## Thursday, 25 January 2018

### On This Day in Math - January 25

*Wik

Only a moment to cut off that head and a hundred years may not give us another like it.
~Count Joseph-Louis de Lagrange,
a Comment to Delambre on Lavoisier's execution, 8 May 1794.

The 25th day of the year; 25 is the smallest square that can be written as a sum of 2 squares. (What's the next?)

There are 25 primes less than 100.

$25 = 5^2$ and $2.5 = \frac{5}{2}$ *Math Year-Round ‏@MathYearRound (are there other examples like this?)

There are exactly 25 square numbers less than or equal to 1,000,000 that are the sum of twin prime pairs. *prime curios

EVENTS
1635 Cardinal Richelieu widens the scope of the Paris literary union (established 1625) to the Academie francaise. *VFR

1770 A sealed paper delivered by mathematician/instrument maker James Short to the Royal Society on 30 April 1752 was opened after his death and read publicly on 25 Jan. 1770. It described a method of working object-lenses to a truly spherical form. It seems, from the journal of Lelande that this was done by eye. "from there by water to Surrey Street to see Mr Short who spoke to me about the difficulty in giving his mirrors a parabolic figure. It is done only by guess-work."
*Richard Watkins

1798, Benjamin Thompson (Count Rumford) presented a paper to the Royal Society, Enquiry concerning the Source of Heat which is excited by Friction, in which he presented the idea that heat represents a form of motion, as opposed to the prevailing idea of being a fluid. He had come to this conclusion from observation that the boring of cannon barrels produces heat from friction. *TIS This experiment gave one of the first calculations of what would be later called the mechanical equivalent of heat. The following summary quote by Thomson highlights the central conclusion of the article:

“What is heat? Is there anything as igneous fluid? Is there anything that can with propriety be called caloric? That heat generated by friction [in the boring experiments] appeared, evidently, to be inexhaustible, [it] cannot possibly be a material substance; … it appears to me to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner heat was excited and communicated in these experiments, except it be MOTION.”

In short, heat was experimentally determined to be or be related to the motion of particles of bodies
*Encyclopedia of Thermodynamics

1839, Michael Faraday publicly announced for the first time the existence of photography as the subject of his Friday Evening Discourse at the Royal Institution. Faraday announced the "Daguerreotype" and Fox Talbot's "photogenic drawings" at the same time, and invited the audience to inspect the specimens displayed in the library. Fox Talbot returned the following week to read a more detailed paper describing his process. Faraday had been instrumental in founding and sustaining (1826) the Friday Evening Discourse series of lectures which continue to this day.*TIS

1931 Max Planck, Quoted in The Observer on this date, "I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness. "

1955, Columbia University scientists developed an atomic clock accurate to within one second in 300 years. *TIS

1962 Professor Mina Reese, dean of graduate studies at CUNY, is named recipient of the MAA’s ﬁrst Award for Distinguished Service to Mathematics. This award was made "for outstanding service to mathematics, other than mathematical research" and for "contributions [that] influence significantly the field of mathematics or mathematical education on a national scale." *Agnes Scott College Web page

1979 Robot violates Asimov's First Law, "A robot may not injure a human being or, through inaction, allow a human being to come to harm." Robert Williams of Michigan was the first human to be killed by a robot. He was 25 years old. The accident at the Ford Motor Company resulted in a $10$ million dollar lawsuit. The jury deliberated for two-and-a-half hours before announcing the decision against Unit Handling Systems, a division of Litton Industries. It ordered the manufacturer of the one-ton robot that killed Williams to pay his family $10$ million dollars. The robot was designed to retrieve parts from storage, but its work was deemed too slow. Williams was retrieving a part from a storage bin when the robot's arm hit him in the head, killing him instantly. In the suit, the family claimed the robot had no safety mechanisms, lacking even a warning noise to alert workers that it was nearby. *CHM

2013 On January 25th Dr. Curtis Cooper of Central Missouri University discovered the 48th known Mersenne prime, 257,885,161-1, a 17,425,170 digit number. I have also seen the 23rd of January, so I shall use both dates until I figure out why two different dates reported.
Singer/Songwriter Helen Arney wrote a little Christmas song about it called Mersenne 48
"The first two verses go like this:
In January Professor Curtis Cooper found a number
Not an ordinary number, but a number that’s humungous...
...so I don’t want your mulled pies and you can keep your minced wine
All I want for Christmas is the world's biggest prime!

It's 2 to the power of 57885161 (minus one)
Mersenne 48 - the perfect gift for everyone
So give me oh give me this Christmas time
A seventeen million digit Christmas prime "

BIRTHS
1627 Robert Boyle (25 Jan 1627; 30 Dec 1691) Irish-English chemist and natural philosopher noted for his pioneering experiments on the properties of gases and his espousal of a corpuscular view of matter that was a forerunner of the modern theory of chemical elements. He was a founding member of the Royal Society of London. From 1656-68, he resided at Oxford where Robert Hooke, who helped him to construct the air pump. With this invention, Boyle demonstrated the physical characteristics of air and the necessity of air for combustion, respiration, and the transmission of sound, published in New Experiments Physio-Mechanical, Touching the Spring of the Air and its Effects (1660). In 1661, he reported to the Royal Society on the relationship of the volume of gases and pressure (Boyle's Law)*TIS

1736 Count Joseph-Louis de Lagrange (25 Jan 1736; 10 Apr 1813)Italian-French mathematician who made great contributions to the theory of numbers and to analytic and celestial mechanics. His most important book is Mécanique analytique (1788; "Analytic Mechanics"), the textbook on which all later work in this field is based.*TIS Lagrange died in his 76th year. He excelled in all fields of analysis and number theory and analytical and celestial mechanics. *SAU

1774 George Dollond (25 Jan 1774; 13 May 1852) British optician who invented a number of precision instruments used in astronomy, geodesy, and navigation. *TIS

1812 William Shanks (25 Jan 1812; June ? ,1882) English mathematician who spent numerous years manually calculating the value of pi. Shanks kept a boarding school at Houghton-le-Spring in a coal mining area near Durham. His calculation of pi reached 707 places by 1873, a feat unchallenged until the use of electronic computers. He used the formula:
pi/4 = 4 tan-1(1/5) - tan-1(1/239).
In 1944, Ferguson's new computation of pi showed Shanks had made a mistake in the 528th decimal place, invalidating the digits calculated beyond. Shanks had omitted two terms which caused his error. By the end of the twentieth century, computers could easily extend the results to over 2 billion places.*TIS

1843 Karl Hermann Amandus Schwarz (25 Jan 1843 in Hermsdorf, Silesia (now Poland)
- 30 Nov 1921 in Berlin, Germany) Schwarz worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem of the calculus of variation, namely surfaces of least area. In 1870 he produced work related to the Riemann mapping theorem. Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem. Weierstrass had shown that Dirichlet's solution to this was not rigorous, see for details. Schwarz's gave a method to conformally map polygonal regions to the circle. Then, by approximating an arbitrary simply connected region by polygons he was able to give a rigorous proof of the Riemann mapping theorem. Schwarz also gave the alternating method for solving the Dirichlet problem which soon became a standard technique.
His most important work is a Festschrift for Weierstrass's 70th birthday. Schwarz answered the question of whether a given minimal surface really yields a minimal area. An idea from this work, in which he constructed a function using successive approximations, led Émile Picard to his existence proof for solutions of differential equations. It also contains the inequality for integrals now known as the 'Schwarz inequality', *SAU He was married to Marie Kummer, a daughter of the mathematician Ernst Eduard Kummer *Wik

1855 Gyula Vályi (5 January 1855 - 13 October 1913) was a Hungarian mathematician and theoretical physicist, a member of the Hungarian Academy of Sciences, known for his work on mathematical analysis, geometry, and number theory.*Wik

1870 Niels Fabian Helge von Koch (Stockholm, January 25, 1870 – ibidem, March 11, 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake(at top), one of the earliest fractal curves to be described. Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a stronger form of the prime number theorem. He described the Koch curve in a 1904 paper entitled "On a continuous curve without tangents constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire"). *Wik

1917 Ilya Prigogine (25 Jan 1917; 28 May 2003) Russian-born Belgian physical chemist who received the Nobel Prize for Chemistry in 1977 for contributions to nonequilibrium thermodynamics, or how life could continue indefinitely in apparent defiance of the classical laws of physics. The main theme of Prigogine's work was the search for a better understanding of the role of time in the physical sciences and in biology. He attempted to reconcile a tendency in nature for disorder to increase (for statues to crumble or ice cubes to melt, as described in the second law of thermodynamics) with so-called "self-organisation", a countervailing tendency to create order from disorder (as seen in, for example, the formation of the complex proteins in a living creature from a mixture of simple molecules). *TIS

1924 Jack Carl Kiefer;(25 Jan 1924 in Cincinnati, Ohio, USA - 10 Aug 1981 in Berkeley, California, USA) Kiefer's main research area was the optimal design of experiments, and about half his 100 publications dealt with that topic. However he also wrote papers on a whole variety of topics in mathematical statistics including decision theory, inventory theory, stochastic approximation, queuing theory, nonparametric inference, estimation, sequential analysis, and conditional inference. His first paper Almost subminimax and biased minimax procedures written jointly with his fellow graduate student at Columbia, Peter Frank, was published in 1951. A paper Sequential minimax search for a maximum which Kiefer published in the Proceedings of the American Mathematical Society in 1953 was based on his master's thesis. The method of search proposed in the paper, namely the Fibonacci Search, became a widely used tool. *SAU

1952 Kenneth John Falconer FRSE (born 25 January 1952, -) is a mathematician working in mathematical analysis and in particular on fractal geometry . He is Professor of Pure Mathematics in the School of Mathematics and Statistics at the University of St Andrews.
He is known for his work on the mathematics of fractals and in particular sets and measures arising from iterated function systems, especially self-similar and self-affine sets. Closely related is his research on Hausdorff and other fractal dimensions. He formulated Falconer's conjecture on the dimension of distance sets and conceived the notion of a digital sundial. In combinatorial geometry he established a lower bound of 5 for the chromatic number of the plane in the Lebesgue measurable case. *Wik

DEATHS
1894 Emil Weyr (1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1935 Alfred Loewy (20 June 1873, 25 Jan 1935) was a German mathematician who worked on representation theory. Loewy rings, Loewy length, and Loewy series are named after him.*Wik

1960 Beno Gutenberg (4 Jun 1889, 25 Jan 1960) American seismologist noted for his analyses of earthquake waves and the information they furnish about the physical properties of the Earth's interior. With Charles Richter, he developed a method of determining the intensity of earthquakes. Calculating the energy released by present-day shallow earthquakes, they showed that three-quarters of that energy occurs in the Circum-Pacific belt. *TIS

1973 Wilhelm Ljunggren (7 Oct 1905 in Oslo, Norway - 25 Jan 1973 in Oslo, Norway) was a Norwegian mathematician, specializing in number theory.
and in particular Diophantine equations. He showed that Ljunggren's equation,

X2 = 2Y4 − 1

has only the two integer solutions (1,1) and (239,13)
Ljunggren also posed the question of finding the integer solutions to the Ramanujan–Nagell equation

2n − 7 = x2

(or equivalently, of finding triangular Mersenne numbers) in 1943, independently of Srinivasa Ramanujan who had asked the same question in 1913. Ljunggren's publications are collected in a book edited by Paulo Ribenboim.*Wik

1994 Stephen Cole Kleene (5 Jan 1909, 25 Jan 1994)American mathematician and logician whose research was on the theory of algorithms and recursive functions. He developed the field of recursion theory with Church, Gödel, Turing and others. He contributed to mathematical Intuitionism which had been founded by Brouwer. His work on recursion theory helped to provide the foundations of theoretical computer science. By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions can be computed.*TIS

1995 Albert William Tucker (28 November 1905 – 25 January 1995) was a Canadian-born American mathematician who made important contributions in topology, game theory, and non-linear programming.In the 1960s, he was heavily involved in mathematics education, as chair of the AP Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA (he was president of the MAA in 1961–1962), and through many NSF summer workshops for high school and college teachers.
In the early 1980s, Tucker recruited Princeton history professor Charles Gillispie to help him set up an oral history project to preserve stories about the Princeton mathematical community in the 1930s. With funding from the Sloan Foundation, this project later expanded its scope. Among those who shared their memories of such figures as Einstein, von Neumann, and Gödel were computer pioneer Herman Goldstine and Nobel laureates John Bardeen and Eugene Wigner.
Albert Tucker noticed the leadership ability and talent of a young mathematics graduate student named John G. Kemeny, whose hiring Tucker suggested to Dartmouth College. Following Tucker's advice, Dartmouth recruited Kemeny, who became Chair of the Mathematics Department and later College President. Years later, Darthmouth College recognized Albert Tucker with an honorary degree. Tucker died in Highstown, N.J. in 1995 at age 89. *Wik

2000 Herta Taussig Freitag (December 6, 1908 - January 25, 2000) Herta obtained a job at a private high school, the Greer School, in upstate New York. There she met Arthur H. Freitag and they were married in 1950. Herta started teaching at Hollins College (now University) in Roanoke, VA in 1948. She received a Ph.D. degree from Columbia University in 1953 and the title of her dissertation was "The Use of the History of Mathematics in its Teaching and Learning on the Secondary Level."
During Herta's years at Hollins she was a frequent guest speaker at local schools and gave lectures at both Virginia and North Carolina Governor's Schools. She published numerous articles in The Mathematics Teacher, The Arithmetic Teacher, and The Mathematics Magazine. At the request of the National Council of Teachers of Mathematics, Professor Freitag wrote the monograph, The Number Story, with her husband. In 1962 she was the first woman to be President of the Maryland-District of Columbia-Virginia Section of the Mathematical Association of America (MAA). Professor Freitag received the Hollins' Algernon Sydney Sullivan Award, which is awarded for recognition of "extraordinary humane and scholarly achievement." She officially retired from Hollins in 1971 to spend time with her husband, who was ill. After his death in 1978, Hollins welcomed her back to the classroom as a leave replacement in 1979-1980 and as a teacher in the Master of Arts in Liberal Studies (MALS) program for several years. Professor Herta Freitag was the first faculty member to receive the Hollins Medal (1979) and the first recipient of the Virginia College Mathematics Teacher of the Year award (1980).
Professor Freitag was very proud of her perfect attendance at the International Conferences of the Fibonacci Association. Most of her work with Fibonacci numbers occurred after she retired, which demonstrates the fallacy of a commonly held belief that mathematicians complete their best work before the age of 40. Professor Freitag published more than thirty articles in the Fibonacci Quarterly after 1985. The November 1996 issue of the Fibonacci Quarterly was dedicated to "Herta Taussig Freitag as she enters her 89th year, in recognition of her years of outstanding service and achievement in the mathematics community through excellence in teaching, problem solving, lecturing and research." This award was given to celebrate her 89th birthday, since 89 is a Fibonacci number. *Biographies of Women Mathematicians, Agnes Scott College web site

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