## Monday, 19 February 2018

### On This Day in Math - February 19

 Copernicus statue at Olsztyn Castle

It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
~Karl Weierstrass

The 50th day of the year; 50 is the smallest number that can be written as the sum of two squares in two distinct ways 50 = 49 + 1 = 25 + 25. *Tanya Khovanova, Number Gossip (What is the next, or what is the smallest number that can be written as the sum of two squares in three distinct ways? For solution from Ben Vitale, see bottom of post)

50 is also expressible as the sum of distinct primes in two ways so that all consecutive primes 2-23 are used :50 = 2 + 5 + 7 + 17 + 19 = 3 + 11 + 13 + 23.

The number 50 is somewhat responsible for the area of number theory about partitions. In 1740 Philip Naudé the younger (1684-1747) wrote Euler from Berlin to ask “how many ways can the number 50 be written as a sum of seven different positive integers?” Euler would give the answer, 522, within a few days but would return to the problem of various types of partitions throughout the rest of his life.

EVENTS
1512 The French invaded Brescia, in Northern Italy, during the War of the League of Cambrai. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, a French soldier sliced Niccolò's jaw and palate with a saber. This made it impossible for Niccolò to speak normally, prompting the nickname "Tartaglia" Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano over the solution of cubics. (see this blog for the unfortunate common mistake about Tartaglia's family name.)

1549 Osiander wrote of Michael Stifel: “He has devised new numbers for the alphabet, namely the triangular numbers, and his fantasies are more absurd than before.” *VFR

1600 The Inquisition brought Giordano Bruno to the Campo dei Fiori in Rome’s center where they chained him to an iron stake and burned him alive for his beliefs that the earth rotated on its axis. *Amir Aczel, Pendulum, pg 9 (This date seems wrong. Thony Christie noted that " Bruno was executed on 17th Feb and not for his cosmology but for his heretical theology." Thanks... several other sources agree with Feb 17th date))

1616 On February 19, 1616, the Inquisition asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe after Nicollo Lorin had accused Galileo of Heretical remarks in a letter to his former student, Benedetto Castelli. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders.*Wik

1671/72 Newton’s ﬁrst publication appears as a letter in the Philosophical Transactions. It deals with his new theory of light, showing that a prism separates white light into its component colors. Huygens, Hooke and others objected so strongly that he vowed not to publish again. Fortunately that vow was not kept. *VFR The full text of that publication is here.

In 1855, M. Le Verrier presented the first weather map at the French Academy of Sciences.*TIS A storm on November 14, 1854 destroyed the French warship Henri IV and damaged other British and French vessels on the Black Sea involved in the Crimean War. A report from the state-supported Paris Observatory indicated that barometric readings showed that the storm had passed across Europe in about four days. Urban Leverrier, director of the Paris Observatory, concluded that had there been a telegraph line between Vienna and the Crimea, the British and French fleets could have received warnings. An earlier map is mentioned, but not shown in a letter dated Dec 1, 1816 in Gilbert's Annalen der Physik from Heinrich Wilhelm Brandes *Report of The International Meterological Congress, 1893

1876 Sylvester began his duties at the newly founded Johns Hopkins, *TIS

1901 Messages from Mars reported in Collier's Magazine. While conducting experiments on high-frequency electrical transmission in 1899 in his Colorado Springs, Colorado laboratory, Nikola Tesla picked up cosmic radio waves on his instruments. Announcing this development, he publicly opined that the messages came from outer space, possibly from inhabitants of Mars. In a Collier’s Weekly article dated February 19, 1901, Tesla wrote, “At the present stage of progress, there would be no insurmountable obstacle in constructing a machine capable of conveying a message to Mars … What a tremendous stir this would make in the world! How soon will it come?” Later discoveries revealed that Tesla had actually picked up common radio waves emitted by interstellar gas clouds. *History. Com

1946 Alan Turing Presents the “Proposal for the Development in the Mathematics Division of an Automatic Computing Engine (ACE).”
This research proposal was presented to a meeting of the Executive Committee of the National Physical Laboratory (NPL) in Teddington, England, and approved at a second meeting held a month later.
Turing based this research on von Neumann’s First Draft of a Report on the EDVAC. He had studied it in summer 1945 when he was recruited by J.R. Womersley to join the staff of the NPL. *CHM

1971 The first warrant is issued to search a computer storage. Although the requirements for obtaining such a warrant were similar to those for searching a home, they ushered in a new era that would lead to increasingly sophisticated methods of encryption to hide computer files from law enforcement agents.*CHM

1972 The New Yorker published an article by A. Adler on “Mathematics and Creativity” that was not well received by the mathematical community. See The [old] Mathematical Intelligencer, no. 2. *VFR An abstract is here

BIRTHS
1473 Nicolaus Copernicus Polish astronomer who proposed that the planets have the Sun as the fixed point to which their motions are to be referred; that the Earth is a planet which, besides orbiting the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes *TIS
An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR
Over 450 years after his death, Copernicus was reburied in the cathedral at Frombork on Poland’s Baltic coast. The astronomer whose ideas were once declared heresy by the Vatican—was reburied with full religious honors.

1837 Aleksandr Nikolayevich Korkin (3 March [O.S. 19 February] 1837–September 1, 1908, all New Style) was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School*Wik

1863 Axel Thue(19 Feb 1863 in Tönsberg, Norway - 7 March 1922 in Oslo, Norway) Thue studied Diophantine equations, showing that, for example, y3 - 2x2 = 1 cannot be satisfied by infinitely many pairs of integers. Edmund Landau, in 1922, described Thue's work as, ".. the most important discovery in elementary number theory that I know. "
Thue's Theorem states, " If f (x, y) is a homogeneous polynomial with integer coefficients, irreducible in the rationals and of degree > 2 and c is a non-zero integer then f (x, y) = c has only a finite number of integer solutions." *SAU

1866 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

1889 Sir Ernest Marsden (19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

DEATHS
1553 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibis and made a favourable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read.[5] In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik

1622 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

1799 Jean-Charles Borda, (4 May 1733 in Dax, France - 19 Feb 1799 in Paris, France) 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 (The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.The Borda count is a popular method for granting awards for sports in the United States, and is used in determining the Most Valuable Player in Major League Baseball, and by the Associated Press and United Press International to rank teams in NCAA sports, to determine the winner of the Heisman Trophy.) [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

1897 Karl (Theodor Wilhelm) Weierstrass (31 Oct 1815, 19 Feb 1897 at age 81) was a German mathematician who is known as the "father of modern analysis" for his rigour in analysis led to the modern theory of functions, and considered one of the greatest mathematics teachers of all-time. He was doing mathematical research while a secondary school teacher, when in 1854, he published a paper on Abelian functions in the famous Crelle Journal. The paper so impressed the mathematical community that he shortly received an honorary doctorate and by 1856, he had a University appointment in Berlin. In 1871, he demonstrated that there exist continuous functions in an interval which have no derivatives nowhere in the interval. He also did outstanding work on complex variables.*TIS Weierstrass died peacefully at the age of 82 at his home in Berlin after a long illness culminating in inﬂuenz. It is reported that his last wish was that the priest say nothing in his praise at the funeral, but to restrict the services to the customary prayers. *VFR

1908 Paul Matthieu Hermann Laurent (2 Sept 1841 in Echternach, Luxembourg - 19 Feb 1908 in Paris, France) He developed statistical formulas for the calculation of actuarial tables and studied heat conduction. *VFR

1916 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

1929 Joseph Valentin Boussinesq (13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
In 1897 he published Théorie de l' écoulement tourbillonnant et tumultueux des liquides, a work that greatly contributed to the study of turbulence and hydrodynamics.*Wik

1938 Edmund Georg Hermann Landau (14 Feb 1877 in Berlin, Germany - 19 Feb 1938 in Berlin, Germany) Although famous as a number theorist, he is best known for his textbooks which are written in an austere deﬁnition-theorem-proof style. His Grundlagen der Analysis is an excellent treatment of the development of our number systems from the Peano postualates. Reading this book is a good way to learn mathematical German. But if you are lazy, it has been translated into English. *VFR Landau gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.*SAU Legend has it that at the age of three, when is mother forgot her umbrella in a carriage, he replied, "It was number 354," and the umbrella was quickly re-acquired.

1940 Otto Toeplitz died in Jerusalem, after having left Germany in the Spring of 1939. He made lasting contributions to the theory of integral equations and the theory of functions of inﬁnitely many variables. Today he is best remembered for two popular works which have been translated into English: The Enjoyment of Mathematics (original 1930, 1957), and The Calculus: A Genetic Approach (ﬁrst published 1949; English 1963). These are some of the most successful attempts to bring higher mathematics to the general public. The later shows his deep interest in the history of mathematics; every calculus teacher could proﬁt from reading it. *VFR

1990 Otto Neugebauer, historian of ancient and medieval mathematics and astronomy. *VFR
(May 26, 1899 – February 19, 1990) He was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages. By studying clay tablets he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." *Wik

@BenVitale: smallest number w/ 3 representations: $325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2+ 15^2$

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