Tuesday, 28 March 2023

On This Day in Math - March 28


*George W. Hart, Sculpture

 `The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps ...'.
Alexandre Grothendieck in a letter in 1982 to Ronald Brown

The 87th day of the year; the sum of the squares of the first four primes is 87. \(87 = 2^2 + 3^2 + 5^2 + 7^2 \)

87 = 3 * 29, \(87^2 + 3^2 + 29^2\)  and \( 87^2 - 3^2 - 29^2 \) are both primes

Among Australian cricket players, it seems, 87 is an unlucky score and is referred to as "the devil's number", supposedly because it is 13 runs short of 100.
87 is the third consecutive day that is semiprime (the product of two primes)

And 87 is, of course, the number of years between the signing of the U.S. Declaration of Independence and the Battle of Gettysburg, immortalized in Abraham Lincoln's Gettysburg Address with the phrase "fourscore and seven years ago..."

87 is the largest number that yields a prime when any of the one-digit primes 2, 5 or 7 is inserted between any two digits. The only other such number is 27 (and trivially, the 1 digit numbers). *Prime Curios

5! - 4! - 3! - 2! - 1! = 87. Remember the old puzzle of making numbers with four 4's. What numbers could you make with the first five factorials using only the four basic arithmetic functions between them


In 1747, the fascination with electricity upon reaching the American colonies was the subject of Benjamin Franklin's first of the famous series of letters in which he described his experiments on electricity to Peter Collinson, Esq., of London. He thanked Collison for his “kind present of an electric tube with directions for using it” with which he and others did electrical experiments. “For my own part I never was before engaged in any study that so totally engrossed my attention and my time as this has lately done; for what with making experiments when I can be alone, and repeating them to my friends and acquaintances, who, from the novelty of the thing, come continually in crowds to see them, I have, during some months past, had little leisure for anything else.”*TIS

1764 In a second trial of John Harrison's marine timekeeper, his son William departed for Barbados aboard the Tartar. As with the first trial, William used H4 to predict the ship's arrival at Madeira with extraordinary accuracy. The watch's error was computed to be 39.2 seconds over a voyage of 47 days, three times better than required to win the maximum reward of £20,000. *Royal Museum Greenwich

H4 is housed in silver pair cases some 5.2 inches (13 cm) in diameter. The clock's movement is highly complex for that period, resembling a larger version of the then-current conventional movement

1802 Olbers, while observing the constellation Virgo, had observed a "star" of the seventh-magnitude not found on the star charts. Over the following week he would observe the motion and determined that it was a planet. In early April he sent the data to Gauss to compute the orbit. On the 18th of April, Gauss computed the orbit in only three hours, placing the orbit between Mars and Jupiter. Olbers named the new planetoid Pallas, and predicted there would be others found in the same area. John Herschel dismissed this speculation as "dreams in which astronomers... indulge" but over 1000 such planetoids have been observed. *Dunnington, Gray, & Dohse; Carl Friedrich Gauss: Titan of Science
Pallas, the third largest asteroid in the asteroid belt and the second such object to be discovered, following the discovery of Ceres,discovered on 1 January 1801, by Giuseppe Piazzi. 
In 1596, Johannes Kepler wrote, "Between Mars and Jupiter, I place a planet," in his Mysterium Cosmographicum, stating his prediction that a planet would be found there. While analyzing Tycho Brahe's data, Kepler thought that too large a gap existed between the orbits of Mars and Jupiter to fit Kepler’s then-current model of where planetary orbits should be found.

In an anonymous footnote to his 1766 translation of Charles Bonnet's Contemplation de la Nature, the astronomer Johann Daniel Titius of Wittenberg noted an apparent pattern in the layout of the planets, now known as the Titius-Bode Law. If one began a numerical sequence at 0, then included 3, 6, 12, 24, 48, etc., doubling each time, and added four to each number and divided by 10, this produced a remarkably close approximation to the radii of the orbits of the known planets as measured in astronomical units, provided one allowed for a "missing planet" (equivalent to 24 in the sequence) between the orbits of Mars (12) and Jupiter (48).

1809 Gauss finished work on his Theoria Motus. It explains his methods of computing planetary orbits using least squares. [Springer’s 1985 Statistics Calendar] *VFR

In 1946, the Census Bureau and the National Bureau of Standards met to discuss the purchase of a computer. The agencies agreed to buy UNIVAC, the world's first general all-purpose business computer, from Presper Eckert and John Mauchly for a mere $225,000. Unfortunately, UNIVAC cost far more than that to develop. Eckert and Mauchly's venture floundered as the company continued to build and program UNIVACs for far less than the development cost. Eventually, the company was purchased by Remington Rand. *TIS

1949 The phrase "Big Bang" is created. Shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders
"Suddenly, an explosive expansion began, ballooning our universe outwards faster than the speed of light. This was a period of cosmic inflation that lasted mere fractions of a second — about 10^-32 of a second, according to physicist Alan Guth’s 1980 theory that changed the way we think about the Big Bang forever." *Space.com  

Big Bang Background Radiation *ESA Planck

1959 Germany issued a stamp commemorating the 400th anniversary of the death of Adam Riese [Scott #799] *VFR I understand that the German expression "nach Adam Riese", is still used today. It means "according to Adam Riese" and it is used in saying something is exactly correct.

In 2006, a substantial "lost" book of manuscripts by Robert Hooke in his own handwriting was bought for the Royal Society by donations of nearly £1 million. The book was just minutes before going on the auction block when a last-minute purchase agreement was made and kept the precious document in Britain. Hooke is now often overlooked, except for his law of elasticity, although in his time, he was a prolific English scientist and contributed greatly to planning the rebuilding of London after the Great Fire of 1666. The document of more than 520 pages of manuscripts included the minutes of the Royal Society from 1661-82. It had been found in a cupboard in a private house by an antiques expert there to value other items. *TIS

1847 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU

1923 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.*Wik

1928 Alexander Grothendieck (28 Mar 1928-13 November 2014) In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. Within algebraic geometry itself, his theory of schemes is used in technical work. His generalization of the classical Riemann-Roch theorem started the study of algebraic and topological K-theory. His construction of new cohomology theories has left consequences for algebraic number theory, algebraic topology, and representation theory. His creation of topos theory has appeared in set theory and logic.
One of his results is the discovery of the first arithmetic Weil cohomology theory: the ℓ-adic étale cohomology. This result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne. To this day, ℓ-adic cohomology remains a fundamental tool for number theorists, with applications to the Langlands program.
Grothendieck influenced generations of mathematicians after his departure from mathematics. His emphasis on the role of universal properties brought category theory into the mainstream as an organizing principle. His notion of abelian category is now the basic object of study in homological algebra. His conjectural theory of motives has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. *Wik

1678 Claude François Milliet Dechales (1621 in Chambéry, France - 28 March 1678 in Turin, Italy) Dechales is best remembered for Cursus seu mundus mathematicus published in Lyons in 1674, a complete course of mathematics. Topics covered in this wide ranging work included practical geometry, mechanics, statics, magnetism and optics as well as topics outwith the usual topics of mathematics such as geography, architecture, astronomy, natural philosophy and music. In 1678 he published in Lausanne his edition of Euclid, The Elements of Euclid Explained in a New but Most Easy Method: Together with the Use of Every Proposition through All Parts of the Mathematics, written in French by That Most Excellent Mathematician, F Claude Francis Milliet Dechales of the Society of Jesus. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's Elements. A second edition was published in 1683, then an edition revised by Ozanam was published in Paris in 1753. An English translation was published in London by M Gillyflower and W Freeman, the translation being by Reeve Williams. A second edition of this English translation appeared in 1696. Schaap writes, "Dechales's separate edition of Euclid, long a favourite in France and elsewhere on the Continent, never became popular in England." *SAU

1794 Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (17 September 1743 – 28 March 1794), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election. Unlike many of his contemporaries, he advocated a liberal economy, free and equal public education, constitutionalism, and equal rights for women and people of all races. His ideas and writings were said to embody the ideals of the Age of Enlightenment and rationalism, and remain influential to this day. He died a mysterious death in prison after a period of being a fugitive from French Revolutionary​ authorities.*Wik
Condorcet committed suicide by poisoning while in jail so that the republican terrorists could not take him to Paris. *VFR (The St Andrews site has the date of his death one day later.)

1840 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU He won the mathematics section prize of the Berlin Academy of Sciences for 1784 in response to a question on the foundations of the calculus. The work was published in his 1787 book Exposition elementaire des principes des calculs superieurs. It was in this book that he first introduced the "lim." (the period would soon fall out use) notation for the limit of a function. he wrote, "lim.\( \frac{\delta x}{\delta x} \). The symbol reappeared in 1821 in Cours d'Analyse by Augustin Louis Cauchy. *Florian Cajori, The History of Notations on the Calculus.

1850 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850.
Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik

1874 Peter Andreas Hansen (8 Dec 1795; 28 Mar 1874) Danish astronomer whose most important work was the improvement of the theories and tables of the orbits of the principal bodies in the solar system. At Altona observatory he assisted in measuring the arc of meridian (1821). He became the director (1825) of Seeberg observatory, which was removed to Gotha in a new observatory built for him (1857). He worked on theoretical geodesy, optics, and the theory of probability. The work in celestial mechanics for which he is best known are his theories of motion for comets, minor planets, moon and his lunar tables (1857) which were in use until 1923. He published his lunar theory in Fundamenta ("Foundation") in 1838, and Darlegung ("Explanation") in 1862-64.*TIS

1950 Ernst David Hellinger (0 Sept 1883 in Striegau, Silesia, Germany (now Strzegom, Poland) - 28 March 1950 in Chicago, Illinois, USA) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. From 1907 to 1909 he was an assistant at Göttingen and, during this time, he ".. edited Hilbert's lecture notes and Felix Klein's influential Elementarmathematik vom höheren Standpunkte aus (Berlin, 1925) which was translated into English (New York, 1932). Years later the story is told that,
Shortly after his arrival at Northwestern, one of the professors in describing Northwest's mathematics program to him remarked that in the honours course Felix Klein's 'Elementary mathematics from an advanced standpoint' was used as a text and "perhaps Hellinger was familiar with it". At this Hellinger ... replied "familiar with it, I wrote it!".

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

Monday, 27 March 2023

Politics and math, A Drama in Three Parts

  Politics and math

I received a nice e-mail from Dan MacKinnon, a Canadian math/computer teacher (who writes a nice recreational math blog)  after my blog about Karl Marx and Mathematics.  
He wrote:
I enjoyed your short post on Karl Marx's mathematics.
I first heard about Marx's mathematical work when I was a student at Dalhousie University in Halifax. While I was there, I heard a story that that back in 1970 a prof there was pushed out by the admin because he was using Marx's stuff as the basis for a course he was teaching on Real Analysis. I wish I knew the whole story - what made it more interesting was that the prof was F.W. Lawvere (pretty famous Category Theorist) and he was pushed out during the October Crisis (a terrorist incident in Montreal, 1970), which was used as a pretext to get rid of a number of radicals and undesirables in a lot of Canadian institutions.   [MY INSERT- I have found online that  “Dalhousie University in 1969 set up a group of 15 Killam-supported researchers with Lawvere at the head; but in 1971 it terminated the group. Lawvere was controversial for his political opinions, for example, his opposition to the 1970 use of the War Measures Act, and for teaching the history of mathematics without permission. (?boy they could lock me up any day?) But in 1995 Dalhousie hosted the celebration of 50 years of category theory with Lawvere and Saunders Mac Lane present.”   Not sure how long it took to be “pushed out”.]
In connection with this this story, I was told that politics and mathematics go together surprisingly often. In the early days of Category Theory, this area of mathematics was perceived as "leftist" - even Saunders Mac Lane's famous book, "Categories for the Working Mathematician" used "working" with a slightly political nuance. I was also told that while category theorists were perceived as progressives, set-theorists were perceived as reactionaries. I have no idea whether or not these supposed political distinctions among mathematicians is true today, or if they were ever true.

I got a  note from Dan McKinnon after I had written this commenting on another reader, Kevin's,  comment that, " I think the early term was "general abstract nonsense" which may still apply in my limited understanding."  Prof. McKinnon's response was, " ..my understanding is that many Category Theorists don't mind the term "abstract nonsense" and have appropriated it somewhat. While at the chalkboard and carrying out some "routine" diagram pasting they'll say "and now by the usual abstract nonsense we get the result..."

Mathematicians getting in trouble because of their political/religious views is not a new idea... as I found in this old cut from the introduction to a geometry textbook.. In this case, one might suggest that bad politics lead to good math.  

And one of my favorite math stories is  from George Gamow's autobiography and is about the Nobel Laureate, Igor Tamm.
 "Here is a story told to me by one of my friends who was at that time

a young professor of physics in Odessa. His name was Igor Tamm (Nobel
Prize laureate in Physics, 1958). Once when he arrived in a neighboring
village, at that period when Odessa was occupied by the Reds, and was
negotiating with a villager as to how many chickens he could get for
half a dozen silver spoons, the village was captured by one of the
Makhno bands, who were roaming the country, harassing the Reds. Seeing
his city clothes (or what was left of them), the capturers [sic]
brought him to the Ataman, a bearded fellow in a tall black fur
hat with machine-gun cartridge ribbons crossed on his broad chest and
a couple of hand grenades hanging on the belt.
'You son-of-a-bitch, you Communist agitator, undermining our Mother
Ukraine! The punishment is death.'
'But no,' answered Tamm, 'I am a professor at the University of Odessa
and have come here only to get some food.'
'Rubbish!' retorted the leader. 'What kind of professor are you ?'
'I teach mathematics.'
'Mathematics?' said the Ataman. 'All right! Then give me an estimate of
the error one makes by cutting off Maclaurin's series at the nth term.
Do this, and you will go free. Fail, and you will be shot!'
Tamm could not believe his ears, since this problem belongs to a rather
special branch of higher mathematics. With a shaking hand, and under
the muzzle of the gun, he managed to work out the solution and handed
it to the Ataman.
'Correct!' said the Ataman. 'Now I see that you really are a professor.
Go home!'
Who was this man? No one will ever know. If he was not killed later, he
may well be lecturing now on higher mathematics in some Ukrainian
I tell this story every other year or so to my physics students when
they cannot be bothered to remember the form of the remainder in Taylor

I imagine that as long as you do math, or teach math in a public environment, we will be subject to political influences.  I’m not sure it is always bad..... but....

On This Day in Math - March 27


Charles Minard's Napoleon's March, 

Modern science, as training the mind to an exact and impartial analysis of facts, is an education specially fitted to promote citizenship.
~Karl Pearson

The 86th day of the year; 86 is conjectured to be the largest number n such that 2n (in decimal) doesn't contain a 0. *Tanya Khovanova, Number Gossip

The 86th prime is 443, and 4433 = 86,938,307. There is no other two digit n, such that the cube of the  nth prime starts with n.  

(An unknown, by their choice, contributor supplied that he found only one one digit number, 2; [2nd prime is 3 and 3^3=27] and only one three digit number, [The 522nd prime is 3,739, its cube is 52,271,672,419 which starts with 522], and only one 4-digit number [The 3,512th prime is 32,749, its cube is 35,123,204,285,749 which starts with 3,51]  ; but both six and seven digit primes have more than one example.)

86 is the sum of four consecutive integers, 86= 20 + 21 + 22 + 23
and of four consecutive squares, 86= 32 + 42 + 52 + 62

The multiplicative persistence of a number is the number of times the iteration of finding the product of the digits takes to reach a one digit number. For 86, with persistence of three, we produce 8*6= 48, 4*8 = 32, and 3*2 = 6.... and 48+32+6 = 86. (how frequently does that occur?)

There are 86 abundant numbers(the sum of the proper divisors is greater than the  number) in a non-leap year, but 86 is not one of them. All the abundant year days are even numbers. The smallest odd abundant number is 945.

1794  Mathematical Murder Mysteries,  On this day in 1794, Nicholas de Condorcet was captured and imprisoned by his French revolutionary rivals. Two days later he was found dead in his prison cell and it is not known if he died from natural causes or whether he was murdered or took his own life.
The Marquis de Condorcet's most important work was on probability and the philosophy of mathematics. *MacTutor
In 1827, Charles Darwin, aged 18, submitted his first report of an original scientific discovery to the Plinian Society in Edinburgh, Scotland. Darwin had discovered several things about the biology of tiny marine organisms found along the Scottish coast. *TIS

1878 Christine Ladd to JJ Sylvester:

1921 On the morning of Easter Sunday, Otto Loewi awoke with the memory he had had an important dream during the night and written down some notes, but when he tried to retrieve them, the writing was hopelessly illegible. After trying to recall the dream all day, he retired early in the evening and eventually the dream came again. The dream was about a way to determine if transmissions between nerve cells was chemical or not. He immediately got out of bed and went to his laboratory. With a single experiment on a frog's heart he confirmed his own thesis of seventeen years before, that the transfer was indeed a chemical process. *Michael Brooks, Free Radicals (pg 24-25)

1936 The Associated Press relesed a story that a new 155 digit perfect number had been found by Dr. S. I. Krieger of Chicago. The number was \(2^{256}(2^{257} - 1)\) by proving the \(2^{257} -1\) was prime. This was shocking since D. H. Lehmer and M. Kraitcik had announced that the number was composite in 1922. The perfection of the number was doubted by most mathematicians, but the actual factoring to prove it was composite didn't happen until 1952 when the SWAC confirmed it was composite by finding a proper divisor. *Beiler, Recreations in the Theory of Numbers.
Lehmer in particular said he could not confirm the factors as he had determined the composite nature by " means of a machine which he constructed with the aid of a grant from the Carnegie Institution of Washington, and advice of Dr. R. C. Burt of Pasadena."  "A photo-electric number sieve," 

1958 The first national high-school mathematics competition in the U.S. was held. Since 1983 it has been known as the American High School Mathematics Examination (AHSME). [The College Mathematics Journal, 16 (1985), p. 331] *VFR

1976 20-Year Old Bill Gates Gives Opening Address to Hobbyists:
Bill Gates gives the opening address at the First Annual World Altair Computer Convention in Albuquerque, N.M. MITS, the company that developed the Altair, had set up shop in the southwestern city to develop its kit computer, which was a hit among hobbyists after it graced the cover of "Popular Mechanics" magazine. Gates, then a 20-year-old erstwhile Harvard student, had helped develop the form of BASIC sold with the Altair. *CHM

1781 Charles Joseph Minard (27 Mar 1781; 24 Oct 1870 at age 89) French civil engineer who made significant contributions to the graphical representations of data. His best-known work, Carte figurative des pertes successives en hommes de l'Armee Français dans la campagne de Russe 1812-1813, dramatically displays the number of Napoleon's soldiers by the width of an ever-reducing band drawn across a map from France to Moscow. At its origin, a wide band shows 442,000 soldiers left France, narrowing across several hundred miles to 100,000 men reaching Moscow. With a parallel temperature graph displaying deadly frigid Russian winter temperatures along the way, the band shrinks during the retreat to a pathetic thin trickle of 10,000 survivors returning to their homeland. *TIS

1824 Johann Wilhelm Hittorf (27 Mar 1824, 28 Nov 1914) German physicist who was a pioneer in electrochemical research. His early investigations were on the allotropes (different physical forms) of phosphorus and selenium. He was the first to compute the electricity- carrying capacity of charged atoms and molecules (ions), an important factor in understanding electrochemical reactions. He investigated the migration of ions during electrolysis (1853-59), developed expressions for and measured transport numbers. In 1869, he published his laws governing the migration of ions. For his studies of electrical phenomena in rarefied gases, the Hittorf tube has been named for him. Hittorf determined a number of properties of cathode rays, including (before Crookes) the deflection of the rays by a magnet. *TIS

1845 Wilhelm Conrad Röntgen (27 Mar 1845 - 10 Feb 1923 at age 77) was a German physicist who discovered the highly penetrating form of radiation that became known as X-rays on 8 Nov 1895. He received the first Nobel Prize for Physics (1901), “in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him.” This high-energy radiation, though first called Röntgen rays, became known as X-rays. His discovery initiated revolutionary improvements in making medical diagnoses and enabled many new advances in modern physics. *TIS "In 1901 he became the first physicist to receive a Nobel prize." *VFR

1855 Sir Alfred Ewing (27 Mar 1855, 7 Jan 1935) was a Scottish physicist who discovered and named hysteresis (1881), the resistance of magnetic materials to change in magnetic force. Ewing was born and educated in Dundee and studied engineering on a scholarship at Edinburgh University. He helped Sir William Thomson, later Lord Kelvin in a cable laying project. In 1878 he became professor of Mechanical Engineering and Physics at Tokyo University, where he devised instruments for measuring earthquakes. In 1903 he moved to the Admiralty as head of education and training, where during WW I, he and his staff took on the task of deciphering coded messages. *TIS

1857 Karl Pearson (27 Mar 1857; 27 Apr 1936 at age 79) English mathematician who was one of the founders of modern statistics. His lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS

1897 Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser. *Wik

1905 László Kalmár (27 March 1905 in Edde (N of Kaposvar), Hungary - 2 Aug 1976 in Mátraháza, Hungary) worked on mathematical logic and theoretical computer science. He was ackowledged as the leader of Hungarian mathematical logic. *SAU

1928 Alexander Grothendieck In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. *VFR


1850 Wilhelm Beer (4 Jan 1797, 27 Mar 1850 at age 53) German banker and amateur astronomer who owned a fine Fraunhofer refractor which he used in his own a private observatory. He worked jointly with Johann Heinrich von Mädler, to produce the first large-scale moon map to be based on precise micrometric measurements. Their four-year effort was published as Mappa Selenographica (1836). This fine lithographed map provided the most complete details of the Moon's surface in the first half of the 19th century. It was the first lunar map divided in quadrants, and recorded the Moon's face in great detail detail. It was drawn to a scale of scale of just over 38 inches to the moon's diameter. Mädler originated a convention for naming minor craters with Roman letters appended to the name of the nearest large crater (ex. Egede A,B, and C).

1888 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik

1923 Sir James Dewar (20 Sep 1842; 27 Mar 1923) British chemist and physicist. Blurring the line between physics and chemistry, he advanced the research frontier in several fields at the turn of the century, and gave dazzling lectures. His study of low-temperature phenomena entailed making an insulating double-walled flask of his own design by creating a vacuum between the two silvered layers of steel or glass (1892). This Dewar flask that has been named for him led to the domestic Thermos bottle. In June 1897, The Scientific American reported that "Dewar has just succeeded in liquefying fluorine gas at a temperature of -185 degrees C." He obtained liquid hydrogen in 1898. Dewar also invented cordite, the first smokeless powder.*TIS

1925 Carl Gottfried Neumann,(7 May 1832 in Königsberg, Germany (now Kaliningrad, Russia) - 27 March 1925 in Leipzig, Germany) He worked on a wide range of topics in applied mathematics such as mathematical physics, potential theory and electrodynamics. He also made important pure mathematical contributions. He studied the order of connectivity of Riemann surfaces.
During the 1860s Neumann wrote papers on the Dirichlet principle and the 'logarithmic potential', a term he coined. In 1890 Émile Picard used Neumann's results to develop his method of successive approximation which he used to give existence proofs for the solutions of partial differential equations.*SAU

1929 Samuil Shatunovsky (25 March 1859 – 27 March 1929) was a Russian mathematician. focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry. Independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis.[1] However, most of his activity was devoted to teaching at Odessa University and writing associated books and study materials.*Wik

1972  Maurits Cornelius Escher (17 June 1898 in Leeuwarden, Netherlands - 27 March 1972 in Laren, Netherlands) an artist whose works have included a considerable mathematical content. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *Wik

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

Sunday, 26 March 2023

On This Day in Math - March 26


“Have you seen the world go around?"

Every human activity, good or bad, except mathematics, must come to an end.
~Paul Erdos

The 85th day of the year; 85 is the largest number for which the sum of 12 + 22+32+42+...+n2= 1+2+3+4+.... +M for some n,M, can you find that M?   85 is the largest such n, with a total of 208,335; but can you find some solutions n,M that are smaller? (Reminder for students, the sums of first n consecutive squares are called pyramidal numbers, the sums of the first n integers are called triangular numbers.)

and a bonus I found at the Prime Curios web site, (8511 - 85)/11 ± 1 are twin primes. (too cool)

85 is the second smallest n such that n, n+1 and n+2 are products of two primes. (called pronic, or oblong numbers) *Don S McDonald

85 is the third, and last, Hoax number of the year.   Yesterday was the second.  A Hoax number is a number with the sum of it's digits equal to  the sum the digits of it's unique prime factors.

There are 85 five-digit primes that begin with 85.

And 85 is the sum of consecutive integers, and the difference of their squares  \(42+43= 43^2 - 42^2 = 85\), and can be expressed as the sum of two squares in two different ways, 92+ 2 2 = 72 + 62 =85


127  On this day in AD 127, Ptolemy made the first astonomical observation from Alexandria that we can date accurately. He made his last observation on 2 February AD 141. 
Ptolemy was the most influential of Greek astronomers and geographers of his time. He propounded the geocentric theory of the solar system that prevailed for 1400 years.*MacTutor

1619 Descartes reported (to Beekman) his first glimpse of “an entirely new science, by which all problems that can be posed, concerning any kind of quantity, continuous or discrete, can be generally solved”  which was to become his analytic geometry (published 1637).
Descartes relies on the “single motions” of his “new types of compasses (often referred to by commentators as “proportional compasses”), which [he says] are no less exact and geometrical…than the common ones used to draw circles” in order to mark out a new class of problems that have legitimate geometrical solutions. He would apply them to to the problems of (1) dividing a given angle into any number of equal parts, (2) constructing the roots of three types of cubic equations, and (3) describing a conic section.
*Stanford Encyclopedia of Philosophy

1760 Guillaume le Gentil sailed from France planning to view the transit of Venus the following year from the east coast of India. Monsoons blew his ship off course, and on the day of the transit, he was becalmed in the Indian Ocean, unable to make any useful observations. Determined to redeem his expedition he books passage to India and builds an observatory to await the 1769 transit in Pondecherry. "The sky remained marvelously clear throughout May, only to cloud over on June 4, the morning of the transit, then clear again as soon as the transit was over."
His ordeal of a decade was not yet over. Stricken with dysentery he had to stay nine months more in India, and then booked passage on a Spanish warship. The ship lost its mast in a hurricane off the Cape of Good Hope, and finally limped into Cadiz. Le Gentil set out across the Pyrenees and returned to Paris after a total absence of eleven years, six months, and thirteen days, only to find that he had been presumed dead and his estate divided among his heirs. *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie, The Renaissance Mathematicus, has a more detailed, and perhaps somewhat more accurate, version of Guillame's great adventure. See it here

1851 French Science reporter Terrien wrote in “le National, “Have you seen the world go around? Would you like to see it rotate? Go to the Parthenon on Thursday…the experiment devised by M. Leon Foucault is carried out there, in the presence of the public, under the finest conditions in the world.” *Amir D Aczel, Pendulum, pg 152
Foucault’s most famous pendulum . He suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. *Wik  

Thony Christie has a wonderful blog about this event and the earlier attempts at the science efforts to prove diurnal rotation, The emergence of modern astronomy - a complex mosaic: Part LI  
In 1859, Edmond Modeste Lescarbault, a French medical doctor and amateur astronomer, reported sighting a new planet in an orbit inside that of Mercury which he named Vulcan. He had seen a round black spot on the Sun with a transit time across the solar disk 4 hours 30 minutes. He sent this information and his calculations on the planet's movements to Jean LeVerrier, France's most famous astronomer. Le Verrier had already noticed that Mercury had deviated from its orbit. A gravitational pull from Vulcan would fit in nicely with what he was looking for. 
In 1860, Le Verrier announced the discovery of Vulcan by to a meeting of the Académie des Sciences in Paris.A number of reputable investigators became involved in the search for Vulcan, but no such planet was ever found, and the peculiarities in Mercury's orbit have now been explained by Albert Einstein's theory of general relativity. *Wik
However, it was not consistently seen again and it is now believed to have been a "rogue asteroid" making a one-time pass close to the sun.*TIS (It was just pointed out to me by @Astroguyz,David Dickinson, that Leonard Nimoy, the actor who is best remembered for his role as the half-Vulcan character of Dr. Spock in the Star Trek series and films was also born on this day in 1931.)

1900 the Roentgen Society of the United States was organised a meeting of doctors from nine states held in Dr. Herber Robarts' office in St. Louis. Dr. Robarts was founder and editor of the American X-Ray Journal, and had been active in radiology since exposing his first X-ray plates in Feb 1896. Robarts was elected as president of the new society and and Dr. J. Rudis-Jicinsky as secretary. They arranged to hold the first annual meeting at the Grand Central Palace in New York City on 13-14 Dec 1900. In 1901, it was renamed as the Roentgen Society of America to include Canadians. It was reorganized at the next annual meeting on 10-11 Dec 1902 as the American Roentgen Ray Society.*TIS

 The 200" Hale mirror was shipped, it had been cast in 1934. Still a great video: *David Dickinson ‏@Astroguyz
The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948 - 1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year. *Caltech Astronomy

1985 Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron.
Alexander's Star was invented by Adam Alexander, an American mathematician, in 1982. It was patented on 26 March 1985, with US patent number 4,506,891, and sold by the Ideal Toy Company. It came in two varieties: painted surfaces or stickers. Since the design of the puzzle practically forces the stickers to peel with continual use, the painted variety is likely a later edition.

1994, A picture was released showing the first moon discovered to be in orbit around an asteroid. The potato-shaped asteroid Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach to the asteroid on 28 Aug 1993. Ida appears to be about about 36 miles long and 14 miles wide. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. The tiny moon is about one mile (1.5-km) across. The names are derived from the Dactyli, a group of mythological beings who lived on Mount Ida, where the infant Zeus was hidden (and raised, in some accounts) by the nymph Ida and protected by the Dactyli. 
This image was obtained when the Galileo spacecraft flew past 243 Ida on August 28, 1993, with the closest approach of 2,410 kilometers (1,500 mi), and was released on March 26, 1994. 

2010 Crocheting Adventures with Hyperbolic Planes by Dr Daina Taimina has won the 2009 Diagram Prize, having received the majority of the public vote for the oddest titled book of the year at thebookseller.com. The first award was given in 1978 for Proceedings of the Second International Workshop on Nude Mice

2011 Dr. Harry Wesley Coover Jr. died on this day He was the inventor of Eastman 910, commonly known as Super Glue.


1516 Conrad Gessner (Konrad Gessner, Conrad Geßner, Conrad von Gesner, Conradus Gesnerus, Conrad Gesner; 26 March 1516 – 13 December 1565) was a Swiss naturalist and bibliographer. His five-volume Historiae animalium (1551–1558) is considered the beginning of modern zoology, and the flowering plant genus Gesneria (Gesneriaceae) is named after him. He is denoted by the author abbreviation Gesner when citing a botanical name. Gessner in 1551 was the first to describe adipose tissue; and in 1565 the first to document the pencil. *Wik See more at The Renaissance Mathematicus blog.

1753 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS

1773 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu) *TIS Nathaniel Bowditch acquired his knowledge of mathematics through self-study while apprenticed to a ship’s chandler. He is most noted for his translation of Laplace’s M´ecanique c´eleste. [DSB 2, 368] *VFR

1789 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS

1803 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

1821 Ernst Engel (26 Mar 1821, 8 Dec 1896) German statistician, the head of the Prussian Statistical Bureau (1860-82), known for the "Engel curve," or Engel's law, which states that the proportion of expenditure on food will fall as income rises, i.e. food is a necessary good. Engel's law applies to goods as a whole. Demand for food, clothing and shelter - and for most manufactured products - doesn't keep pace with increases in incomes. Engel curves are useful for separating the effect of income on demand from the effects of changes in relative prices. Engel also examined the relationship between the size of the Prussian rye harvest and the average price of rye over a number of years prior to 1860, probably the first empirical study of the relationship between price and supply. *TIS

1848 Konstantin Alekseevich Andreev (26 March 1848 in Moscow, Russia - 29 Oct 1921 Near Sevastopol, Crimea) Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions. *SAU

1862 Philbert Maurice d'Ocagne (26 March 1862 in Paris, France - 23 Sept 1938 in Le Havre, France) In 1891 he began publishing papers on nomography, the topic for which he is most remembered today. Nomography consists in the construction of graduated graphic tables, nomograms, or charts, representing formulas or equations to be solved, the solutions of which were provided by inspection of the tables. An advertisement for a colloquium at the Edinburgh Mathematical Society gave the following description of d'Ocagne's course:
It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired.
 Nomographs are still used in wide areas of science and technology. The book below is an excellent coverage of the history and modern usage.

1875 Max Abraham (26 Mar 1875, 16 Nov 1922) German physicist whose life work was almost all related to Maxwell's theory. The text he wrote was the standard work on electrodynamics in Germany for a long time. Throughout his life, he remained strongly opposed to Einstein's Theory of Relativity, objecting to its postulates which he felt were contrary to classical common sense. He further held that the experimental evidence did not support that theory. In 1902, he had developed a theory of the electron in which he held that an electron was a perfectly rigid sphere with a charge distributed evenly over its surface. He also believed in the ether theory, thought that future astronomical data would validate it, and thus relativity was not in fact a good description of the real world. *TIS

1902 Marion Gray (26 March 1902, 16 Sept 1979) graduated from Edinburgh University and then went to Bryn Mawr College in the USA. She completed her doctorate there and returned to posts at Edinburgh and Imperial College London. She returned to the USA and worked for AT&T for the rest of her career. The Gray graph is named after her.*SAU The Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive *Wik

1903 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1908 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.
He was appointed at UCLA in 1950 and worked there until retirement.
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

1913 Paul Erdös (26 Mar 1913; 20 Sep 1996 at age 83) Hungarian mathematician, who was one of the century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. At age 20, he discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and moved to the USA by the late 1930s when his Jewish origins made a return to Hungary impossible. Affected by McCarthyism in the 1950s, he spent much of the next ten years in Israel. Writing his many hundreds of papers made him one of history's most prolific mathematicians. *TIS His forte is posing and solving problems. One of his customs is to offer cash prizes for problems he poses. These awards range from $5 to $10,000 depending on how difficult he judges them to be. Erdos has written over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927. [Gallian, Contemporary Abstract Algebra, p 378]*VFR
McGill University Professor Willy Moser, a friend and collaborator of Erdos, tells of the "trial" of hosting Erdos. Once when Erdos was staying with him, Moser set up five dinners for him with five of erdos' old friends. Moser's wife pointed out that after the many times he had visited these homes and never brought a gift, perhaps Moser should remind him to bring candy or flowers. When he suggested the idea to Erdos, he thought it was a great idea and asked Moser, "Would you pick me up five boxes of chocolates?"  
Erdos is the origin of the coordinates for measuring mathematicians.

1922 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

1938 Sir Anthony James (Tony) Leggett (26 March 1938, ), has been a Professor of Physics at the University of Illinois at Urbana-Champaign since 1983.
Professor Leggett is widely recognized as a world leader in the theory of low-temperature physics, and his pioneering work on superfluidity was recognized by the 2003 Nobel Prize in Physics. He has shaped the theoretical understanding of normal and superfluid helium liquids and strongly coupled superfluids. He set directions for research in the quantum physics of macroscopic dissipative systems and use of condensed systems to test the foundations of quantum mechanics. *Wik


1609 John Dee (13 July 1527– *SAU gives 26 March 1609 in Mortlake, London, England) was an English mathematician, astronomer, astrologer, occultist, navigator, imperialist[4] and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.
Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".
In his lifetime Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional adviser and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.*Wik
I have Woolley's book, and enjoyed it.

1797 James Hutton (3 June 1726 in Edinburgh, Scotland - 26 March 1797 in Edinburgh, Scotland) geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

1748 Sir Charles Brian Blagden FRS (17 April 1748 – 26 March 1820) was a British physician and scientist. He served as a medical officer in the Army (1776–1780) during the Revolutionary War, and later held the position of Secretary of the Royal Society (1784–1797).
Blagden experimented on himself to study human ability to withstand high temperatures. In his report to the Royal Society in 1775, he was first to recognize the role of perspiration in thermoregulation.
Blagden's experiments on how dissolved substances like salt affected the freezing point of water led to the discovery that the freezing point of a solution decreases in direct proportion to the concentration of the solution, now called Blagden's Law Blagden won the Copley Medal in 1788 and was knighted in 1792. In 1783, Blagden, then assistant to Henry Cavendish, visited Antoine Lavoisier in Paris and described how Cavendish had created water by burning "inflammable air". Lavoisier's dissatisfaction with the Cavendish's "dephlogistinization" theory led him to the concept of a chemical reaction, which he reported to the Royal Academy of Sciences on 24 June 1783, effectively founding modern chemistry. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1789.
He died in Arcueil, France in 1820, and was buried at Père Lachaise Cemetery in Paris. *Wik

1914 John S Mackay (22 Oct 1843 in Auchencairn near Kirkudbright, Kirkcudbrightshire, Scotland - 26 March 1914 in Edinburgh, Scotland)graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU

1933 József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. *Wik

1974 Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II as part of the Manhattan Project. The Franck–Condon principle and the Slater–Condon rules are named after him.
He was the director of the National Bureau of Standards (now NIST) from 1945 to 1951. In 1946, Condon was president of the American Physical Society, and in 1953 was president of the American Association for the Advancement of Science.
During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science.
Condon became widely known in 1968 as principal author of the Condon Report, an official review funded by the United States Air Force that concluded that unidentified flying objects (UFOs) have prosaic explanations. The lunar crater Condon is named for him.
Years later, Carl Sagan reported how Condon described one encounter with a loyalty review board. A board member stated his concern: "Dr. Condon, it says here that you have been at the forefront of a revolutionary movement in physics called...quantum mechanics. It strikes this hearing that if you could be at the forefront of one revolutionary movement...you could be at the forefront of another". Condon said he replied: "I believe in Archimedes' Principle, formulated in the third century B.C. I believe in Kepler's laws of planetary motion, discovered in the seventeenth century. I believe in Newton's laws...." and continued with a catalog of scientists from earlier centuries, including the Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.[35] He once said privately: "I join every organization that seems to have noble goals. I don't ask whether it contains Communists".*Wik

1996 Hewlett-Packard Co-Founder David Packard Dies:
Hewlett-Packard Company co-founder David Packard dies after several weeks of illness. With fellow Stanford graduate Bill Hewlett, Packard founded Hewlett-Packard in a Palo Alto garage in 1938, spurring the development of what has come to be known as Silicon Valley. The company's first product was an oscillator, eight of which Disney used in its groundbreaking film ""Fantasia."" Since then, HP has made a name in personal computers, laser printers, calculators, accessories, and test equipment.*CHM

1966 Anna Johnson Pell Wheeler (5 May 1883 in Calliope (now Hawarden), Iowa, USA - 26 March 1966 in Bryn Mawr, Pennsylvania, USA) In 1899 she entered the University of South Dakota where she showed great promise in mathematics. The professor of mathematics, Alexander Pell, recognised her talents and helped persuade Anna Johnson that she should follow a career in mathematics. She received an A.B. degree in 1903.
After winning a scholarship to study for her master's degrees at the University of Iowa, she was awarded the degree for a thesis The extension of Galois theory to linear differential equations in 1904. A second master's degree from Radcliffe was awarded in 1905 and she remained there to study under Bôcher and Osgood.
Anna Johnson was awarded the Alice Freeman Palmer Fellowship from Wellesley College to study for a year at Göttingen University. There she attended lectures by Hilbert, Klein, Minkowski, Herglotz and Schwarzschild. She worked for her doctorate at Göttingen. While there Alexander Pell, her former mathematics professor came to Göttingen so that they could marry.
After returning to the United States, where her husband was by now Dean of Engineering, she taught courses in the theory of functions and differential equations. In 1908 Anna Pell returned to Göttingen where she completed the work for her doctorate but, after a disagreement with Hilbert, she returned to Chicago, where her husband was now on the university staff, without the degree being awarded.
At Chicago she became a student of Eliakim Moore and received her Ph.D. in 1909, her thesis Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations being the one written originally at Göttingen. From 1911 Anna Pell taught at Mount Holyoke College and then at Bryn Mawr from 1918. Anna Pell's husband Alexander, who was 25 years older than she was, died in 1920. In 1924 Anna Pell became head of mathematics when Scott retired, becoming a full professor in 1925.
After a short second marriage to Arthur Wheeler, during which time they lived at Princeton and she taught only part-time, her second husband died in 1932. After this Anna Wheeler returned to full time work at Bryn Mawr where Emmy Noether joined her in 1933. However Emmy Noether died in 1935. The period from 1920 until 1935 certainly must have been one with much unhappiness for Anna Wheeler since during those years her father, mother, two husbands and close friend and colleague Emmy Noether died. Anna Wheeler remained at Bryn Mawr until her retirement in 1948.
The direction of Anna Wheeler's work was much influenced by Hilbert. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.
Perhaps the most important honour she received was becoming the first woman to give the Colloquium Lectures at the American Mathematical Society meetings in 1927.

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 & Campbel

Saturday, 25 March 2023

Things You May Not Know About Four


The English number four comes to us from the Gothic fidwor which is probably from the same proto root that gave the Latin quattuor. The Greek root for four which still shows up in many mathematical names is tetra. The Pythagoreans had a prayer addressed to four, or at least to fourfoldness, "O holy, holy tetraktys.." which was thought to represent the four elelments: fire, water, air, and earth.

Bill Bryson, in Mother Tounge (pgs 113,114) explains the loss of the "u" in forty. Why is there no "u" in forty?
Four, fourteen, and fourth all have it. So did fourty in the writings of Chaucer. In fact, until the 17th Century when, as Bryson says, "But then, as if by universal decree, it just quietly vanished. No one seems to have remarked on it at the time."

The way four was written has changed over time more than many numbers. Wikipedia's page on the number four shows the following progression for the development of our current 4.

Karl Menninger in Number Words and Number Symbols points out that several of the shapes were used at the same time, and gives a photo (Fig. 260) from the Bamberger Rechembuch of 1483 in which two of the forms are used in the same example of a multiplication problem. He also has this graphic showing three different variants of a four in succesive years by Durer.

The Wikipedia page also gives several interesting tidbits about the uniqueness of four. Among them are the following; "Four is the only English number that, when spelled out, has the number of letters that it names", "Four is the first positive non-Fibonacci number", and "Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y^2 - z^2. Four is also the smallest composite number, and a solution to Brocard's Problem (For what values of n is n! + 1 a perfect square) since 4! + 1 = 5^2.

The fact that the word four has as many letters as the number it names was extended by Martin Gardner into an observation about all numbers. Take any number, use the number of letters in the name to get a new number. Repeat with the new number and eventually, it seems (I have not seen a proof, nor have I ever found an exception) you come to four. For example if we start with thirty, it has 6 letters, so we take six, which has 3 letters, so we write three, which has 5 letters, and at last we come to five, which has four letters.

Barney Hughes posted a note about the use of four as a base for counting. "Ed's remark about base-four would have me note that several tribes of California Indians, notably those living in and around Ventura, counted by fours. A complete list of their words for the numbers, 1 to 64, is in Old Mission Library-Archives, Santa Barbara, a holograph by an early nineteenth century missionary. (I have seen it.) While I am at it: there were some twenty linguistic families in California and they used 4,5, 8, 10, and 20 for their bases, all depending on where they lived rather than on the language or dialect they spoke."