, died 28 January 2012) is a Polish astrophysicist whose work is concerned with fundamental issues of cosmology.
Juszkiewicz's scientific interests include the theory of gravitational instability, origins of the large-scale structure, microwave background radiation and Big Bang nucleosynthesis. He wrote nearly one hundred research papers, mostly in the area of cosmology. Calculated results based on observed motions of pairs of galaxies, obtained in 2000 by Roman Juszkiewicz and the group led by him, aimed at estimating the amount of dark matter in the Universe, were confirmed by the recently published data from the South Pole's ACBAR detector. *Wik

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