## Wednesday 24 July 2024

### On This Day in Math - July 24

In mathematics the art of proposing a question
must be held of higher value than solving it.

~Goerg Cantor

Today is the 205th day of the year; there are 205 pairs of twin primes less than ten thousand. *Number Gossip

Every number greater than 205 is the sum of distinct primes of the form 6n + 1. *Prime Curios

205 is the number of walks of length 5 between any two distinct vertices of the complete graph K_5

205 is the smallest un-primeable odd composite  .  It can not be turned into a prime by changing only one of its digits.  (nice exploration for young students)

205 = 14^2 + 3^2 = 13^2+6^2

205 = 103^2 - 102^2 = 23^2 - 18^2 The first is from a property of every odd number, the second is from a property of any number greater than 35 that ends in five.

205 = 2 x 41 + 41 + 41 x 2 also 54 + 45 + 7 + 54 + 45. or 99 + 7 + 99

205 is a palindrome in duodecimal (base 12, (151) =1 x 12^2 + 5 x 12 + 1), and in bases 9, 11, 13, and 16.

205 is the smallest un-primeable odd composite  .  It can not be turned into a prime by changing only one of its digits.  (Language fact: A prime which cannot be turned into another prime by changing a single digit is called weakly prime. These are all pretty big, the smallest being 294001.)

205 is a semi-prime, 5 x 41.  It is also a reversible semi-prime, or emirpimes, since it's reversal, 502 = 2 x 251, is also a semi-prime

EVENTS

In 1673, Edmund Halley entered Queen's College, Oxford, as an undergraduate. Halley had attended the prestigious St. Paul's school, where in 1671, he was appointed captain, a position resembling today's student body president. He was an excellent student, and by the time he entered Queen's College, Oxford. At this young age, Halley already possessed, "... the basic facts and computations not only of navigation but also those which the practical astronomer is concerned when he sets about the delicate task of measuring the positions of celestial bodies in the sky," according to Colin Ronan in his book Edmond Halley: genius in eclipse *TIS

 *Wik

1860 Yale University authorized the granting of Doctor of Philosophy degrees. The ﬁrst such degrees in the U.S. were awarded in 1861 by Yale to Eugene Schuyler, James Morris Whiton, and Arthur Williams Wright. [Kane, p. 215] *VFR

Arthur Williams Wright (September 8, 1836 – December 19, 1915) was an American physicist. Wright spent most of his scientific career at Yale University, where he received the first science Ph.D. awarded outside of Europe. His research, which ranged from electricity to astronomy, produced the first X-ray image and experimented with Röntgen rays. He also proved instrumental in securing funding for the first dedicated physics laboratory building in the United States, the Sloane Physical Laboratory.

Eugene Schuyler (February 26, 1840 – July 16, 1890)[1] was a nineteenth-century American scholar, writer, explorer and diplomat. Schuyler was one of the first three Americans to earn a Ph.D. from an American university;[2] and the first American translator of Ivan Turgenev and Lev Tolstoi. He was the first American diplomat to visit Russian Central Asia, and as American Consul General in Istanbul he played a key role in publicizing Turkish atrocities in Bulgaria in 1876 during the April Uprising. He was the first American Minister to Romania and Serbia, and U.S. Minister to Greece.

Whitton, it seems was a language man who wrote several books about languages including , "

• HandboHandbook of Exercises and Reading Lessons for Beginners in Latin

•  (Boston: James Munroe and Company, 1860); First Lessons in Greek:

• The Beginner’s Companion-Book to Hadley’s Greek Grammar

• (New York: D. Appleton & Co., 1862, 1863, 1866, 1872, 1881);

• *Wik

• Arthur William Wright

1911, American Hiram Bingham discovered the Lost City of the Incas, Vilcapampa (now called Machu Picchu), where the last Incan Emperors found refuge from the conquistadors.*TIS

1950, the first successful rocket launch from Cape Canaveral took place. "Bumper" No. 8 was a captured German V-2 rocket with the payload replaced by another rocket 700-pound Army-JPL Wac Corporal rocket on top. It was fired from Long-Range Proving Ground at Cape Canaveral. The first-stage V-2 climbed 10 miles, separated from the second-stage Corporal which traveled 15 more miles. (V-2 exploded). A previous attempt on 19 July 1950 of a similar launch was aborted on the pad.

1951  John Bardeen notified AT&T Bell Laboratories that he would be leaving the company where, along with Walter Brattain and William Shockley, he had developed one of the most essential components of modern computing: the point-contact transistor.

The transistor replaced vacuum tubes, allowing the size of computers to decrease dramatically while their power increased. Despite this triumph, Bardeen was unhappy with Shockley, whom he felt was limiting his and Brattain's involvement with further refinements to the transistor. Bardeen took a position at the University of Illinois at Urbana-Champaign. *CHM

 *CHM

1991, a University of Manchester scientist announced the finding a planet outside of solar system. Andrew G. Lyne of the University of Manchester subsequently retracted his claim for a planet around pulsar PSR 1829-10 at the Jan 1992 meeting of the American Astronomical Society in Atlanta. He said that the modulation of radio waves coming from the pulsar was caused not by the presence of a planet but was in fact an artifact of the Earth's motion around the Sun. That possibility that had been considered but then discounted in earlier studies of the data.*TIS

BIRTHS

1786 Joseph Nicolas Nicollet (July 24, 1786 – September 11, 1843), also known as Jean-Nicolas Nicollet, was a French geographer, astronomer, and mathematician known for mapping the Upper Mississippi River basin during the 1830s. Nicollet led three expeditions in the region between the Mississippi and Missouri Rivers, primarily in Minnesota, South Dakota, and North Dakota.

Before emigrating to the United States, Nicollet was a professor of mathematics at Collège Louis-le-Grand, and a professor and astronomer at the Paris Observatory with Pierre-Simon Laplace. Political and academic changes in France led Nicollet to travel to the United States to do work that would bolster his reputation among academics in Europe. He was elected a member of the American Philosophical Society in 1842.

Nicollet's maps were among the most accurate of the time, correcting errors made by Zebulon Pike, and they provided the basis for all subsequent maps of the American interior. They were also among the first to depict elevation by hachuring and the only maps to use regional Native American placenames. Nicollet's Map of the Hydrographical Basin of the Upper Mississippi was published in 1843, following his death. Nicollet Tower, located in Sisseton, South Dakota is a monument to Nicollet and his work and was constructed in 1991.

1827 Edward Olney (ALL-nee*) (July 24, 1827 - January 16, 1887) was born in Moreau, Saratoga County, New York. His ancestry can be traced back to Thomas Olney who accompanied Roger Williams in founding the city of Providence and colony of Rhode Island. Benjamin Olney's family moved to Oakland County, Michigan, in 1833 and, a few months later, settled on a farm in Weston, Wood County, Ohio.
Opportunities for formal education on the frontier were sparse, and Olney was largely self-taught. Calloway tells about Edward hiring a neighbor boy to drive the team of oxen on the Olney farm so that he could attend school for six weeks in order to master Day's Algebra. During this time he also ran an arithmetic school at home in the evenings in order to earn the money to pay for his substitute driver.
At age 19, Olney began his career as a teacher in the local elementary schools, while studying mathematics, natural science, and languages on his own. Cajori reports that "though he had never studied Latin, he began teaching it and kept ahead of the class because he 'had more application'." In 1848 Olney was hired as a teacher in the district school at Perrysburg, Ohio. The following year he was named principal of the grammar department in the new Union School. Over the next five years he would become the school's superintendent, marry Miss Sarah Huntington (a teacher at the school), and receive an honorary A. M. degree from Madison University (now Colgate University) in Hamilton, New York. Today there is an Olney School in Lake Township, Wood County, named after him.
In 1853 Olney was appointed Professor of Mathematics at Kalamazoo College, Michigan, where he remained for ten years and established the first mathematics curriculum at that institution. He inspired his colleagues and students alike with "his high Christian aims; his generous, self-sacrificing spirit; his thoroughness in government and discipline; and the inspiration which attended him." Although he insisted that his students recite using exact and correct language, he always tried to simplify the explanations of concepts and processes and make them more understandable. Kalamazoo college later conferred the honorary degree, LL. D. upon him.
In 1863 Olney was named Professor of Mathematics at the University of Michigan, succeeding George P. Williams, whose title was then changed to Professor of Physics. In those days the freshmen at Michigan were taught by inexperienced instructors, but once a week they had to recite for Professor Olney. His reputation for being a stern disciplinarian and a stickler for correct details earned him the nickname "Old Toughy." Nevertheless, he took great pains to see that the poorer students obtained help in making up their deficiencies. According to a former student, G. C. Comstock, "He was not a harsh man, and although the students stood in awe of him, I think that he was generally liked by them."
While he was at Michigan, Professor Olney began writing a series of successful mathematics textbooks for use in both grammar schools and colleges. In many places these displaced the works of such highly regarded authors as Charles Davies and Elias Loomis. Among the titles are: Elements of Arithmetic for Intermediate, Grammar, and Common Schools (1877), A University Algebra (1873), Elementary Geometry (1883), Elements of Trigonometry (1870), and A General Geometry and Calculus (1871) (online). Olney's treatment of calculus was criticized for using infinitesimal methods, but praised for giving "the elegant method, discovered by Prof. James C. Watson [Professor of Astronomy at Michigan], of demonstrating the rule for differentiating a logarithm without the use of series." It is said that Olney preferred geometry to analysis, and when teaching calculus, he would attempt to translate analytical expressions into their geometrical equivalents. This, along with his own struggles in self-education, contributed to his great success as a teacher and textbook author. Edward Olney died on January 16, 1887, after suffering for three years from the effects of a stroke. *David E. Kullman

1851 Friedrich Hermann Schottky. (24 July 1851 – 12 August 1935) was a German mathematician who worked on elliptic, abelian, and theta functions and invented Schottky groups. He was born in Breslau, Germany (now Wrocław, Poland) and died in Berlin.
He is also the father of Walter H. Schottky, the German physicist and inventor of a variety of semiconductor concepts.*Wik

1853 Henri-Alexandre Deslandres (July 24, 1853 – January 15, 1948) French astrophysicist who invented a spectroheliograph (1894) to photograph the Sun in monochromatic light (about a year after George E. Hale in the U.S.) and made extensive studies of the solar chromosphere and solar activity. He worked at the Paris and Meudon Observatories. His investigation of molecular spectra produced empirical laws presaging those of quantum mechanics. He observed spectra of planets and stars and measured their radial velocities of, and he determined the rotation rates of Uranus, Jupiter and Saturn (shortly after James E. Keeler).*TIS

1856 Emile Picard (24 July 1856 – 11 December 1941) born. Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. Modern students of complex variables are probably familiar with two of his named theorems. His lesser theorem states that every nonconstant entire function takes every value in the complex plane, with perhaps one exception. His greater theorem states that an analytic function with an essential singularity takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He also made important contributions in the theory of differential equations, including work on Picard–Vessiot theory, Painlevé transcendents and his introduction of a kind of symmetry group for a linear differential equation, the Picard group. In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of algebraic topology. In addition to his path-breaking theoretical work, Picard also made important contributions to applied mathematics, including the theories of telegraphy and elasticity. His collected papers run to four volumes.
Like his contemporary, Henri Poincaré, Picard was much concerned with the training of mathematics, physics, and engineering students. He wrote a classic textbook on analysis and one of the first textbooks on the theory of relativity. Picard's popular writings include biographies of many leading French mathematicians, including his father in law, Charles Hermite.*Wik

He has to be the perfect Stereotype of Every French Inspector in cinema.

1871 Paul Epstein (July 24, 1871 – August 11, 1939) was a German mathematician. He is known for his contributions to number theory, in particular the Epstein zeta function.
Epstein was raised in Frankfurt where his father was a professor. He received his PhD in 1895 from the University of Strasbourg. From 1895 to 1918 he was a Privatdozent at the University in Strasbourg, which at that time was part of the German Empire. At the end of World War I the city of Strasbourg reverted to France, and Epstein, being German, had to return to Frankfurt.
Epstein was appointed to a non-tenured post at the university and he lectured in Frankfurt from 1919. Later he was appointed professor at Frankfurt. However, after the Nazis came to power in Germany he lost his university position. Because of his age he was unable to find a new position abroad, and finally committed suicide by abusing barbital, fearing Gestapo torture. *Wik

1888 Dunham Jackson (July 24, 1888, Bridgewater, Massachusetts – November 6, 1946) was a mathematician who worked within approximation theory, notably with trigonometrical and orthogonal polynomials. He is known for Jackson's inequality. He was awarded the Chauvenet Prize in 1935. His book Fourier Series and Orthogonal Polynomials (dated 1941) was reprinted in 2004.
Harold Bacon recalls that Jackson was an inspired writer of limericks. When Bacon purchased Jackson's "The Theory of Approximations" he took it to Jackson's office and requested he sign it, suggesting a limerick. Without any visible prethought Jackson wrote on the flyleaf:

There was a young fellow named Bacon
Whose judgement of books was mistaken
In a moment too rash
He relinquished some cash
And his faith in the Author was shaken

*Steven Krantz, Mathematical Apocrypha Redux

1923 Christine Mary Hamill (July 24, 1923 – March 24, 1956) was an English mathematician who specialized in group theory and finite geometry. After receiving her Ph.D. at the University of Cambridge in 1951, she was appointed to a lectureship in the University of Sheffield and later was appointed lecturer in the University College, Ibadan, Nigeria.*Wik

1928  Vera Florence Cooper Rubin (July 23, 1928 – December 25, 2016)  Dr. Rubin was a pioneer, doing paradigm-shifting work on the galaxy rotation problem, which provides major evidence of dark matter. She was born in Philadelphia to Jewish immigrants. She grew up in Philadelphia and Washington, DC. Her interest in astronomy began at an early age and was encouraged by her parents. She was the sole graduate in astronomy in 1948 at
@Vassar
College.  Princeton rejected her for their graduate program in astronomy because of her sex--they did not allow women in that program until 1975 (!). She instead attended
@Cornell
, where she earned her master's degree. Her research was controversial and she had to fight to be allowed to present her work to the American Astronomical Society.
@AAS_Office
She fought sexism throughout her education but persisted, earning her PhD from
@Georgetown
in 1954. Her dissertation argued galaxies "clump" together, rather than being distributed randomly. She held academic positions and also worked from home while caring for her young children for about 10 years. She worked at  and also broke new ground at Palomar Observatory, where she had to create her own women's restroom. Her collaborator Kent Ford and she are responsible for discovering the Rubin-Ford effect, again highly controversial work. Her courage would ultimately be proven justified when the Rubin-Ford effect was validated. Her work on the rotation curves of spiral galaxies provided evidence of dark matter. (Wikipedia screenshot breaks it down clearly.) Dr. Rubin became the second woman astronomer elected to National Academy of Sciences, and won the National Medal of Science, among myriad honors. The LSST observatory was renamed for her in 2019, in recognition of her achievements and advocacy for women in science. Dr. Rubin died on Christmas, 2016, at age 88, survived by 4 children, all PhDs. Though their father of course also deserves credit, that legacy of education and achievement is remarkable, a testament to the wholeness of a life dedicated to both learning and family. *GWOMaths

DEATHS

1934 Hans Hahn (September 27, 1879 – July 24, 1934) was an Austrian mathematician who is best remembered for the Hahn-Banach theorem. He also made important contributions to the calculus of variations, developing ideas of Weierstrass. *SAU

1964 Finlay Freundlich (May 29, 1885 – July 24, 1964) was a distinguished German astronomer who worked with Einstein on measurements of the orbit of Mercury to confirm the general theory of relativity. He left Germany to avoid Nazi rule and became the Napier Professor of Astronomy at St Andrews. *SAU

1974 Sir James Chadwick (20 October 1891 – 24 July 1974) English physicist who received the Nobel Prize for Physics (1935) for his discovery of the neutron. He studied at Cambridge, and in Berlin under Geiger, then worked at the Cavendish Laboratory with Rutherford, where he investigated the structure of the atom. He worked on the scattering of alpha particles and on nuclear disintegration. By bombarding beryllium with alpha particles, Chadwick discovered the neutron - a neutral particle in the atom's nucleus - for which he received the Nobel Prize for Physics in 1935. In 1932, Chadwick coined the name "neutron," which he described in an article in the journal Nature. He led the UK's work on the atomic bomb in WW II, and was knighted in 1945*TIS

1983 Eberhard Frederich Ferdinand Hopf (April 4, 1902, Salzburg, Austria-Hungary – July 24, 1983, Bloomington, Indiana) was a mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) which is one of the most important techniques in the theory of elliptic partial differential equations.*Wik
"The modern theory of relativity of Mr Einstein predicts an influence of any field of gravitation upon light passing near to the sun. The gravitation would have, according to the investigation of Einstein, the effect of deflecting the ray of the star, and Mr Einstein asked me if I would try to prove his results by observations." *SAU

 *SAU

1992 Lillian Rose Vorhaus Kruskal Oppenheimer (October 24, 1898 in New York City – July 24, 1992) was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis.
She was the mother of three sons William Kruskal(developed the Kruskal-Wallis one-way analysis of variance), Martin David Kruskal(co-inventor of solitons and of surreal numbers), and Joseph Kruskal ( Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph) who all went on to be prominent mathematicians. Her grandson Clyde P. Kruskal (son of Martin) is an American computer scientist,working on parallel computing architectures, models, and algorithms. *Wik
 *Origami Heaven

2005 Sir Richard Doll (28 October 1912 – 24 July 2005) British epidemiologist who was one of the first two researchers to link cigarette smoking to lung cancer, as published in the British Medical Journal in 1950. In the same journal, fifty years later, Doll published (22 Jun 2004) the first research that quantified the damage over the lifetime of a generation, based on a 50-year study of a group of almost 35,000 British doctors who smoked. The study found that almost half of persistent cigarette smokers were killed by their habit, and a quarter died before age 70. Persons who quit by age 30 had normal life expectancy. Even quitting at age 50 saved six more years of life over those who continued smoking. He studied other health effects, such as those caused by asbestos and electromagnetic fields.*TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell