Pat'sBlog

Thursday, 4 May 2017

On This Day in Math - May 4

I had a feeling once about Mathematics - that I saw it all.
Depth beyond depth was revealed to me - the Byss and Abyss.
I saw - as one might see the transit of Venus or even the Lord Mayor's Show
- a quantity passing through infinity and changing its sign from plus to minus.
I saw exactly why it happened and why the tergiversation
was inevitable but it was after dinner
and I let it go.

~Winston Churchill

The 124th day of the year;124 =σ( 1! * 2! * 4!) *Prime Curios (The sigma function of a positive integer n is the sum of the positive divisors of n)

124 is also an Odious number: a number with an odd number of 1's in its binary expansion.

124 in base two is expressed as 1111100.

and ±1 ± 2 ± 3 ± 4 ± 5 ± 6 ± 7 ± 8 ± 9 ± 10 ± 11 ± 12 = 0 has 124 solutions (collect the whole set) *Math Year-Round ‏@MathYearRound

EVENTS

1612 Galileo writing to Mark Welser, “The spots seen at sunset are observed to change place from one evening to the next, descending from the part of the sun then uppermost, and the morning spots ascend from the part then below …”, *Galileo's Sunspot Letters at http://mintaka.sdsu.edu
The Letters were written to the wealthy Augsburg Magistrate Mark Welser (1558-1614), a well-known patron of the new sciences, in responses to Christoph Scheiner's own Letters on Sunspots, published through Wesler in 1612.
Galileo and Scheiner were later to quarrel bitterly over priority of discovery of sunspots; in fact the first recorded sunspot observation is on 8 December 1610 by the Englishman Thomas Harriott (1560-1621), and the first publication by Johann Fabricius.
The title page of Galileo's letters, published by Wesler, is shown below. The lynx depicted on the Title page indicates Galileo's membership in the Lincean academy (Accademia dei Lincei, for the "sharp-eyed")

1675 Charles II orders Royal Greenwich Observatory be built to solve Longitude problem. * Nat. Maritime Museum@NMMGreenwich

1694 David Gregory and Newton disagree on "kissing numbers" during Gregory's visit to Newton in Cambridge. Newton asserted that 12 was the maximum number of spheres that could be placed touching around a central sphere. Gregory held out that a 13th was possible. Kepler had shown a completely rigid arrangement of 12 spheres around one in his Six-cornered Snow. His method is called a hexagonal packing. But Newton and Gregory both knew that placing the surrounding 12 spheres at the vertices of an icosahedron around the central sphere, there was enough space to move the balls around, In fact, any two balls could be moved around and interchanged while all twelve balls were still in contact with the central one. The maximum "kissing number" is known for the first four dimensions, but beyond that only the eighth (240) and twenty-fourth(196,560) are exactly known. *Plus Math, *Wik (Newton was right, but it wasn't proven until 1953.)

1697 John Wallis sends a letter to the Royal Society "Concerning the Cycloeid Known to Cardinal Cusanus, about the Year 1450." (modern scholars can not find any evidence to support his statement.) *Wik

1756 A letter from John Elliot, a young naval officer, to his father.
"There is no News here worth troubling you with, only the discovery of the longitude by a Hanovarien, it is perform’d by an Observation of the Moon & any fix’d Star by knowing there distance at a given place & observing there diff[erence]e at Sea given the difference of time[. T]he obs[ervatio]n is simple & easey but the Calculation is extreamly perplexd. I had this from a Man that is making the Instrument."
The Hanovarien mentioned is Tobias Mayer. *Richard Dunn, Board of Longitude Project, Royal Museums Greenwich

1780 The American Academy of Arts and Sciences, the ﬁrst national arts and sciences society in the U.S., was founded on this date in Boston “to cultivate every art and science which may tend to advance the interest, dignity, honor and happiness of a free, independent and virtuous people.” James Bowdoin was the ﬁrst president. *VFR [The original incorporators were later joined by Benjamin Franklin, George Washington, Thomas Jefferson, Charles Bulfinch, Alexander Hamilton, and John Quincy]*TIS

In 1933, the discovery of radio waves from the centre of the Milky Way galaxy was described by Karl Jansky in a paper he read to the International Radio Union in Washington. The galactic radio waves were very low intensity, short wavelength (14.6 m, frequency about 20 MHz) and required sensitive apparatus for their detection. Their intensity varied regularly with the time of day, and with the seasons. They came from an unchanging direction in space, independent of terrestrial sources. He had conducted his research on static hiss at the radio research department of Bell Telephone Labs, Holmdel, N.J. The New York Times carried a front page report the next day.*TIS

1935 Albert Einstein, in a letter to the New York Times, writes, "In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began". *Dwight E. Neuenschwander, Emmy Noether's Wonderful Theorem

In 1989, the space probe Magellan was carried in the cargo bay by the STS-30 Space Shuttle Atlantis mission launched from Kennedy Space Center in Florida. The space probe was named after the 16th-century Portuguese explorer Ferdinand Magellan. This was the first planetary spacecraft to be released from a shuttle in Earth orbit. It arrived at its planned polar orbit around Venus on 10 Aug 1990, which it circled once every 3-hr 15-min. As the planet rotated slowly beneath it, Magellan collected radar images of the surface in strips about 17-28 km (10-17 mi) wide and radioed back the information. Its mission included taking other measurements. On 11 Oct 1994, it was directed towards the surface, collecting data until it burned up in the atmosphere.*TIS

1995 Commodore Bought By German Company:
German electronics company Escom AG paid $10 million for the rights to the name, patents and intellectual property of Commodore Electronics Ltd. A pioneer in the personal computer industry, Commodore halted production in 1994 and declared bankruptcy. Escom AG planned to resume production of Commodore personal computers, including its most recent model, the Amiga. The company later sold its Amiga rights. *CHM

2000 A rare conjunction occurs on the New Moon including all seven of the traditional celestial bodies known from ancient times up until 1781 with the discovery of Uranus. The May 2000 conjunction consisted of: the Sun and Moon, Mercury, Venus, Mars, Jupiter, and Saturn. *Wik

2011 Star Wars Day, as told to me by a student..."May the Fourth be with you."

BIRTHS

1733 Jean-Charles Borda, (4 May 1733; died 20 Feb 1799 at age 65.) a major ﬁgure in the French navy who participated in several scientific voyages and the American revolution. Besides his contributions to navigational instruments he did important work on ﬂuid mechanics, even showing that Newton’s theory of ﬂuid resistance was untenable. He is best known for the voting system he created in 1770.*VFR [He was one of the main driving forces in the introduction of the decimal system. Borda made good use of calculus and experiment to unify areas of physics. For his surveying, he also developed a series of trigonometric tables. In 1782, while in command of a flotilla of six French ships, he was captured by the British. Borda's health declined after his release. He is one of 72 scientists commemorated by plaques on the Eiffel tower.]*TIS

1821 Pafnuty Lvovich Chebyshev (May 16 [O.S. May 4] 1821 – December 8 [O.S. November 26] 1894)Russian mathematician who founded the St. Petersburg mathematical school (sometimes called the Chebyshev school), who is remembered primarily for his work on the theory of prime numbers, including the determination of the number of primes not exceeding a given number. He wrote about many subjects, including the theory of congruences in 1849, probability theory, quadratic forms, orthogonal functions, the theory of integrals, the construction of maps, and the calculation of geometric volumes. Chebyshev was also interested in mechanics and studied the problems involved in converting rotary motion into rectilinear motion by mechanical coupling. The Chebyshev parallel motion is three linked bars approximating rectilinear motion. *Wik [I remember a poem about the Chebyshev's theorem first conjectured by Bertrand but proved by Chebyshev.... Chebyshev said it, so I'll say it again, there's always a prime, between N and 2N {there are many variants} PB]

1845William Kingdon Clifford (4 May 1845 – 3 March 1879 ) He played an important role in introducing the ideas of Riemann and other writers on non-Euclidean geometry to English mathematicians. “Clifford was a ﬁrst-class gymnast, whose repertory apparently included hanging by his toes from the crossbar of a weather cock on a church tower, a feat beﬁtting a High Churchman, as he then was.” *VFR
English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honor, with interesting applications in contemporary mathematical physics and geometry. He was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression "mind-stuff". *Wikipedia {He enjoyed children and wrote children's stories including "The Little People."} "An atom must be at least as complex as a grand piano. "
Though Clifford never constructed a full theory of spacetime and relativity, there are some remarkable observations he made in print that foreshadowed these modern concepts: In his book Elements of Dynamic (1878), he introduced "quasi-harmonic motion in a hyperbola". He wrote an expression for a parametrized unit hyperbola, which other authors later used as a model for relativistic velocity. Elsewhere he states,

The geometry of rotors and motors ... forms the basis of the whole modern theory of the relative rest (Static) and the relative motion (Kinematic and Kinetic) of invariable systems.

This passage makes reference to biquaternions, though Clifford made these into split-biquaternions as his independent development. The book continues with a chapter "On the bending of space", the substance of general relativity. Clifford also discussed his views in On the Space-Theory of Matter in 1876.

1862 Alice Liddell (4 May 1852 – 16 November 1934), subject of the Alice in wonderland stories. 4 May is also probably the date on which the mad hatter's tea party took place. Charles Wells suggested to me that perhaps that was the date on which young Alice and Charles Dodgson went for a row with her dad and Dodgson first told the tale. There are, Charles points out, two references to the date being the fourth (the white rabbit for instance has a watch that tells the date, not the time and asks Alice the date) and two referring to the month of May . It turns out that that boat ride was on July 4 of 1862. There is however evidence in the book that Dodgson intended to make the story on Alice's date of birth. In that year, for example, the date of her birth there was exactly two days difference between solar and lunar time. Thus the Hatter's response to the date, "Two days wrong" perhaps. Anyway, a novel idea (bad pun) Charles, and thanks for the comment.

1876 Heinrich Jung (4 May 1876 in Essen, Germany - 1953 in Halle, Germany) was a German mathematician who worked on algebraic functions. *SAU

1926 David Allan Bromley (4 May 1926; 10 Feb 2005 at age 78) was a Canadian-American physicist who was considered the “father of modern heavy ion science” for his pioneering experiments on both the structure and dynamics of atomic nuclei. He was a leader in developing particle accelerators detection systems and computer-based data acquisition and analysis systems. While at Atomic Energy of Canada (1955-60) he installed the first tandem Van Der Graaff accelerator. He was founder and director (1963-89) of the A.W. Wright Nuclear Structure Laboratory at Yale University, which has produced more experimental nuclear physicists than any other facility. During this time he became active on numerous national and international science policy boards. From 1980-89, he was a member of the White House Science Council.*TIS

DEATHS

1615 Adriaan van Roomen (29 September 1561 – 4 May 1615) One of Roomen's most impressive results was finding π to 16 decimal places. He did this in 1593 using 230 sided polygons. Roomen's interest in π was almost certainly as a result of his friendship with Ludolph van Ceulen.*SAU [van Roomen posed a problem to solve a 45th degree polynomial set equal to a complex square root with another square root inside it (here). Viete solved the equation establishing the use of trigonometry as a tool in algebraic solutions. ] {van Roomen also found a new solution to the classic Problem of Apollonius but it was not a "classic" construction in that it could not be done with only a straightedge and compass. Gergone (see below) found a proof that was constructable with the classic tools.}

1677 Isaac Barrow (Oct 1630, 4 May 1677) died of an overdose of drugs probably opium. Neil Middlemiss ‏pointed out that the original source of this information may be Aubrey's "Brief Lives" wherein he claims, "his pill (an opiate)...he took it excessively at Mr. Wilson's...and 'twas the cause of his death."
Barrow had taken opiates with fasting previously in Constantinople when suffering from fever. Over dosing on opiates may have been somewhat common in the period, a tweet from @HookesLondon casually mentions another in 1672:" Colwall at Garways. Mr Chamberlain told of Lady Viners death kild by opium."

Isaac Barrow was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form. In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. During his tenure of this chair he published two mathematical works of great learning and elegance, the first on geometry and the second on optics. In 1669 he resigned his professorship in favor of Isaac Newton . *Wik
I just learned from a twit from @mathshistory that Barrow was the "first to recognize that integration and differentiation are inverse operations" He is buried in the Chapel at Trinity College.

1859 Joseph Diaz Gergonne (19 June 1771 Nancy, France—4 May 1859 Montpellier, France)... Finding problems getting his mathematics papers published, Gergonne established his own mathematics journal, the first part appearing in 1810. The Journal was officially called the Annales de mathématiques pures et appliquées but became known as Annales de Gergonne . Gergonne's mathematical interests were in geometry so it is not surprising that it was this topic which figured most prominently in his journal. In fact many famous mathematicians published in the twenty-one volumes of the Annales de Gergonne which appeared during a period of twenty-two years. In addition to Gergonne himself (who published around 200 articles), Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, Galois and many others had papers appear in the Journal. Gergonne provided an elegant solution to the Problem of Apollonius in 1816. This problem is to find a circle which touches three given circles. Gergonne introduced the word polar and the principle of duality in projective geometry was one of his main contributions. *SAU

1936 Alfred Cardew Dixon (22 May 1865 in Northallerton, Yorkshire, England - 4 May 1936 in Northwood, Middlesex, England) Alfred Dixon graduated from London and Cambridge and then had professorial appointments in Galway and Belfast. He worked on ordinary and partial differential equations. *SAU

1961 Herbert Westren Turnbul (31 Aug 1885, l4 May 1961 at age 75). English mathematician who made extensive and notable contributions to the study of algebraic invariants and concomitants of quadratics. Turnbull was also interested in the history of mathematics, writing The Mathematical Discoveries of Newton (1945), and began work on the Correspondence of Isaac Newton. *TIS

1974 Otton Marcin Nikodym (13 Aug 1887 in Zablotow, Galicia, Austria-Hungary (now Ukraine) - 4 May 1974 in Utica,New York, USA) On 2 April 1919, the Polish Mathematical Society was founded by sixteen mathematicians - among them Otton Nikodym. In 1924, under strong pressure from Sierpinski, Nikodym agreed to take his doctoral examination at Warsaw University. It seems he did not care much for the title or publication - his response to Sierpinski's persuasion was, "Am I going to be any wiser because of that?"
Nikodym's name is mostly known in measure theory (e. g. the Radon-Nikodym theorem and derivative, the Nikodym convergence theorem, the Nikodym-Grothendieck boundedness theorem), in functional analysis (the Radon-Nikodym property of a Banach space, the Frechet-Nikodym metric space, a Nikodym set), projections onto convex sets with applications to Dirichlet problem, generalized solutions of differential equations, descriptive set theory and the foundations of quantum mechanics. *SAU

2001 Anne Anastasi (19 Dec 1908, 4 May 2001 at age 92) American psychologist known as the "test guru," for her pioneering development of psychometrics, the measurement and understanding of psychological traits. Her seminal work, Psychological Testing (1954), remains a classic text in the subject. In it, she drew attention to the ways in which trait development is influenced by education and heredity. She explored how variables in the measurement of those traits include differences in training, culture, and language. In 1972, she became the first woman to be elected president of the American Psychological Association in half a century. For her accomplishments, she was awarded the National Medal of Science in 1987.*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

Wednesday, 3 May 2017

On This Day in Math - May 3

As for everything else, so for a mathematical theory:

beauty can be perceived but not explained.

Arthur Cayley

The 123rd day of this year; The number formed by the concatenation of odd numbers from 123 down to 1 is prime. (ie 123121119...531 is Prime) *Prime Curios (Who figures stuff like this out???)

Japan Airlines Flight 123, was the world's deadliest single-aircraft accident in history

And here is an interesting curiosity from the archimedes-lab.org/numbers file:
Write down any number (excluding the digit 0):
64861287124425928
Now, count up the number of even and odd digits, and the total number of digits it contains, as follows:
12 | 5 | 17
Then, string those 3 numbers together to make a new number, and perform the same operation on that:
12517
1 | 4 | 5
Keep iterating:
145
1 | 2 | 3
You will always arrive at 123.

EVENTS

1375 BC, the oldest recorded eclipse occurred, according to one plausible interpretation of a date inscribed on a clay tablet retrieved from the ancient city of Ugarit, Syria (as it is now). This date is one of two plausible dates usually cited from the record, though 5 Mar 1223 is the more favoured date by most recent authors on the subject. Certainly by the 8th century BC, the Babylonians were keeping a systematic record of solar eclipses, and possibly by this time they may have been able to apply numerological rules to make fairly accurate predictions of the occurrence of solar eclipses. The first total solar eclipse reliably recorded by the Chinese occurred on 4 Jun 180 *TIS
(A new historical dating of the tablet, and mention in the text of the visibility of the planet Mars during the eclipse as well as the month in which it occurred enables us to show that the recorded eclipse in fact occurred on 5 March 1223 BC. This new date implies that the secular deceleration of the Earth's rotation has changed very little during the past 3,000 years. *nature.com) With thanks to Bill Thayer ‏@LacusCurtius

1661 Equipment used by Hevelius with a telescope to project an astronomical image onto a sheet of paper. This arrangement was used in his historic observation of the transit of Mercury on May 3, 1661. His surviving books are filled with great images by himself and his second wife, Elisabeth Koopman whom he would marry two years after this transit. * Maria Popova at brainpickings.org
This was the first observation of a transit of Mercury inthe MOnth of May. The two previous transits had both been in November in 1631 and 1651. This observation was visible in London and occurred on the day of the Coronation of King Charles II . It was observed by Christiaan Huygens in London. *Wik

1715 May 3 A total solar eclipse was observed in England from Cornwall in the south-west to Lincolnshire and Norfolk in the east. This eclipse is known as Halley's Eclipse, after Edmund Halley (1656–1742) who predicted this eclipse to within 4 minutes accuracy. Halley observed the eclipse from London where the city of London enjoyed 3 minutes 33 seconds of totality. He also drew a predictive map showing the path of totality across England. The original map was about 30 km off the observed eclipse path. After the eclipse, he corrected the eclipse path, and added the path and description of the 1724 total solar eclipse.Note: Great Britain didn't adopt the Gregorian calendar until 1752, so the date was considered 22 April 1715. *Wik… The Royal Society reports: Edmund Halley, a Fellow of the Royal Society, is most famous for his work on the orbits of comets, predicting when the one that now bears his name would be seen; however, his interests were more widespread. In 1715 the first total solar eclipse for 500 years took place over England and Wales. Halley, a talented mathematician, realized that such an event would generate a general curiosity and requested that the ‘curious’ across the country should observe ‘what they could’ and make a record of the time and duration of the eclipse. At the time, there were only two universities in England and their astronomy professors did not have much luck in observing the event: ‘the Reverend Mr Cotes at Cambridge had the misfortune to be oppressed by too much company’ and ‘Dr John Keill by reason of clouds, saw nothing distinctly at Oxford but the end’. The event did indeed capture the imagination of the nation and the timings collected allowed Halley to work out the shape of the eclipse shadow and the speed at which it passed over the Earth (29 miles per minute).

1834 In response to a letter from William Whewell at Cambridge suggesting the names "anode" and "cathode"; Faraday says ,"All your names I and my friend approve of or nearly all as to sense & expression, but I am frightened by their length & sound when compounded. As you will see I have taken deoxide and skaiode because they agree best with my natural standard East and West. I like Anode & Cathode better as to sound, but all to whom I have shewn them have supposed at first that by Anode I meant No way." (within a few weeks he would change his mind about using the two terms, see 15 may, 1834)

1841 L. G. J. Jacobi, who made a lengthy study of Euler’s and d’Alembert’s works, wrote “It is worth noting that it is impossible today to choke down a single line of d’Alembert’s mathematics, while most of Euler’s works can be read with delight, and they died in the same year [1783]. D’Alembert seems to have been entirely absorbed in belles-lettres.” [Hawkins, Jean D’Alembert, p 63]. *VFR

1849 Arthur Cayley called to the Bar. He abandoned his fellowship at Cambridge and took up law as he didn’t want to take Holy Orders. During his 14 years at the bar he wrote nearly 300 mathematical papers. *VFR
1902 The San Francisco Section of the AMS was founded at a gathering of twenty mathematicians at the Academy of Sciences, San Francisco, CA. [AMS Semicentennial Publications, vol 1, p 8].

1934 Henri-Leon Lebesgue elected foreign member of the Royal Society. From 1899 until 1903 he taught at the Lyc´ee at Nancy, France, where he wrote his famous doctoral thesis “Int´egrale, longueur, aire,” which proposed a now standard extension of the Riemann integral. See The Mathematical Intelligencer, 6(1984), no. 2, p. 8. *VFR

1997 Garry Kasparov beat IBM's Deep Blue in the first match of what many considered a test of artificial intelligence. The world's best chess player, Kasparov eventually lost the match and $1.1 million purse to the IBM supercomputer, which he had claimed could never surpass human chess ability. After losing the sixth and final game of the match, Kasparov accused IBM of building a machine specifically to beat him. Observers said he was frustrated by Deep Blue's quickness although they expected him to win with unconventional moves. *CHM On February 10, 1996, Deep Blue became the first machine to win a chess game against a reigning world champion (Garry Kasparov) under regular time controls. However, Kasparov won three and drew two of the following five games, beating Deep Blue by a score of 4–2 (wins count 1 point, draws count ½ point). The match concluded on February 17, 1996.
Deep Blue was then heavily upgraded (unofficially nicknamed "Deeper Blue")[11] and played Kasparov again in May 1997, winning the six-game rematch 3½–2½, ending on May 11. *Wik

2016 Three computer scientists have announced the largest-ever mathematics proof: a file that comes in at a whopping 200 terabytes1, roughly equivalent to all the digitized text held by the US Library of Congress. The researchers have created a 68-gigabyte compressed version of their solution — which would allow anyone with about 30,000 hours of spare processor time to download, reconstruct and verify it — but a human could never hope to read through it.
Computer-assisted proofs too large to be directly verifiable by humans have become commonplace, and mathematicians are familiar with computers that solve problems in combinatorics — the study of finite discrete structures — by checking through umpteen individual cases. Still, “200 terabytes is unbelievable”, says Ronald Graham, a mathematician at the University of California, San Diego. The previous record-holder is thought to be a 13-gigabyte proof2, published in 2014.
The puzzle that required the 200-terabyte proof, called the Boolean Pythagorean triples problem, has eluded mathematicians for decades. In the 1980s, Graham offered a prize of US$100 for anyone who could solve it. (He duly presented the cheque to one of the three computer scientists, Marijn Heule of the University of Texas at Austin, earlier this month.) The problem asks whether it is possible to colour each positive integer either red or blue, so that no trio of integers a, b and c that satisfy Pythagoras’ famous equation a2 + b2 = c2 are all the same colour. For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were coloured blue, 4 would have to be red.
In a paper posted on the arXiv server on 3 May, Heule, Oliver Kullmann of Swansea University, UK, and Victor Marek of the University of Kentucky in Lexington have now shown that there are many allowable ways to colour the integers up to 7,824 — but when you reach 7,825, it is impossible for every Pythagorean triple to be multicoloured1. There are more than 102,300 ways to colour the integers up to 7,825, but the researchers took advantage of symmetries and several techniques from number theory to reduce the total number of possibilities that the computer had to check to just under 1 trillion. It took the team about 2 days running 800 processors in parallel on the University of Texas’s Stampede supercomputer to zip through all the possibilities. The researchers then verified the proof using another computer program. *Evelyn Lamb, nature.com

BIRTHS

1695 Henri Pitot (3 May 1695; 27 Dec 1771 at age 76) French hydraulic engineer who invented the Pitot tube (1732), an instrument to measure flow velocity either in liquids or gases. With subsequent improvements by Henri Darcy, its modern form is used to determine the airspeed of aircraft. Although originally a trained mathematician and astronomer, he became involved with an investigation of the velocity of flowing water at different depths, for which purpose he first created the Pitot tube. He disproved the prevailing belief that the velocity of flowing water increased with depth. Pitot became an engineer in charge of maintenance and construction of canals, bridges, drainage projects, and is particularly remembered for his kilometer-long Roman-arched Saint-Clément Aqueduct (1772) at Montpellier, France.*TIS

1860 Vito Volterra (3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations.In 1922, he joined the opposition to the Fascist regime of Benito Mussolini and in 1931 he was one of only 12 out of 1,250 professors who refused to take a mandatory oath of loyalty. His political philosophy can be seen from a postcard he sent in the 1930s, on which he wrote what can be seen as an epitaph for Mussolini’s Italy: Empires die, but Euclid’s theorems keep their youth forever. However, Volterra was no radical firebrand; he might have been equally appalled if the leftist opposition to Mussolini had come to power, since he was a lifelong royalist and nationalist. As a result of his refusal to sign the oath of allegiance to the fascist government he was compelled to resign his university post and his membership of scientific academies, and, during the following years, he lived largely abroad, returning to Rome just before his death.*Wik
André WEIL spent 1925-1926 studying with Volterra. Volterra was President of the the ACCADEMIA DEI LINCEI (or Lyncei). This was the first modern learned society. It was founded in Rome by Prince Federigo Cesi in 1603. The word 'lincei' means 'lynx-eyed', but actually derives from the Greek argonaut Linkeus, the eponym of the animal. Lynxes are on the crest of the Accademia

1874 V(agn) Walfrid Ekman (3 May 1874, 9 Mar 1954 at age 79) Swedish physical oceanographer and mathematical physicist whose research into the dynamics of ocean currents led to his name remaining associated with terms for particular phenomena of the ocean or atmosphere, including Ekman spiral, Ekman transport and Ekman layer. Fridtjof Nansen pointed out to Ekman that he had noticed that icebergs drift at an angle of 20°-40° to the prevailing wind, rather than directly with the wind. In 1902, Ekman published an explanation, known now as the Ekman spiral, describing movement of ocean currents influenced by the Earth's rotation. He also developed experimental techniques and instruments such as the Ekman current meter and Ekman water bottle.*TIS

1892 Sir George Paget Thomson (3 May 1892; 10 Sep 1975 at age 83) English physicist who shared (with Clinton J. Davisson of the U.S.) the Nobel Prize for Physics in 1937 for demonstrating that electrons undergo diffraction, a behaviour peculiar to waves that is widely exploited in determining the atomic structure of solids and liquids. He was the son of Sir J.J. Thomson who discovered the electron as a particle. *TIS

1902 Alfred Kastler (3 May 1902; 7 Jan 1984 at age 81) French physicist who won the Nobel Prize for Physics in 1966 for his discovery and development of methods for observing Hertzian resonances within atoms. This research facilitated the greater understanding of the structure of the atom by studying the radiations that atoms emit when excited by light and radio waves. He developed a method called "optical pumping" which caused atoms in a sample substance to enter higher energy states. This idea was an important predecessor to the development of masers and the lasers which utilized the light energy that was re-emitted when excited atoms released the extra energy obtained from optical pumping. *TIS

1924 Isadore Manuel Singer (April 24, 1924), Detroit Michigan. "Singer is justifiably famous among mathematicians for his deep and spectacular work in geometry, analysis, and topology, culminating in the Atiyah-Singer Index theorem and its many ramifications in modern mathematics and quantum physics." *SAU

1933 Steven Weinberg (3 May 1933, )American nuclear physicist who shared the 1979 Nobel Prize for Physics (with Sheldon Lee Glashow and Abdus Salam) for work in formulating the electroweak theory, which explains the unity of electromagnetism with the weak nuclear force. *TIS

DEATHS

1657 Johann Baptist Cysat (1586, 3 May 1657), Latinized as Cysatus was a Swiss astronomer who entered the Jesuit order (1604), and by 1611 was studying at the Jesuit college in Ingolstadt, Bavaria, under Christoph Scheiner, whom he assisted in the observation of sunspots. From 1618, he taught mathematics there. As an early user of a telescope, he was the first to make substantial telescopic observation of a comet (1 Dec 1618 to 22 Jan 1619), Although he discovered the Orion Nebula independently (1619), it had been first noted by Peiresc in 1610. Cysat wrote to Kepler describing a lunar eclipse (1620) and observed the transit of Mercury (1631). It is the comet study for which Cysat is noted. His measurements of its position were made using a 6-foot radius wooden sextant. He published his data and analysis in an 80-page booklet, Mathemata astronomica de locu...cometae... (1619). *TIS

1764 Francesco Algarotti (11 Dec 1712, 3 May 1764 at age 51) Italian scholar of the arts and sciences, recognized for his wide knowledge and elegant presentation of advanced ideas. At age 21, he wrote Il Newtonianismo per le dame (1737; "Newtonianism for Ladies"), a popular exposition of Newtonian optics. He also wrote about architecture, opera and painting. *TIS

1779 John Winthrop (December 19, 1714 – May 3, 1779) was the 2nd Hollis Professor of Mathematics and Natural Philosophy in Harvard College. He was a distinguished mathematician, physicist and astronomer, born in Boston, Mass. His great-great-grandfather, also named John Winthrop, was founder of the Massachusetts Bay Colony. He graduated in 1732 from Harvard, where, from 1738 until his death he served as professor of mathematics and natural philosophy. Professor Winthrop was one of the foremost men of science in America during the 18th century, and his impact on its early advance in New England was particularly significant. Both Benjamin Franklin and Benjamin Thompson (Count Rumford) probably owed much of their early interest in scientific research to his influence. He also had a decisive influence in the early philosophical education of John Adams, during the latter's time at Harvard. He corresponded regularly with the Royal Society in London—as such, one of the first American intellectuals of his time to be taken seriously in Europe. He was noted for attempting to explain the great Lisbon earthquake of 1755 as a scientific—rather than religious—phenomenon, and his application of mathematical computations to earthquake activity following the great quake has formed the basis of the claim made on his behalf as the founder of the science of seismology. Additionally, he observed the transits of Mercury in 1740 and 1761 and journeyed to Newfoundland to observe a transit of Venus. He traveled in a ship provided by the Province of Massachusetts - probably the first scientific expedition ever sent out by any incipient American state. *Wik

1880 Jonathan Homer Lane (August 9, 1819, Geneseo, New York – May 3, 1880, Washington D.C.) U.S. astrophysicist who was the first to investigate mathematically the Sun as a gaseous body. His work demonstrated the interrelationships of pressure, temperature, and density inside the Sun and was fundamental to the emergence of modern theories of stellar evolution. *TIS Simon Newcomb, in his memoirs, describes Lane as "an odd-looking and odd-mannered little man, rather intellectual in appearance, who listened attentively to what others said, but who, so far as I noticed, never said a word himself." Newcomb recounts his own role in bringing Lane's work, in 1876, to the attention of William Thomson who further popularized the work. Newcomb notes, "it is very singular that a man of such acuteness never achieved anything else of significance." *Wik

1885 Ernst Ferdinand Adolf Minding (23 Jan 1806 in Kalisz,Russian Empire (now Poland) - 3 May 1885 in Dorpat, Russia (now Tartu, Estonia))His work, which continued Gauss's study of 1828 on the differential geometry of surfaces, greatly influenced Peterson. In

1830 Minding published on the problem of the shortest closed curve on a given surface enclosing a given area. He introduced the geodesic curvature although he did not use the term which was due to Bonnet who discovered it independently in 1848. In fact Gauss had proved these results, before either Minding of Bonnet, in 1825 but he had not published them.
Minding also studied the bending of surfaces proving what is today called Minding's theorem in 1839. The following year he published in Crelle's Journal a paper giving results about trigonometric formulae on surfaces of constant curvature. Lobachevsky had published, also in Crelle's Journal, related results three years earlier and these results by Lobachevsky and Minding formed the basis of Beltrami's interpretation of hyperbolic geometry in 1868.
Minding also worked on differential equations, algebraic functions, continued fractions and analytic mechanics. In differential equations he used integrating factor methods. This work won Minding the Demidov prize of the St Petersburg Academy in 1861. It was further developed by A N Korkin. Darboux and Émile Picard pushed these results still further in 1878. *SAU

1988 Lev Semenovich Pontryagin (3 September 1908 – 3 May 1988) One of the 23 problems posed by Hilbert in 1900 was to prove his conjecture that any locally Euclidean topological group can be given the structure of an analytic manifold so as to become a Lie group. This became known as Hilbert's Fifth Problem. In 1929 von Neumann, using integration on general compact groups which he had introduced, was able to solve Hilbert's Fifth Problem for compact groups. In 1934 Pontryagin was able to prove Hilbert's Fifth Problem for abelian groups using the theory of characters on locally compact abelian groups which he had introduced. *SAU [He was buried at the Novodevichie Memorial Cemetery in Moscow.

1988 Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician. He was known for his research to commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several important papers.*Wik

Tuesday, 2 May 2017

On This Day in Math - May 2

We call a thing big or little

with reference to what it is wont to be,

as we speak of a small elephant

or a big rat.

D'Arcy Thompson, "On Growth and Form"

The 122nd day of the year; there are 122 different ways to partition the number 24 into distinct parts. Euler showed that this is the same as the number of ways to partition a number into odd parts.

122 ends in the digit two when written in base 3, 4, 5, 6, 8, 10, 12, 15, and 20. How unusual is that?

EVENTS

1775 Benjamin Franklin completed the first scientific study of the Gulf Stream. His observations began in 1769 when as deputy postmaster of the British Colonies he found ships took two weeks longer to bring mail from England than was required in the opposite direction. Thus, Franklin became the first to chart the Gulf Stream.He described the Gulf Stream as a river of warm water and mapped it as flowing north from the West Indies, along the East Coast of North America and east across the Atlantic Ocean to Europe. *TIS

In 1800, English chemist William Nicholson was the first to produce a chemical reaction by electricity. He had been working with Anthony Carlisle, a London surgeon, experimenting with Allesandro Volta's voltaic pile. The new effect was discovered when wires from the poles of the battery being used came into contact with water and bubbles of gas were released as current flowed through the water. Closer examination of the electrolysis showed oxygen was released at the (positive) anode, and hydrogen appeared at the cathode. Electricity had separated the molecules of water. Further, the effect of the amount of hydrogen and oxygen set free by the current was proportional to the amount of current used.*TIS

1983 Microsoft Introduces 2-button Mouse:
Microsoft Corp. announced the two-button Microsoft Mouse, which it introduced to go along with its new Microsoft Word processor. Microsoft built about 100,000 of these fairly primitive units for use with IBM and IBM-compatible personal computers but sold only 5,000 before finding success in a 1985 version that featured, among other improvements, near-silent operation on all surfaces.*CHM
In ensuing years, as mice made their way to personal computers, there was something of a battle waged between proponents of 2-button and 3-button mice, with Logitech favoring the 3-button variety

BIRTHS

1588 Etienne Pascal (Clermont, May 2, 1588 - Paris, September 24, 1651), for whom the limacon of Pascal was named. He was the father of Blaise Pascal. The limacon was named by another Frenchman Gilles-Personne Roberval in 1650 when he used it as an example of his methods of drawing tangents
i.e. differentiation.
The name "limacon" comes from the Latin limax meaning 'a snail'. Étienne Pascal corresponded with Mersenne whose house was a meeting place for famous geometers including Roberval.
Dürer should really be given the credit for discovering the curve since he gave a method for drawing the limacon, although he did not call it a limacon, in Underweysung der Messungpublished in 1525. *SAU [Etienne Pascal was one of the "nine lovers of literature established a regular meeting. In 1635, Richelieu organized them into an Académie Libre or ACADÉMIE FRANÇAIS.." This was the forerunner of the ACADÉMIE DES SCIENCES. pb]

1601 Athanasius Kircher (2 May 1601; 28 Nov 1680 at age 79) German Jesuit priest and scholar, sometimes called the last Renaissance man. Kircher's prodigious research activity spanned a variety of disciplines including geography, astronomy, physics, mathematics, language, medicine, and music. He made an early, though unsuccessful attempt to decipher hieroglyphics of the Coptic language. During the pursuit of experimental knowledge, he once had himself lowered into the crater of Vesuvius to observe its features soon after an eruption. He made one of the first natural history collections. Kircher studied animal luminescence, writing two chapters of his book Ars Magna Lucis et Umbrae to bioluminescence, and debunked the idea that that an extract made from fireflies could be used to light houses.*TIS

1773 Henrik Steffens (2 May 1773–13 February 1845), was a Norwegian-born Danish philosopher, scientist, and poet. He was one of the so-called "Philosophers of Nature", a friend and adherent of Schelling and of Schleiermacher. More than either of these two thinkers he was acquainted with the discoveries of modern science, and was thus able to correct or modify the highly imaginative speculations of Schelling. He held that, throughout the scheme of nature and intellectual life, the main principle is Individualisation. As organisms rise higher in the scale of development, the sharper and more distinct become their outlines, the more definite their individualities. This principle he endeavoured to deduce from his knowledge of geology, in contrast to Lorenz Oken, who developed the same theory on biological grounds. His influence was considerable, and both Schelling and Schleiermacher modified their theories in deference to his scientific deductions.*Wik

1860 Sir D'Arcy Wentworth Thompson (2 May 1860; 21 Jun 1948 at age 88)
Scottish zoologist and classical scholar, who is noted for his influential work On Growth and Form (1917, new ed. 1942). It is a profound consideration of the shapes of living things, starting from the simple premise that “everything is the way it is because it got that way.” Hence one must study not only finished forms, but also the forces that moulded them: “the form of an object is a ‘diagram of forces’, in this sense, at least, that from it we can judge of or deduce the forces that are acting or have acted upon it.”' One of his great themes is the tremendous light cast on living things by using mathematics to describe their shapes and fairly simple physics and chemistry to explain them..*TIS
He graduated from Cambridge University in Zoology and was appointed Professor of Biology at Dundee and later Professor of Natural History at St Andrews. He combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. He became an honorary member of the EMS in 1933.*SAU [The University of Dundee and the University of St Andrews joined to host a celebration of Thompson's sesquicentennial birth year (2010) with a series of events. They have a photo gallery still available at the time of this writing. ]

1868 Robert W. Wood (2 May 1868; 11 Aug 1955 at age 87) was an American physicist who photographed the reflection of sound waves in air, and investigated the physiological effects of high-frequency sound waves. The zone plate he devised could replace the objective lens of a telescope. He invented an improved diffraction grating, did research in spectroscopy, and extended the technique of Raman spectroscopy (a method to study matter using the light scattered by it.) He made photographs showing both infrared and ultraviolet radiation and was the first to photograph ultraviolet fluorescence. Wood was the first to observe the phenomenon of field emission in which charged particles are emitted from conductors in an electric field. *TIS
According to a post at Greg Ross' Futility Closet:

"How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:
The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.
This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”

1901 Edouard Zeckendorf (2 May 1901 - 16 May 1983) was a Belgian doctor, army officer and mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem. Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.
Zeckendorf was born in Liège in 1901. He was the son of a Dutch dentist. In 1925, Zeckendorf graduated as a medical doctor from the University of Liège and joined the Belgian Army medical corps. When Germany invaded Belgium in 1940, Zeckendorf was taken prisoner and remained a prisoner of war until 1945. During this period, he provided medical care to other allied POWs. *Wik

1928 Jacques-Louis Lions (2 May 1928 in Grasse, Alpes-Maritimes, France - 17 May 2001 in Paris, France) French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John Von Neumann prize in 1986. *Wik

Sumio Iijima (May 2, 1939, )is a Japanese physicist, often cited as the discoverer of carbon nanotubes. Although carbon nanotubes had been observed prior to his "discovery"1, Iijima's 1991 paper generated unprecedented interest in the carbon nanostructures and has since fueled intense research in the area of nanotechnology. For this and other work Sumio Iijima was awarded, together with Louis Brus, the inaugural Kavli Prize for Nanoscience in 2008. *Wik (Quotes of Sumio Iijma by Arjen Dijksman)

DEATHS

1519 Leonardo da Vinci (15 Apr 1452, 2 May 1519 at age 67) Italian painter, draftsman, sculptor, architect, and engineer. Da Vinci was a great engineer and inventor who designed buildings, bridges, canals, forts and war machines. He kept huge notebooks sketching his ideas. Among these, he was fascinated by birds and flying and his sketches include such fantastic designs as flying machines. These drawings demonstrate a genius for mechanical invention and insight into scientific inquiry, truly centuries ahead of their time. His greater fame lies in being one of the greatest painters of all times, best known for such paintings as the Mona Lisa and The Last Supper.*TIS

1925 Johann Palisa (6 Dec 1848, 2 May 1925 at age 76)Austrian astronomer who was a prolific discoverer of asteroids, 122 in all, beginning with Asteroid 136 Austria (on 18 Mar 1874, using a 6" refractor) to Asteroid 1073 Gellivara in 1923 - all by visual observation, without the aid of photography. In 1883, he joined the expedition of the French academy to observe the total solar eclipse on May 6 of that year. During the eclipse, he searched for the putative planet Vulcan, which was supposed to circle the sun within the orbit of Mercury. In addition to observing the eclipse, Palisa collected insects for the Natural History Museum in Vienna. He also prepared two catalogs containing the positions of almost 4,700 stars. He remains the most successful visual discoverer in the history of minor planet research.*TIS

1967 Robert Daniel Carmichael (1 March 1879 in Goodwater, Coosa County, Alabama, USA - 2 May 1967 in Merriam, Northeast Johnson County, Kansas, USA) Carmichael is known for his mathematical research in what are now called the Carmichael numbers (numbers satisfying properties of primes described by Fermat's Little Theorem although they are not primes- see below), Carmichael's theorem, and the Carmichael function, all significant in number theory and in the study of the prime numbers. Carmichael might have been the first to describe the Steiner system S(5,8,24), a structure often attributed to Ernst Witt. While at Indiana University Carmichael was involved with special theory of relativity. *Wik Fermat had proved that if n is prime then xn-1 = 1 mod n for every x coprime to n. A 'Carmichael number' is a non-prime n satisfying this condition for any x coprime to n. It was given this name since Carmichael discovered the first such number, 561, in 1910 (there are several base ten Carmichael numbers below 561 for the interested student to search for). For many years it was an open problem as to whether there were infinitely many Carmichael numbers, but this was settled in 1994 by W R Alford, A Granville, and C Pomerance in their paper There are infinitely many Carmichael numbers. *SAU

1981 David Wechsler (12 Jan 1896, 2 May 1981 at age 85) U.S. psychologist and inventor of several widely used intelligence tests for adults and children. During WW I, while assisting Edwin Garrigues Boring (1886-1968) in testing army recruits, Wechsler realized the inadequacies of the Army Alpha Tests (designed to measure abilities of conscripts and match them to suitable military jobs). He concluded that academically defined "intelligence" did not apply to "real life" situations. After leaving the military and more years of research, he developed the Wechsler Adult Intelligence Scale, and introduced deviation scores in intelligence tests. He developed the Wechsler Memory Scale in 1945, Wechsler Intelligence Scale for Children (1949), and Wechsler Preschool and Primary Scale of Intelligence (1967). *TIS

1982 Salomon Bochner (20 Aug 1899, 2 May 1982 at age 82) Galician-born American mathematician and educator responsible for the development of the Bochner theorem of positive-definite functions and the Bochner integral.*TIS
In 1925 he started work in the area of almost periodic functions, simplifying the approach of Harald Bohr by use of compactness and approximate identity arguments. In 1933 he defined the Bochner integral, as it is now called, for vector-valued functions. Bochner's theorem on Fourier transforms appeared in a 1932 book. His techniques came into their own as Pontryagin duality and then the representation theory of locally compact groups developed in the following years.
Subsequently he worked on multiple Fourier series, posing the question of the Bochner–Riesz means. This led to results on how the Fourier transform on Euclidean space behaves under rotations.
In differential geometry, Bochner's formula on curvature from 1946 was most influential. Joint work with Kentaro Yano (1912–1993) led to the 1953 book Curvature and Betti Numbers. It had broad consequences, for the Kodaira vanishing theory, representation theory, and spin manifolds.*WIK

2004 John Hammersley (21 March 1920-2 May 2004) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. *Wik when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)
During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, `On the enfeeblement of mathematical skills by `Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. (from his Independent obituary)

2010 Clive W. Kilmister (1924 – May 2, 2010) was a British Mathematician who specialized in the mathematical foundations of Physics, especially Quantum Mechanics and Relativity and published widely in these fields (see References). He was one of the discoverers of the Combinatorial Hierarchy, along with A. F. Parker-Rhodes, E. W. Bastin, and J.C.Amson. He was strongly influenced by astrophysicist Arthur Eddington and was well known for his elaboration and elucidation of Eddington’s fundamental theory.
Kilmister attended Queen Mary College London for both his under- and postgraduate degrees. His PhD was supervised by cosmologist George McVittie (himself a student of Eddington), and his dissertation was entitled ‘’The Use of Quaternions in Wave-Tensor Calculus’’ which related to Eddington’s work. Kilmister received his doctoral degree in 1950. His own students included Brian Tupper (1959, King's College London, now professor emeritus of general relativity and cosmology at University of New Brunswick Fredericton [2]), Samuel Edgar (1977, University of London), and Tony Crilly (reader in mathematical sciences at Middlesex University and author of The Big Questions: Mathematics (1981).
Kilmister was elected as a member of the London Mathematical Society during his doctoral studies (March 17, 1949). Upon graduation, he began his career as an Assistant Lecturer in the Mathematics Department of King’s College in 1950. The entirety of his academic career was spent at King’s. In 1954, Kilmister founded the King’s Gravitational Theory Group, in concert with Hermann Bondi and Felix Pirani, which focused on Einstein’s theory of general relativity. At retirement, Kilmister was both a Professor of Mathematics and Head of the King’s College Mathematics Department.
He was Gresham Professor of Geometry, 1972-88. *Wik

Monday, 1 May 2017

On This Day in Math - May 1

The only way to learn a new programming language

is by writing programs in it.

- B. Kernighan & D. Ritchie

The 121st day of the year; 121 will be the largest year day of the form n!+1 which is a square number. Brocard conjectured in 1904 that the only solutions of n! + 1 = m² are n = 4, 5, and 7. There are no other solutions with $n \lt 10^ 9$. 121 is also the only square of the form 1 + n + n²+ n³ + n⁴. *What's So Special About This Number

121 is also a Smith Number, a composite number for which the sum of its digits is equal to the sum of the digits in its prime factorization. Smith numbers were named by Albert Wilansky of Lehigh University. He noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:
4937775 = 3 × 5 × 5 × 65837, while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42.
There are 49 Smith numbers below 1000, collect the whole set.

121 is a palindrome in base ten, and also in base 3 (11111), base 7 (232) and base 8(171). No other year day is a base ten palindrome and also palindrome in as many other (2-9) bases.

EVENTS

1006 Supernova is observed in the constellation Lupus, the Wolf. *VFR
[SN 1006 was a supernova, widely seen on Earth beginning in the year 1006 AD; Earth was about 7,200 light-years away from the supernova. It was the brightest apparent magnitude stellar event in recorded history reaching an estimated -7.5 visual magnitude. First appearing in the constellation of Lupus between April 30 and May 1 of that year, this "guest star" was described by observers in China, Egypt, Iraq, Japan, Switzerland, and possibly North America....A petroglyph by the Hohokam in White Tank Mountain Regional Park Maricopa County, Arizona, has been interpreted as the first known North American representation of the supernova. ]*Wik
["Having looked at the White Tanks rock art panel, I am appalled," says Edwin C. Krupp, Director of the Griffith Observatory in Los Angeles and author of Archaeoastronomy and the Roots of Science. "Panels like this are not rare. There is no reason to link it to any supernova event. There is nothing persuasive about the imagery to support the extraordinarily detailed claim. The authors say nothing about all of the other imagery on the boulder and select two details for their discussion. These two details are in themselves dubiously interpreted."
"This Supernova 1006 petroglyph interpretation is nothing but assumptions and wishful thinking," he adds.] (Sky and Telescope Magazine)
Make up your own mind, I think this is it...

1514 The catalogue of a Cracow professor’s books included “a manuscript of six leaves expounding the theory of an author who asserts that the earth moves while the sun stands still.” The professor was unable to identify the author, as Copernicus prudently withheld his name from his Commentariolus. *VFR
[Around 1514 he distributed a little book, not printed but hand written, to a
few of his friends who knew that he was the author even though no author is
named on the title page. This book, usually called the Little Commentary,
set out Copernicus's theory of a universe with the sun at [near!? HV] its
centre. The Little Commentary is a fascinating document. It contains seven
axioms which Copernicus gives, not in the sense that they are self evident,
but in the sense that he will base his conclusions on these axioms and
nothing else; see . What are the axioms? Let us state them:

1.There is no one centre in the universe.

2.The Earth's centre is not the centre of the universe.

3.The centre of the universe is near the sun.

4.The distance from the Earth to the sun is imperceptible compared with
the distance to the stars.

5.The rotation of the Earth accounts for the apparent daily rotation of
the stars.

6.The apparent annual cycle of movements of the sun is caused by the
Earth revolving round it.

7.The apparent retrograde motion of the planets is caused by the motion
of the Earth from which one observes.

Here, for the sake of brevity, I have thought it desirable to omit the
mathematical demonstrations intended for my larger work.

It is likely that he wrote the Little Commentary in 1514 and began writing
his major work De revolutionibus in the following year.] *SAU

1624 If you lived in New York City at any point from colonial times to World War II, then you'd really have some complaints come May 1. May Day, that oh-so-pleasant-sounding spring day, was also known as "Moving Day" because it was the day when everyone moved. Yep, everyone.

According to legend, Moving Day originated from the Dutch. They set out on their first journey to Manhattan on May 1 (eventually "buying" Manhattan from the Native Americans with trinkets and beads) and celebrated that journey every year thereafter by moving houses — creating a tradition that would last for several centuries while Manhattan grew and grew.

In the days before rent control, custom called for landlords to notifiy tenants of their rent increase for the coming year on February 1, giving them three months to make new housing arrangements before their price increase went into effect on, you guessed it, May 1.

On that day, horse-drawn carriages flooded the streets, carting the belongings of every New York renter back and forth and, of course, creating mass chaos. apartmenttherapy.com

1631 Fermat received the degree of Bachelor of Civil Laws from the University of Orleans. He practiced law, but did mathematics.

1683 In Ole Rømer's position as royal mathematician, he introduced the first national system for weights and measures in Denmark . Initially based on the Rhine foot, a more accurate national standard was adopted in 1698. Later measurements of the standards fabricated for length and volume show an excellent degree of accuracy. His goal was to achieve a definition based on astronomical constants, using a pendulum. This would happen after his death, practicalities making it too inaccurate at the time. Notable is also his definition of the new Danish mile of 24,000 Danish feet (circa 7,532 m). * Wik Römer was Cassini's assistant and first determined the speed of light at the Paris Observatory in 1675, by observing differences in times for the moons of Jupiter depending on whether the earth was near or far from Jupiter, getting about 3.2 x 108 m/sec. (However, another source says he didn't compute the speed, merely noted that there was a difference, which showed that light had a finite speed. Others did the calculation, using various values for the distance of the earth from the sun and obtained results ranging from 2.6 to 5.6 x 108 m/sec, all of which are attributed to Roemer. [Sobel, pp. 29-30] says he calculated the speed in 1676 and got a slight underestimate. [Don Glass, ed.; Why You Can Never Get to the End of the Rainbow and Other Moments of Science; Indiana Univ Press, Bloomington, Indiana, 1993, p. 102] says Roemer announced his results to the Académie des Sciences in Sep 1676, correctly predicting the eclipse of Io on 9 Nov would be 10 minutes late and says Roemer got a speed of light about 2.3 x 108 m/sec.)

1804 George Baron publishes the first copy of the Mathematical Correspondent. This was the first mathematics journal published in the United States, and in fact, the first specialized science journal of any kind in the US. The founder and editor-in-chief, George Baron, was the first Superintendent and mathematics professor at what would become the US Military Academy at West Point, NY. *Wik

1854 Lord Kelvin reads a paper to the Royal Society of Edinburgh on which he attempts to weigh the ether. "There must be a medium forming a continuous material communication throughout space to the remotest visible body." He felt that air and ether were the same thing and that the Earth's athmosphere extended throughout space.*The correspondence between Sir George Gabriel Stokes and Sir ..., Volume 1, pg XXXii, By Sir George Gabriel Stokes, Baron William Thomson Kelvin

In 1851, the Great Exhibition of the Works of Industry of All Nations opened in Hyde Park, London, England. This was the first international exhibition to be held in any country. Housed in Paxton's magnificent Crystal Palace, it provided a showcase for many thousands of inventions. The legacy of the Great Exhibition of 1851, still lives on today. Several great institutions were founded with the profits, including the Victoria and Albert Museum and Imperial College. Scholarships which were setup and still continue reaped an immense contribution to the world's body of knowledge. Recipients included several Nobel prize winnners: one scholarship went to Ernest Rutherford, a son of a New Zealand farmer. *TIS

1861 Oswego Training School, Oswego, N.Y., established. It was the ﬁrst state normal school at which students actually conducted classes. In 1861, Edward Austin Sheldon founded what would become SUNY Oswego as the first urban teacher training program in the United States.

1888 Nikola Tesla was issued several patents relating to the induction magnetic motor, alternating current (AC) sychronous motor, AC transmission and electricity distribution (Nos. 381,968-70; 382,279-82) *TIS

1893 The Chicago World’s Fair opened. Felix Klein came from Germany. The plaster models he brought along created a classroom vogue. (MathDL MAA) [It may be that some give Klein's visit to much credit for the use of models in schools. Cajori's "The Teaching and History of Mathematics in the United States", published in 1890 suggests that "most" high schools and colleges used models in geometry classes. Klein was surely a dominant influence in the use of models in Germany, and that use spread to the US; but it seems not to have been Klein's visit that sparked their use. Interestingly, Hans Freudenthal in his "Weeding and sowing: preface to a science of mathematical education", credits Klein with being the first to use "model" in the sense of an abstract mathematical idea in his description of a non-Euclidean geometry. After the Fair Klein traveled around the country visiting several colleges. The New York Mathematical Society had a special meeting in his honor at Columbia College on Sept 30. pb]

1902 As the slight and aged Lord Kelvin was led slowly down the aisle of Anderson Hall by Rochester University President, Dr. Rush Rhees, students stood quietly in honor, and then, broke out into a rousing cheer for a scientist, a British Scientist. Lord Kelvin had visited America five years earlier, and five years later he would be dead.*David Lindley , Degrees Kelvin: a tale of genius, invention, and tragedy

1930 The name for Pluto is announced to the world: The name Pluto was proposed by Venetia Burney (1918–2009), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, a name for the god of the underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian at the University of Oxford's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in the United States.
The object was officially named on March 24, 1930. Each member of the Lowell Observatory was allowed to vote on a short-list of three: Minerva (which was already the name for an asteroid), Cronus (which had lost reputation through being proposed by the unpopular astronomer Thomas Jefferson Jackson See), and Pluto. Pluto received every vote. The name was announced on May 1, 1930. Upon the announcement, Madan gave Venetia five pounds (£5) as a reward.
It has been noted that the first two letters of Pluto are the initials of Percival Lowell, and Pluto's astronomical symbol (♇) is a monogram constructed from the letters 'PL'. *Wik

1935 Austria issued a stamp for Mother’s Day portraying “Mother and Child” after a painting by Albrecht Durer. He is the mathematician that has the most stamps issued dealing with him. [Scott #376; Germany Scott #362 was issued in 1926–7, so this is the second stamp devoted to D¨urer].

In 1949, Gerard Kuiper discovered Nereid, the second satellite of Neptune, the outermost and the third largest of Neptune's known satellites. (Orbit: ave 5,513,400 km, diameter: 340 km). Nereid's orbit is the most highly eccentric of any planet or satellite in the solar system; its distance from Neptune varies from 1,353,600 to 9,623,700 kilometers. Nereid's odd orbit indicates that it may be a captured asteroid or Kuiper Belt object. The name, Nereid refers to the sea nymphs who dwell in the Mediterranean sea, the 50 daughters of Nereus and Doris. Kuiper, a Dutch-American astronomer (1905-1973) also studied the surface of the Moon; discovered Miranda, a moon of Uranus; and found an atmosphere on Titan, a moon of Saturn. *TIS

In 1958, the discovery of the powerful Van Allen radiation belts that surround Earth was published in the Washington Evening Star. The article covered the report made by their discoverer James. A. Van Allen to the joint sysmposium of the National Academy of Sciences and the American Physical Society in Washington DC. He used data from the Explorer I and Pioneer III space probes of the earth's magnetosphere region to reveal the existence of the radiation belts - concentrations of electrically charged particles. Van Allen (born 7 Sep 1914) was also featured on the cover of the 4 May 1959 Time magazine for this discovery. He was the principal investigator on 23 other space probes. *TIS

1964 John Kemeny and John Kurtz run the ﬁrst BASIC program at Dartmouth. In 1964, first BASIC program was run on a computer at about 4:00 a.m. Invented at Dartmouth University by professors John G. Kemeny and Thomas E. Kurtz, the first implementation was a BASIC compiler. Basic is an acronym for Beginner's All-purpose Symbolic Instruction Code, designed to be an easy programming language to learn quickly how to write simple programs. Originally for mainframes, BASIC was adopted for use on personal computers when they became available. *TIS
[Work on the compiler and the operating system was done concurrently, and so the first BASIC programs were run in batch mode as part of the development process during early 1964. However on May 1, 1964 at 4 a.m. ET, John Kemeny and John McGeachie ran the first BASIC programs to be executed successfully from terminals by the DTSS system. It is not completely clear what the first programs were. However, the programs either consisted of the single line:PRINT 2 + 2 {Let us hope it printed "4" (PB)}or were implementations of the Sieve of Eratosthenes, according to a 1974 interview in which Kemeny and McGeachie took part.] *Wik

BIRTHS

1591 Adam Schall von Bell (1 May 1591; 15 Aug 1666 at age 75) German missionary and astronomer, a Jesuit, who in China (from 1619) revised the Chinese calendar, translated Western astronomical books and was head of Imperial Board of Astronomy (1644-64). He became a trusted adviser (1644-61) to Emperor Shun-chih, first emperor of the Ch'ing dynasty (1644-1911/12) who made him a mandarin. He lost power after the emperor's death (1661). Although then tried (1664) and convicted for plotting against the emperor and state, his sentence was commuted. *TIS

1793 Jakob Philipp Kulik (1 May 1793 in Lemberg, Austrian Empire (now Lviv, Ukraine) - 28 Feb 1863 in Prague, Czech Republic) Austrian mathematician known for his construction of a massive factor tables.
Kulik was born in Lemberg, which was part of the Austrian empire, and is now Lviv located in Ukraine.In 1825, Kulik mentioned a table of factors up to 30 millions, but this table does no longer seem to exist. It is also not clear if it had really been completed.
From about 1825 until 1863 Kulik produced a factor table of numbers up to 100330200 (except for numbers divisible by 2, 3, or 5). This table basically had the same format that the table to 30 millions and it is therefore most likely that the work on the "Magnus canon divisorum" spanned from the mid 1820s to Kulik's death, at which time the tables were still unfinished. These tables fill eight volumes totaling 4212 pages, and are kept in the archives of the Academy of Sciences in Vienna. Volume II of the 8 volume set has been lost.*Wik

1825 Johann Jakob Balmer ((May 1, 1825 – March 12, 1898)Swiss mathematician and physicist who discovered a formula basic to the development of atomic theory. Although a mathematics lecturer all his life, Balmer's most important work was on spectral series by giving a formula relating the wavelengths of the spectral lines of the hydrogen atom (1885) at age 60. Balmer's famous formula is = hm2/(m2-n2). Wavelengths are accurately given using h = 3654.6x10-8-cm, n = 2, and m = 3, 4, 5, 6, 7. He suggested that giving n other small integer values would give other series of wavelengths for hydrogen. Why this prediction agreed with observation was not understood until after his death when the theoretical work of Niels Bohr was published in 1913. *TIS

1891 Louis Melville Milne-Thomson, CBE (1 May 1891 – 21 August 1974) was an English applied mathematician who wrote several classic textbooks on applied mathematics, including The Calculus of Finite Differences, Theoretical Hydrodynamics, and Theoretical Aerodynamics. He is also known for developing several mathematical tables such as Jacobian Elliptic Function Tables. The Milne-Thomson circle theorem is named after him.[1] Milne-Thomson was made a Commander of the Order of the British Empire (CBE) in 1952.*Wik

1908 Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn and in Jamaica, Queens. After graduating from Boys High School in Brooklyn, he studied mathematics at New York University, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey. Designated a physicist, he worked in the engineering lab where radar was developed. After the war he continued investigating electromagnetism, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences.
Kline resumed his mathematical teaching at NYU, becoming a full professor in 1952. He taught at New York University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly mathematics teaching. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on solving problems posed in other fields rather than building structures of interest only to other mathematicians. *Wik

1908 Hans Herbert Schubert (1 May 1908 in Weida, Thüringen Germany - 24 Nov 1987 in Halle, Germany) German mathematician who worked on differential equations. *SAU

1924 Evelyn Boyd Granville (May 1, 1924 - ) was the second African-American woman in the U.S. to receive a PhD in mathematics. (The first was Euphemia Haynes who was awarded her PhD from Catholic University in 1943.)
With financial support from her aunt and a small partial scholarship from Phi Delta Kappa, Granville entered Smith College in the fall of 1941. She majored in mathematics and physics, but also took a keen interest in astronomy. She was elected to Phi Beta Kappa and to Sigma Xi and graduated summa cum laude in 1945. Angeles]]. In L.A., Granville accepted the position of Research Specialist with the Space and Information Systems Division of the North American Aviation Company, but returned to IBM the following year. Both positions involved trajectory analysis and orbit computation. In 1967, Granville’s marriage ended in divorce. At the same time, IBM was cutting staff in Los Angeles, so Granville applied for a teaching position at California State University in Los Angeles, California.
She moved to California State University at Los Angeles in 1967 as a full professor of mathematics and married Edward V. Granville in 1970. After retiring from California State in 1984 she joined the faculty of the University of Texas at Tyler as professor and chair of mathematics. There she developed elementary school math enrichment programs. One of three African American women honored by the National Academy of Science in 1999, she has been awarded honorary degrees by Smith College and Lincoln University. *Wik
Dr. Scott Williams at Buffalo has a website about Black Women in Mathematics including many biographies.

1926 Peter David Lax (1 May 1926 - ) is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields. Lax is listed as an ISI highly cited researcher. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.
Lax holds a faculty position in the Department of Mathematics, Courant Institute of Mathematical Sciences, New York University*Wik

DEATHS

1870 Gabrial Lamé (July 22, 1795 – May 1, 1870) worked on a wide variety of different topics. His work on differential geometry and contributions to Fermat's Last Theorem are important. He proved the theorem for n = 7 in 1839. [he proved that x⁷+y⁷=z⁷ could not be true for integral values of x, y, z all greater than 0]
He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:

$\left|\,{x\over a}\,\right|^n + \left|\,{y\over b}\,\right|^n =1$

where n is any positive real number.

He is also known for his running time analysis of the Euclidean algorithm. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digits of b. He also proved a special case of Fermat's last theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics. *Wik

2015 Murray Marshall ---It is with deep sadness that the family of Murray Marshall announces his sudden passing on Friday, May 1, 2015 at the age of 75 years. He was born in Hudson Bay Junction to Fred and Olive Marshall, the middle of three sons. After graduation from Hudson Bay High School, he attended the University of Saskatchewan where he completed his B.A and B. Ed. He completed his Ph.D. in mathematics at Queen's University and then returned to join the faculty at the University of Saskatchewan. Murray married Mary Cey in 1966 -

Pat'sBlog

Thursday, 4 May 2017

On This Day in Math - May 4

Wednesday, 3 May 2017

On This Day in Math - May 3

Tuesday, 2 May 2017

On This Day in Math - May 2

Monday, 1 May 2017

On This Day in Math - May 1

Blog Archive

Stat Counter