## Saturday 16 March 2024

### On This Day in Math - March 16

 Memorial for Ohm ,

Whenever I meet in Laplace with the words 'Thus it plainly appears', I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.
~Nathaniel Bowditch

The 75th day of the year; the aliquot divisors of 75 are 1,3,5,15, and 25. Their sum is a perfect square, 49. Their product is also a perfect square, 5625. (Can you find other numbers with this property?)

75 is also the larger of the smallest pair of betrothed (quasi-amicable) numbers. 48 and 75 are a betrothed pair since the sum of the proper divisors of 48 is 76 and 75+1 = 76 and the sum of the proper divisors of 75 is 49, with 48+1=49. (There is only a single other pair of betrothed numbers that can be a year day)

75 and 76 form the first pair of adjacent numbers in base ten which are NOT a palindrome in any base $2 \leq b \leq 10$

275 + 75 is prime

75 is a Keith # or repfigit (75 appears in a Fibonacci-like sequence created by its digits) 7, 5, 12, 17, 29, 46, 75 ...  (75 is the sixth of seven year days which are repfigits.  Can you find the others?)

EVENTS

1713 Saunderson to Jones (Nicholas Saunderson to William Jones): “There has been nothing published here since my last to you, excepting a treatise, which is not worth mentioning, by one Mr. Green, fellow of Clare Hall of this university. If there had been anything in it instructive or diverting I should have sent it to you; but I can ﬁnd nothing in it but ill manners and elaborate nonsense from one end to the other. The gentleman has been reputed mad for these two years last past, but never gave the world such ample testimony of it before.” [Rigaud, Correspondence of Scientiﬁc Men of the Seventeenth Century, I, *263] *VFR

Jones who coined Pi, by Hogarth

1763 Jerome Lalande writes in his diary about a visit to England, and "I went to see the Tower, and from there by water to Surrey Street to see Mr Short (James Short FRS was an optician who had been called to London to teach mathematics to William, Duke of Cumberland)
who spoke to me about the difficulty in giving his mirrors a parabolic figure. It is done only by guess-work." *Richard Watkins
Lalande was a French astronomerfreemason and writer. On 8 May and again on 10 May 1795 a star was observed and recorded at his observatory with uncertainty noted on its position with a colon, this notation could also indicate an observing error so it was not until the original records of the observatory were reviewed that it was established with certainty that the object was Neptune and the position error between the two nights was due to the planet's motion across the sky.

1802 The United States Military Academy at West Point established by act of congress. This school was the ﬁrst engineering school in the U.S. Charles Davies, a noted math textbook writer, taught there.*VFR (The academy opened on July 4, 1802. Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.)
Nininger Hall, part of the original Cadet Barracks

1830 The New York Stock Exchange had its slowest trading day, only 31 shares trading hands. *VFR

1867  First publication of an article by Joseph Lister outlining the discovery of antiseptic surgery, in "The Lancet".  The second appeared in July of the same year.
At the Dublin meeting of the British Medical Association in August 1867, Lister stated “previous to its introduction, the 2 large wards in which most of my cases of accident and of operation are treated were amongst the unhealthiest in the whole of surgical division at the Glasgow Royal Infirmary (…) but since the antiseptic treatment has been brought into full operation, (…) my wards (…) have completely changed their character; so that during the last 9 months not a single instance of pyaemia, hospital gangrene or erysipelas has occurred in them.” *Natl Lib of Medicine

1916 On his seventieth birthday in 1916, Mittag-Leffler and his wife signed their last will and testament. They gave their entire fortune to found a Mathematical Institute which now bears their names. It is in their villa in Djursholm, near Stockholm, Sweden. A sumptuous volume giving a complete catalog of Mittag-Leffler’s library was also published at this time, and this library is now housed in the Institute. Naturally it is a favorite haunt of historians of mathematics. *VFR (See Births,1846 below)

1916 Srinivasa Ramanujan graduated from Cambridge with a Bachelor of Arts by Research (the degree was called a Ph.D. from 1920). He had been allowed to enroll in June 1914 despite not having the proper qualifications. Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England.
This paper, as it appeared originally, is not complete. Since the London Mathematical Society was in
some financial difficulty at that time, Ramanujan had to suppress part of what he had written in order
to save expense.
Highly composite numbers are sometimes used to search for primes, since the proof that primes are infinite uses a product of all "known" primes.

1926 Clark University Physics Professor, Robert H. Goddard, conducted the ﬁrst successful open-air test of a liquid-fuel rocket. “The rocket soared only forty-one feet, hardly the ‘extreme altitudes’ Goddard had envisioned, yet the occasion was anologous to the ﬁrst ﬂight of the Wright brothers at Kitty Hawk nearly a quarter of a century earlier.” *William A. Koelsch, Clark University, 1887–1987
He thought stable flight could be obtained by mounting the rocket ahead of the fuel tank. The tank was shielded from the flame by a metal cone and was pulled behind the rocket by the lines for gasoline fuel and oxygen. The design worked, but did not produce the hoped-for stability. The rocket burned about 20 seconds before reaching sufficient thrust (or sufficiently lightening the fuel tank) for taking off. During that time it melted part of the nozzle. It took off to a height of 41-ft, leveled off and within 2.5 seconds hit the ground 184 feet away, averaging about 60 mph. The camera ran out of film, so no photographic record of that flight remains. *TIS

1928 Chandrasekhara Raman presented the results from his Feb 28 ground breaking experiments in light scattering at a meeting of scientists in Bangalore on 16 March 1928. The results would lead to his wining the Nobel Prize in Physics in 1930. *Wik

1962
The first Titan II was launched on this day and the entire missile system met all of its test objectives. The Titan II was declared operational in 1963 under the numerical designation LGM-25C. A total of 54 Titan II missiles were deployed in six separate squadrons each responsible for nine missiles.

1966  Gemini 8 launched with Neil Armstrong and David R. Scott aboard, conducts the 1st docking of two spacecraft in orbit, flight aborted after critical system failure with the crew returned safely to Earth.  Gemini 8 was the sixth crewed spaceflight in NASA's Gemini program, and was the 14th crewed American flight.

1986 The Manchester Guardian Weekly announces that Colin Rourke of Warwick and his student Eduardo Rego of Oporto University in Portugal have solved the 82 year old Poincare conjecture which states that loops on spheres in n-dimensions can be shrunk to points. Obviously, Mr. Rego will get his Ph.D. *VFR The article in the Guardian was by Ian Stewart. In November 1986, Rourke was at the University of California, Berkeley, conducting a seminar to explain and defend his proof. By the end of the week, Rourke's audience, which included some of the world's top topologists, had pointed out a gap in his proof, one that Rourke could not fill. In the end, there was no valid proof. The problem was solved by the reclusive Russian mathematician Grigori Perelman in November of 2002

1990 Internet Extends Beyond U.S. to Europe: The National Science Foundation announces it will extend its network with a high-speed data link to Europe. Five years earlier, the Internet in its modern form had started to develop rapidly thanks to the formation of the NSFNET, which linked five supercomputer centers in the United States. Later in 1990, Europe contributed to the growth of the Internet when CERN's Tim Berners-Lee developed HTML, the language used for the World Wide Web.*CHM

BIRTHS

1750 Caroline Lucretia Herschel (16 Mar 1750, 9 Jan 1848) German-born British astronomer, sister of Sir William Herschel, who assisted in his astronomical researches making calculations associated with his studies. In her own telescope observations, she found three nebulae (1783) and eight comets (1786-97). In 1787, King George III gave Caroline a salary of 50 pounds per year as assistant to William. She published the Index to Flamsteed's Observations of the Fixed Stars and a list of his mistakes in 1797. At the age of 10 she had been struck with typhus, which subsequently stunted her growth. She never grew taller than 4' 3" and remained frail throughout her life. *TIS
[The following inscription is engraved on Miss Herschel's tomb. It begins: "Hier ruhet die irdische Hülle von CAROLINA HERSCHEL, Geboren zu Hannover den 16ten Marz 1750, Gestorben, den 9ten Januar 1848." But, for the convenience of our young readers, we give it in English:—

HERE RESTS THE EARTHLY CASE OF

CAROLINE HERSCHEL.

BORN AT HANOVER, MARCH 10, 1750.

DIED JANUARY 9, 1848.

"The eyes of her now glorified were, while here below, directed towards the starry heavens. Her own discoveries of comets, and her share in the immortal labours of her brother, William Herschel, bear witness of this to succeeding ages.

"The Royal Irish Academy of Dublin, and the Royal Astronomical Society of London, enrolled her name among their members.

"At the age of 97 years 10 months, she fell asleep in calm rest, and in the full possession of her faculties; following into a better life her father, Isaac Herschel, who lived to the age of 60 years, 2 months, 17 days, and has lain buried not far off since the 29th of March 1767."

This epitaph was mainly written by Miss Herschel herself, and the allusion to her brother is characteristic.]
*from The Project Gutenberg EBook of The Story of the Herschels, by Anonymous

1789 Georg Simon Ohm (16 Mar 1789; 6 Jul 1854 at age 65) German physicist (high school teacher) who showed by experiment (1825) that there are no “perfect” electrical conductors. All conductors have some resistance. He stated the famous Ohm's law (1826): “If the given temperature remains constant, the current flowing through certain conductors is proportional to the potential difference (voltage) across it.” or V=iR. *TIS

1821 Heinrich Eduard Heine (16 March 1821 in Berlin, Germany - 21 Oct 1881 in Halle, Germany) Heine is best remembered for the Heine-Borel theorem. He was responsible for the introduction of the idea of uniform continuity.*SAU

1846 Magnus Gösta Mittag-Leffler (16 Mar 1846; 7 Jul 1927 at age 81) Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem. *TIS One of the stories that circulates from time to time about Mittag-Leffler and the fact that there is no Nobel Prize in mathematics is that Nobel disliked Mittag-Leffler for having an affair with Nobel's wife and so he did not create a prize in Mathematics. Only problem; Nobel never married, and there is little if any evidence that Mittag-Leffler ever met Nobel's mistress, Sophie Hess.

1853 Heinrich (Gustav Johannes) Kayser (16 Mar 1853, 14 Oct 1940) was a German physicist who discovered the presence of helium in the Earth's atmosphere. Prior to that scientists had detected helium only in the sun and in some minerals. Kayser's early research work was on the properties of sound. In collaboration with the physicist and mathematician Carl D.T. Runge, Kayser carefully mapped the spectra of a large number of elements. He wrote a handbook of spectroscopy (1901–12) and a treatise on the electron theory (1905).*TIS

1915 Kunihiko Kodaira(16 Mar 1915; 26 Jul 1997 at age 82) Japanese mathematician who was awarded the Fields Medal in 1954 for his work in algebraic geometry and complex analysis. Kodaira's work includes applications of Hilbert space methods to differential equations which was an important topic in his early work and was largely the result of influence by Weyl. Through the influence of Hodge, he also worked on harmonic integrals and later he applied this work to problem in algebraic geometry. Another important area of Kodaira's work was to apply sheaves to algebraic geometry. In around 1960 he became involved in the classification of compact, complex analytic spaces. One of the themes running through much of his work is the Riemann-Roch theorem. He won the 1985 Wolf Prize. *TIS
 *Wik

1916 Frederick Reines (/ˈraɪnəs/ RY-nəs;[1] March 16, 1918 – August 26, 1998) was an American physicist. He was awarded the 1995 Nobel Prize in Physics for his co-detection of the neutrino with Clyde Cowan in the neutrino experiment. He may be the only scientist in history "so intimately associated with the discovery of an elementary particle and the subsequent thorough investigation of its fundamental properties."

A graduate of Stevens Institute of Technology and New York University, Reines joined the Manhattan Project's Los Alamos Laboratory in 1944, working in the Theoretical Division in Richard Feynman's group. He became a group leader there in 1946. He participated in a number of nuclear tests, culminating in his becoming the director of the Operation Greenhouse test series in the Pacific in 1951.

In the early 1950s, working in Hanford and Savannah River Sites, Reines and Cowan developed the equipment and procedures with which they first detected the supposedly undetectable neutrinos in June 1956. Reines dedicated the major part of his career to the study of the neutrino's properties and interactions, which work would influence study of the neutrino for many researchers to come. This included the detection of neutrinos created in the atmosphere by cosmic rays, and the 1987 detection of neutrinos emitted from Supernova SN1987A, which inaugurated the field of neutrino astronomy. *Wik

1947 Dr. Keith Devlin (March 16, 1947, Kingston upon Hull, UK; ) is a co-founder and Executive Director of Stanford University's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 32 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. *Stanford Edu

1954 John E. Laird (March 16, 1954 Ann Arbor, Michigan - ) is a computer scientist who, with Paul Rosenbloom and Allen Newell, created the Soar cognitive architecture at Carnegie Mellon University. Laird is a Professor of the Computer Science and Engineering Division of the Electrical Engineering and Computer Science Department of the University of Michigan. He was the director of the Artificial Intelligence Laboratory there from 1994 to 1999. *Wik

1968 Sir David William Cross MacMillan FRS FRSE (born 16 March 1968) is a Scottish chemist and the James S. McDonnell Distinguished University Professor of Chemistry at Princeton University, where he was also the chair of the Department of Chemistry from 2010 to 2015. He shared the 2021 Nobel Prize in Chemistry with Benjamin List "for the development of asymmetric organocatalysis". MacMillan used his share of the \$1.14 million prize to establish the May and Billy MacMillan Foundation.

He is considered to be one of the founders of organocatalysis. organic chemistry, organocatalysis is a form of catalysis in which the rate of a chemical reaction is increased by an organic catalyst. This "organocatalyst" consists of carbon, hydrogen, sulfur and other nonmetal elements found in organic compounds. Because of their similarity in composition and description, they are often mistaken as a misnomer for enzymes due to their comparable effects on reaction rates and forms of catalysis involved.

DEATHS

 Bowditch gravestone,Mount Auburn CemeteryCambridgeMiddlesex CountyMassachusetts, USA
1838 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)(I can give no explanation for the discrepancy in the date of death on his tombstone.)
1841 Félix Savart (30 Jun 1791, 16 Mar 1841 at age 49)French physicist who researched various manifestations of vibration. With Jean-Baptiste Biot, he developed the Biot-Savart Law (1820) concerning the magnetic field intensity around a current-carrying wire. After earning a degree in medicine (1816), he took an interest in physics, beginning with a study of the violin to explain the contributions from its components to the sound from the strings. He presented a memoir on the subject to the Paris Academy of Sciences in 1819. He conducted extensive research in acoustics, the nodal patterns of vibrating systems (including air columns), and related enquiries into the elasticity of substances. He also investigated the voice and hearing. He devised a rotating toothed wheel to produce a sound of any frequency by a reed held against it, to measure high frequency hearing limits. *TIS

1914 Edward Singleton Holden (November 5, 1846 – March 16, 1914) was an American astronomer. Born in St. Louis, Missouri in 1846 to Jeremiah and Sarah Holden. From 1862-66, he attended Washington University in St. Louis, where he obtained a B.S. degree. He later trained at West Point in the class of 1870.In 1873 he became professor of mathematics at the US Naval Observatory, where he made a favorable impression on Simon Newcomb. He was director of Washburn Observatory at the University of Wisconsin–Madison from 1881 to 1885. He was elected a member of the American National Academy of Sciences in 1885.
On August 28, 1877, a few days after Asaph Hall discovered the moons of Mars Deimos and Phobos, he claimed to have found a third satellite of Mars. Further analysis showed large mistakes in his observations.
He was president of the University of California from 1885 until 1888, and the first director of the Lick Observatory from 1888 until the end of 1897. Meanhwile in 1893 while at the observatory he published a book on Mughal Emperors, The Mogul emperors of Hindustan, A.D. 1398- A.D. 1707. He resigned as a result of internal dissent over his management among his subordinates. While at the Lick Observatory, he was the founder of the Astronomical Society of the Pacific and its first President (1889–1891).
In 1901 he became the librarian of the United States Military Academy at West Point, where he remained until his death.
His cousin, George Phillips Bond, was director of Harvard College Observatory.
He discovered a total of 22 NGC objects during his work at Washburn Observatory.
He wrote many books on popular science (and on other subjects, such as flags and heraldry), including science books intended for children. For example the book Real Things In Nature. A Reading Book of Science for American Boys and Girls published in 1916.*Wik

1922 George Bruce Halsted (23 Nov 1853 in Newark, New Jersey, USA - 16 March 1922 in New York, USA) His main interests were the foundations of geometry and he introduced non-euclidean geometry into the United States, both through his own research and writings as well as by his many important translations. Halsted gave commentaries on the work of Lobachevsky, Bolyai, Saccheri and Poincaré and made translations of their works into English. His work on the foundations of geometry led him to publish Demonstration of Descartes's theorem and Euler's theorem in the Annals of Mathematics in 1885. His other main interest was in mathematical education and, as a mathematics educator, he criticised the careless way that mathematics was presented in the textbooks of the time. He contributed over ninety article to the American Mathematical Monthly and wrote many biographies of mathematicians such as Lambert, Farkas Bolyai, Lobachevsky, De Morgan, Sylvester, Chebyshev, Cayley, Hoüel and Klein. *SAU

1933 Alfréd Haar (11 Oct 1885 in Budapest, Hungary - 16 March 1933 in Szeged, Hungary) was a Hungarian mathematician who is best remembered for his work on analysis on groups, introducing a measure on groups, now called the Haar measure. *SAU

1940 Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English.
He was distinguished for his work in Greek Mathematics and author several books on Greek mathematicians. It is primarily through Heath's translations that modern English-speaking readers are aware of what Archimedes did.
He died in Ashtead, Surrey. *Wik

1941 Edward Lindsay Ince (30 Nov 1891 in Amblecote, Staffordshire, England
- 16 March 1941 in Edinburgh, Scotland) Ince graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions. *SAU

1980 William Prager (May 23, 1903, Karlsruhe - 16 March 1980 in Zurich, Switzerland) was a German-born US applied mathematician. He was a lecturer at Darmstadt, a deputy director at University of Göttingen, professor at Karlsruhe, University of Istanbul, the University of California, San Diego and Brown University, where he advised Bernard Budiansky.
The Society of Engineering Science has awarded the Wiliam Prager Medal in Solid Mechanics since 1983 in his honor.*Wik

1992 Yves-André Rocard (22 May 1903 in Vannes, France - 16 March 1992 in Paris, France) French mathematician and physicist who helped develop the atomic bomb for France.
ysics at the École normale supérieure in Paris.

As a member of a Resistance group during the Second World War he flew to the UK in a small plane as part of a dangerous mission and was able to provide British intelligence with invaluable information. There he met up with Charles de Gaulle who named him Director of Research in the Forces navales françaises libres (the Navy of Free France). He became particularly interested in the detection of solar radio emissions by British Radar, which were causing military problems by jamming detection during periods of high emission, and was able to create a new radio navigational beam station.

1918 Sir Derek Harold Richard Barton FRS FRSE (8 September 1918 – 16 March 1998) was an English organic chemist and Nobel Prize laureate for 1969.

Barton was an English chemist, a joint recipient (with Norwegian Odd Hassel) of the 1969 Nobel Prize for Chemistry for research that helped establish conformational analysis (the study of the 3-D geometric structure of complex molecules). In a brief paper in Experienta entitled “The Conformation of the Steroid Nucleus” (1950), Barton showed that organic molecules in general and steroid molecules in particular could be assigned a preferred conformation based on work of chemical physicists, in particular by Odd Hassel. Conformational analysis is useful in the elucidation of configuration, in the planning of organic synthesis, and in the analysis of reaction mechanisms. It is fundamental to a complete understanding of enzymatic processes. *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