## Saturday 22 February 2020

### On This Day in Math - February 22

 Illustration from "On the forms of plane quartics", by Ruth Gentry

Suppose a contradiction were to be found in the axioms of set theory. Do you seriously believe that a bridge would fall down?
~Frank P. Ramsey

The 53rd day of the year; the month and day are both prime a total of 53 times in every leap year, but not today.

If you reverse the digits of 53 you get its hexadecimal representation; no other two digit number has this quality.

The sum of the first 53 primes is 5830, which is divisible by 53. It is the last year day for which n divides the sum of the first n primes.

53 is the smallest prime p such that 1p1 (ie, 1531) , 3p3, 7p7 and 9p9 are all prime.(Can you find the 2nd smallest?)

EVENTS

1535 On this day the contestants, Tartaglia and Fiore, were to deliver the answer to the 30 questions they were asking of their opponent to a notary. I assume the contest went on the same day, and it may not have taken long. Thony Christie at the Renaissance Mathematicus described it this way, "Tartaglia sat down and almost instantly gave the correct answers to Fiore’s entire list, who was completely unable to solve a single one of Tartaglia’s questions. This whitewash made Tartaglia a star amongst the reckoning masters." In Mario Livio's "The Equation That Couldn't be Solved" he says that Tartaglia finished all 30 of Fiore's questions in less than two hours. All 30 of Fiore's questions were of the form ax3 + bx = c, and Tartaglia had discovered a general solution for that type of cubic only eight days before the contest.

1630 Popcorn was introduced to the English colonists at their ﬁrst Thanksgiving dinner on this date (admit it, you thought it was in November) by Quadequina, brother of Massasoit. As his contribution to the dinner he offered a deerskin bag containing several bushels of “popped” corn. *Kane, Famous First Facts, p. 481 Popcorn is a type of corn with smaller kernels than regular corn, and when heated over a flame, it "pops" into the snack we know it as today. Native Americans were growing it for more than a thousand years before the arrival of European explorers. In 1964, scientists digging in southern Mexico found a small cob of popcorn discovered to be 7,000 years old. (don't you wonder if they tried to pop some of it?) Today, the United States grows nearly all of the world's popcorn. *TIS

1805 Francois Arago picked to head the completion of the measurement of the Paris Meridian. He was a 19yr old student at the Ecole Polytechnique. He was nominated by his professor, Dennis Poisson and appointed on Feb 2, 1805 to finish the work began by Mechain and Delambre. He would leave for Spain on Sept 3 of the following year *Amir D Aczel, Pendulum, pg 75-78

1876 The Johns Hopkins University Founded... commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed \$7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*Wik

1877 J. J. Sylvester, at a commencement address at Johns Hopkins, gave his view on the relation between teaching and research: “An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking ﬁsh, and it is certain that the more anyone gives himself up to the study of oratorial effect, the less he will ﬁnd himself in a fit state of mind to mathematicize.” See Midonick, The Treasury of Mathematics, p. 768. *VFR

1880 American Poet Sidney Lanier (1842–1922) read his “Ode to The Johns Hopkins University”, which indicated the original faculty was “Led by the soaring-genius’d Sylvester.” [Osiris, 1(1936), p. 112] *VFR

1926 At its fiftieth anniversary celebration, Johns Hopkins University awarded a long overdue doctorate to Christine Ladd-Franklin. Now a sprightly 79, she attended the ceremonies to collect her degree 44 years late. [New York Times, 23 February 1926, p. 12. Thanks to Judy Green. Also see Rossiter, Women Scientists in America, p. 46.] *VFR She applied to Johns Hopkins University as a graduate student, a university not traditionally open to women. A fellow contributor to the publication, Educational Times, who was familiar with her work, James J. Sylvester, noticed her name on a list of applicants and urged the university to admit her. In 1878, she was accepted on the terms that she would only attend his lectures.

1965 Rwanda, in central Africa, issued a series of stamps honoring the National University of Rwanda at Butare. Included in the picture is a radical sign, in fact, this is the only stamp which includes a radical sign, a symbol which originated in Germany. For the complicated history of this symbol, see Math Words,
[Scott #84, 88] *VFR

2016 JAVIER CILLERUELO AND FLORIAN LUCA  proved that for any base greater than 4 EVERY POSITIVE INTEGER IS A SUM OF THREE PALINDROMES )

BIRTHS
1785 Jean-Charles-Athanase Peltier (22 Feb 1785; 27 Oct 1845 at age 60)
French physicist who discovered the Peltier effect (1834), that at the junction of two dissimilar metals an electric current will produce heat or cold, depending on the direction of current flow. In 1812, Peltier received an inheritance sufficient to retire from clockmaking and pursue a diverse interest in phrenology, anatomy, microscopy and meteorology. Peltier made a thermoelectric thermoscope to measure temperature distribution along a series of thermocouple circuits, from which he discovered the Peltier effect. Lenz succeeded in freezing water by this method. Its importance was not fully recognized until the later thermodynamic work of Kelvin. The effect is now used in devices for measuring temperature and non-compressor cooling units. *TIS

1796 (Lambert) Adolphe (Jacques) Quetelet (22 Feb 1796, 17 Feb 1874 at age 78) was a Belgian mathematician, astronomer, statistician, and sociologist known for his pioneering application of statistics and the theory of probability to social phenomena, especially crime. At an observatory in Brussels that he established in 1833 at the request of the Belgian government, he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale (1835) Quetelet presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. *TIS Quetelet created the Body Mass Index in a paper in 1832. It was known as the Quetelet Index until it was termed the Body Mass Index in 1972 by Ancel Keys.

1817 Carl Borchardt (22 Feb 1817 in Berlin, Germany - 27 June 1880 in Rudersdorf (near Berlin), Germany) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1824 Pierre (-Jules-César) Janssen (22 Feb 1824, 23 Dec 1907) was a French astronomer who in 1868 devised a method for observing solar prominences without an eclipse (an idea reached independently by Englishman Joseph Norman Lockyer). Janssen observed the total Sun eclipse in India (1868). Using a spectroscope, he proved that the solar prominences are gaseous, and identified the chromosphere as a gaseous envelope of the Sun. He noted an unknown yellow spectral line in the Sun in 1868, and told Lockyer (who subsequently recognized it as a new element he named helium, from Greek "helios" for sun). Janssen was the first to note the granular appearance of the Sun, regularly photographed it, and published a substantial solar atlas with 6000 photographs (1904). *TIS

1849 Nikolay Yakovlevich Sonin (February 22, 1849 – February 27, 1915) was a Russian mathematician.
Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler–Maclaurin summation formula. Other topics Sonin studied include Bernoulli polynomials and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration. Together with Andrey Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian. He died in St. Petersburg.*Wik

1856 Micaiah John Muller Hill born. He worked in hydrodynamics, on the three-body problem, and has a diﬀerential equation named after him. *VFR He was Vice-Chancellor of the University of London from 1909 to 1911. His books on Euclids fifth and sixth books, and on the Theory of Proportion are available on the internet.

1857 Heinrich Rudolf Hertz (22 Feb 1857, 1 Jan 1894) was a German physicist who was the first to broadcast and receive radio waves. He studied under Kirchhoff and Helmholtz in Berlin, and became professor at Bonn in 1889. His main work was on electromagnetic waves (1887). Hertz generated electric waves by means of the oscillatory discharge of a condenser through a loop provided with a spark gap, and then detecting them with a similar type of circuit. Hertz's condenser was a pair of metal rods, placed end to end with a small gap for a spark between them. Hertz was also the first to discover the photoelectric effect. The unit of frequency - one cycle per second - is named after him. Hertz died of blood poisoning in 1894 at the age of 37. *TIS

1862 Ruth Gentry (February 22, 1862 - October 15, 1917) grew up in Indiana and received her A.B. degree at Indiana State Normal (now Indiana State University) in 1880. After ten years of teaching at preparatory schools, she earned a degree in mathematics from the University of Michigan in 1890. She spent the following year as a Fellow in Mathematics at Bryn Mawr, then became the first mathematician and the second recipient of the Association of College Alumnae European Fellowship, which she used in 1891-92 to attend lectures at the University of Berlin (but was not allowed to enroll for a degree). After a further semester attending mathematics lectures at the Sorbonne in Paris, Gentry returned to Bryn Mawr to become one of Charlotte Scott's first two graduate students. She received her Ph.D. in 1896 on the topic "On the Forms of Plane Quartic Curves." As she writes at the beginning of this thesis:
"Many papers dealing with curves of the fourth order, or Quartic Curves, are to be found in the various mathematical periodicals; but these leave the actual appearance of the curve as a whole so largely to the reader's imagination that it is here proposed to give a complete enumeration of the fundamental forms of Plane Quartic Curves as they appear when projected so as to cut the line infinity the least possible number of times, together with evidence that the forms presented can exist."
Gentry taught at Vassar College from 1896 until 1902, where she was the first mathematics faculty member to hold a Ph.D. degree. She was promoted to associate professor in 1900, but left Vassar two years later to become the associate principal and head of the mathematics department at a private school in Pittsburgh, Pennsylvania, a position she held until 1905. After that she spent some time as a volunteer nurse and traveled in the United States and Europe, but she became increasingly ill and died at the age of 55. She was a member of the American Mathematical Society from 1894 until her death in 1917 in Indianapolis, Indiana. *Agnes Scott College web page

1903 Frank Plumpton Ramsey (22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik

1928 BASIC co-inventor Thomas Kurtz is born. With John Kemeny, Kurtz developed the easy-to-learn programming language for his students at Dartmouth College in the early 1960s. He said: "If Fortran is the lingua franca ... BASIC is the lingua playpen." *CHM

DEATHS

1512 Amerigo Vespucci (9 Mar 1451, 22 Feb 1512 at age 60)Spanish astronomer whose name was given to the New World - America - because it was he and not Columbus, who realized and announced that Columbus had discovered a new continent. *TIS

1687 Francesco Lana de Terzi (Brescia, Lombardy 1631 – 22 February 1687 Brescia, Lombardy) was an Italian Jesuit, mathematician, naturalist and aeronautics pioneer. Having been professor of physics and mathematics at Brescia, he first sketched the concept for a vacuum airship and has been referred to as the Father of Aeronautics for his pioneering efforts, turning the aeronautics field into a science by establishing "a theory of aerial navigation verified by mathematical accuracy". He also developed the idea that developed into Braille. *Wik

1901 George Francis FitzGerald (3 Aug 1851 in Kill-o'-the Grange, Monkstown, Co. Dublin, Ireland - 21 Feb 1901 in Dublin, Ireland) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS

1941 Dayton Clarence Miller (13 Mar 1866, 22 Feb 1941 at age 74)American physicist. Author of The Science of Musical Sounds (1916). Miller's collection of nearly 1,650 flutes and other instruments, and other materials mostly related to the flute, is now at the Library of Congress. To provide a mechanical means of recording sound waves photographically, he invented the phonodeik (1908). He became expert in architectural ecoustics. During WW I, he was consulted concerning using his photodeik to help locate enemy guns. Miller spent considerable research effort on repeating the Michelson and Morley experiment, proposed by Maxwell, to detect a stationary aether. He spent some time working with Morley (1902-4), then more time at Mt. Wilson, recording results favoring the presence of the aether.*TIS

1975 Oskar Perron ( 7 May 1880 in Frankenthal, Pfalz, Germany - 22 Feb 1975 in Munich, Germany)was a German mathematician best known for the Perron paradox:
Suppose the largest natural number is N. Then if N is greater than 1 we have N2 greater than N contradicting the definition. His publications cover a wide range of mathematical topics. His work in analysis is certainly remembered through the Perron integral. However he also worked on differential equations, matrices and other topics in algebra, continued fractions, geometry and number theory. *SAU

1984 Maxwell Herman Alexander "Max" Newman, FRS (7 February 1897 – 22 February 1984) was a British mathematician and codebreaker. After WWII he continued to do research on combinatorial topology during a period when England was a major center of activity, notably Cambridge under the leadership of Christopher Zeeman. Newman made important contributions leading to an invitation to present his work at the 1962 International Congress of Mathematicians in Stockholm at the age of 65, and proved a Generalized Poincaré conjecture for topological manifolds in 1966. He died in Cambridge.*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