## Thursday 1 August 2024

### On This Day in Math - August 1

Regarding all these basic topics in infinitesimal calculus which we teach today as canonical requisites ... the question is never raised, "Why so?" or "How does one arrive at them?" Yet all these matters must at one time have been goals of an urgent quest, answers to burning questions, at the time, namely, when they were created. If we were to go back to the origins of these ideas, they would lose that dead appearance of cut-and-dried facts and instead take on fresh and vibrant life again.
Otto Toeplitz - The calculus : A genetic approach (Chicago, 1963)

This is the 213th day of the year; 213 is a square free number as it has no repeated prime factors. How many days of the year are square free?

For 213, the sum of the digits and the product of the digits are equal, and forms a prime when one is added or subtracted.

The average prime factor of 213 is a prime number. [213 = 3*71 and (3+71)/2=37 ]

The square of 213 is a sum of distinct factorials: 2132 = 45369 = 1! + 2! + 3! + 7! + 8!, it is the smallest 3 digit number with this property. (what's next?)

EVENTS

1767 “Mason and Dixon ﬁnished drawing the world’s longest straight line.” [366 Dumb Days in History, by Tom Koch]

For those not familiar with the names and the line in question, "The Mason–Dixon line is a demarcation line separating four U.S. states, Pennsylvania, Maryland, Delaware and West Virginia. It was surveyed between 1763 and 1767 by Charles Mason and Jeremiah Dixon as part of the resolution of a border dispute involving Maryland, Pennsylvania, and Delaware in the colonial United States."

"Dixie, also known as Dixieland or Dixie's Land, is a nickname for all or part of the Southern United States. While there is no official definition of this region (and the included areas have shifted over the years), or the extent of the area it covers, most definitions include the U.S. states below the Mason–Dixon line that seceded and comprised the Confederate States of America, almost always including the Deep South.[1] The term became popularized throughout the United States by songs that nostalgically referred to the American South."*Wik

In 1774, Joseph Priestley, British Presbyterian minister and chemist, identified a gas which he called "dephlogisticated air" -- later known as oxygen. Priestley found that mercury heated in air became coated with "red rust of mercury," which, when heated separately, was converted back to mercury with "air" given off. Studying this "air" given off, he observed that candles burned very brightly in it. Also, a mouse in a sealed vessel with it could breathe it much longer than ordinary air. A strong believer in the phlogiston theory, Priestley considered it to be "air from which the phlogiston had been removed." Further experiments convinced him that ordinary air is one fifth dephlogisticated air, the rest considered by him to be phlogiston. *TIS

Named from the Greek oxys + genes, "acid-former", oxygen was discovered in 1772 by  German-Sweedish chemist Carl Wilhelm Scheele  (although Joseph Priestley published his findings first) and independently by Priestly in 1774. Oxygen was given its name by the French scientist, Antoine Lavoisier.

 Joseph Priestley

1786 Caroline Herschel discovered her first comet, Comet Herschel C/1786 P1 and became history's first woman with this distinction **(see below). Her comet came to be known as the "first lady's comet" and brought with it the fame that secured her own place in history books.*The Woman Astronomer
** The Renaissance Mathematicus pointed out in a blog that "Maria Margarethe Kirch (née Winkelmann), the wife of Gottfried Kirch the Astronomer Royal of Berlin, discovered the comet of 1702 (C/1702 H1) that is forty-eight years before Caroline Herschel was born. Unfortunately the discovery was published by her husband and it was he who was incorrectly acknowledged as the discoverer. In 1710 Gottfried admitted the error and publicly acknowledged Maria as the discoverer but she was never official credited with the discovery.
Both Maria Kirch and Caroline Herschel were excellent astronomers with much important work to their credit. However credit where credit is due, Caroline was not the first woman to discover a comet, Maria was."

1814 Almost a month after eloping with Georgiana Whitmore; a marriage of which his father did not approve, Charles Babbage writes to his friend John Herschel, who knew nothing of his secret romance, "I am married and have quarreled with my father." Then after a few lines of self-justification, he explains some theorems he has been working on. Herschel was shocked, and responded on the seventh of the same month.*Anthony Hyman, Charles Babbage: Pioneer of the Computer

 Charles Babbage and his "Engine"

In 1831, New London Bridge opened to traffic. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendour by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for \$2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971.*TIS

1861 First use of "weather forecast". From the BBC I read, "Telling people what had happened was useful, but not as useful as telling them what was going to happen. The man who made the first attempt to bridge that gap, and who coined the phrase "weather forecast", was Admiral Robert Fitzroy. Thirty years before, he had been captain of the Beagle voyage that carried , so he was no stranger to the perils of weather when at sea. In 1854, Fitzroy was given the job of collecting data on weather at sea, leading what later became the Met Office. After a few years, he saw that weather systems could be tracked. He became convinced that predictions were possible and that storm warnings would save many lives. His bosses did not agree that predictions were realistic, but in spite of them Fitzroy started to issue storm warnings in 1861. Then, on the 1st of August 1861 (exactly 151 years ago), Fitzroy issued the first ever weather forecast for the general public, published in The Times. This earned him a slap on the wrist and a huge amount of criticism, because it was considered that the forecasts could not possibly be accurate. After a lot of debate, the public forecasts ended in 1866."   A tweet from @ Rebekah Higgitt corrected this to : weather predictions existed long before (including, but not only, astrological), but Aug 1861 *is* 1st use of term "weather forecast"..

1944 The MARK I computer began operation at Harvard. *VFR

1946 President Harry Truman signs the McMahon Act creating the Atomic Energy Commission.

* HT to Ben Gross ‏@bhgross144

1947 The Netherlands issued a postage stamp honoring Jans (Johan) de Witt (1625–1672), who did important early work dealing with analytic geometry. *VFR Besides being a statesman Johan de Witt, also was an accomplished mathematician. In 1659 he wrote "Elementa Curvarum Linearum" as an appendix to his translation of René Descartes' "La Géométrie". In this, De Witt derived the basic properties of quadratic forms, an important step in the field of linear algebra. *Wik

In 1957, the Solar Building (Bridgers and Paxton Office Building), Albuquerque NM, was the first commercial building to be heated by the sun's energy. It was subsequently listed in the National Register of Historic Places for its "exceptional importance," in the area of engineering because it was an early solar-heated commercial building, the equipment for which survived largely intact. It was constructed when active solar-energy systems were still considered experimental. The site is privately owned, at 213 Truman St., NE., Albuquerque, NM. The architectural design was provided by Wright and Stanley.*TIS

1963 Greece issued a postage stamp picturing the “Acropolis at Dawn” by Lord Baden-Powell.*VFR

To commemorate the realization of the 11th World Scout Jamboree in Greece, the Hellenic Post issued a special series of 5 stamps which circulated on August 1st, 1963, on the day the Jamboree officially opened.

1. DENOMINATION : 1 DRACHMA

“Athens at dawn”. A water-colour painted by Lord Baden-Powell of Gilwell in 1872, depicting the Acropolis and surrounding area. 2.5 million stamps of this denomination were circulated.

1967US Navy recalls Hopper to head COBOL effort.  The US Navy recalls Captain Grace Murray Hopper to active duty to help develop the programming language COBOL. With a team drawn from several computer manufacturers and the Pentagon, Hopper -- who had worked on the Mark I and II computers at Harvard in the 1940s -- created the specifications for COBOL (COmmon Business Oriented Language) with business uses in mind. These early COBOL efforts aimed at creating easily-readable computer programs with as much machine independence as possible. Designers hoped a COBOL program would run on any computer for which a compiler existed with only minimal modifications.
Hopper made many major contributions to computer science throughout her very long career, including what is likely the first compiler ever written, "A-0." She appears to have also been the first to coin the word "bug" in the context of computer science, taping into her logbook a moth which had fallen into a relay of the Harvard Mark II computer. She died on January 1, 1992.
The U.S. Navy commissioned their most advanced ship, the U.S.S. Hopper (DDG 70), on September 6, 1997 named in honor of Grace Hopper. *CMH

Log book showing the "bug" found caught in a Mark II relay

1980 Michael Aschbaher wrote Daniel Gorenstein that he had completed the classiﬁcation of the ﬁnite simple groups. This culminated a 20-year eﬀort by some 300 group theorists. The complete proof is about 5000 pages long. [Mathematics Magazine 54 (1981), p. 41

1986   Apple discontinues production of the Macintosh XL, effectively ending the life of the Apple Lisa computer platform. In January of 1985, the Macintosh line of computers was gaining momentum but the Lisa line of computers was not selling well. In order to salvage what they could from the Lisa and offer a more powerful Macintosh computer, Apple created the Macintosh XL model by modifying a Lisa 2/10 computer to run the Macintosh operating system. Apple discontinued the Lisa in April of 1985, but continued production of the hybrid Lisa/Mac Macintosh XL until this date. *This Day in Tech History

1987 The Italian Stronzo Bestiale appeared as a co-author in an erudite physics papers connecting fractal geometry, irreversibility, and the second law of thermodynamics,(Diffusion in a periodic Lorentz gas) along with the U.S. scientists Bill Moran and William G. Hoover. Until Bestiale joined them, the paper had been rejected. But Moran and Hoover had simply made this person up, and named him after hearing two Italian women on an aeroplane constantly referring to someone called “stronzo bestiale,”, which they discovered was not actually a person’s name, but meant “total asshole”. You can even get a T-shirt “I’m friends with Stronzo Bestiale”. *lenfisherscience

2011   Carolin Crawford selected as the Gresham Professor of Astronomy. *Wik

Crawford studied the Mathematical Tripos and received a Bachelor of Arts honours degree in mathematics at Newnham College, Cambridge in 1985. In 1988 she received her PhD[5] for research undertaken at the Institute of Astronomy, Cambridge on cooling flows.

After her PhD, Crawford progressed through a series of postdoctoral and research fellowships at Balliol College, Oxford, the Institute of Astronomy, Trinity Hall, Cambridge and Newnham College, Cambridge.[6] From 1996 to 2007 she held a Royal Society University Research Fellowship.

In 2004 she was appointed a Fellow and College Lecturer at Emmanuel College, Cambridge, where was also the undergraduate admissions tutor for the Physical Sciences. She held this position in conjunction with her role as Public Astronomer at the Institute of Astronomy, which she first took on in 2005.

She served as Gresham Professor of Astronomy at Gresham College from 2011 to 2015, a position in which she delivered free public lectures on astronomy and astrophysics in the City of London.[8]

Crawford's "primary research interests are in combining X-ray, optical and near-infrared observations to study the physical processes occurring around massive galaxies at the core of clusters of galaxies. In particular, she observes the complex interplay between the hot intra-cluster medium, filaments of warm ionized gas, cold molecular clouds, star formation and the radio plasma flowing out from the central supermassive black hole.

BIRTHS

1817 Sir (Joseph) Henry Gilbert (1 August 1817 - 23 December 1901) English chemist who as co-director with John Bennet Lawes of the Rothamsted Experimental Station, Hertfordshire, for over 50 years established a premier reputation for research at the first organized agricultural experimental station in the world. Their work applied skills in chemistry, meteorology, botany, animal and vegetable physiology, and geology to determine practical improvements for agricultural methods. They studied the nitrogen requirements of plants, how the element was taken up by plants, and the effects of nitrogen fertilizers on grain production and quality. In the 1840s, they initiated the manufacture of superphosphate fertilizer, one of their inventions.*TIS

 First Astronomy Class at Vassar College 1866

1818 Maria Mitchell (August 1, 1818 – June 28, 1889) First professional woman astronomer in the United States, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Scienes.
She became professor of astronomy at Vassar College in 1865, the first person (male or female) appointed to the faculty.  She was also named as Director of the Vassar College Observatory. After teaching there for some time, she learned that despite her reputation and experience, her salary was less than that of many younger male professors. She insisted on a salary increase, and got it. She taught at the college until her retirement in 1888, one year before her death.She died at age 70 in Lynn, Mass. *TIS

1861 Ivar Otto Bendixson (August 1, 1861 – 1935) taught at Stockholm, then from 1913 to 1927 he was rector of Stockholm University. He worked on set theory and differential equations. He is best remembered for the Poincaré - Bendixson theorem. *SAU

1881 Otto Toeplitz (1 August 1881, Breslau – 15 February 1940, Jerusalem) born in Breslau, Germany. In 1905 he received his Ph.D. in algebraic geometry at the university there and then moved to G¨ottingen, where he was deeply inﬂuenced by the work of Hilbert. He was also interested in the history of mathematics and held that only a mathematician of stature is qualiﬁed to be a historian of mathematics. In 1949 he published an introduction to the calculus on a historical basis. This delightful book is available in English as The Calculus. A Genetic Approach. *VFR

1905 Helen Battles (Sawyer) Hogg (1 Aug 1905, 28 Jan 1993) was a Canadian astronomer who located, cataloged and measured the distances to variable stars in globular clusters (stars with cyclical changes of brightness found within huge, dense conglomerations of stars located in the outer halo of the Milky Way galaxy). Her interest in astronomy was spurred when she witnessed a total eclipse of the sun in 1925. Alongside her career work, she was also foremost in Canada in popularizing astronomy, about which she wrote a column in the Toronto Star for thirty years. She was the first woman to become president of the Royal Canadian Institute. In 1989, the observatory at the National Museum of Science and Technology in Ottawa was dedicated in her name.*TIS

1913 Mischa Cotlar (August 1,1913, Sarny, Russian Empire – January 16, 2007, Buenos Aires, Argentina) was a mathematician who started his scientific career in Uruguay and worked most of his life on it in Argentina and Venezuela.

His contributions to mathematics are in the fields of harmonic analysis, ergodic theory and spectral theory. He introduced the Cotlar–Stein lemma. He was the author or co-author of over 80 articles in refereed journals.

According to Alberto Calderón, Cotlar showed in 1955 "that theorems on singular integrals can be generalized and put in the framework of ergodic theory." According to Krause, Lacey, and Wierdl, Karl E. Petersen in 1983 published an "especially direct proof" of Cotlar's 1955 theorem.

In January 1994 in Caracas, an international conference was held in his honor.*Wik

1924 Georges Charpak (1 August 1924 – 29 September 2010) was a French physicist who was awarded the Nobel Prize in Physics in 1992 "for his invention and development of particle detectors, in particular the multiwire proportional chamber". This was the last time a single person was awarded the physics prize. *Wik

1937 Barry Edward Johnson (1 Aug 1937 Woolwich, London, England – 5 May 2002 Newcastle upon Tyne, England) is well known for his work on Banach algebras and operator algebras, in particular, studying cohomology in these algebras. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. In these he examined the theory of centralizers and the continuity of transformations. In 1964 he wrote a joint paper with Ringrose Derivations of operator algebras and discrete group algebras and his next papers continued to examine the continuity of homomorphisms, derivations and linear operators. He developed cancer on February 2000 and fought the disease bravely. Despite his deteriorating physical condition, he continued to undertake cutting edge mathematical research. He died of cancer in St Oswald's Hospital in Newcastle upon Tyne aged 64. *SAU

1945 Douglas Dean Osheroff (born August 1, 1945) is an American physicist who shared with David M. Lee and Robert Richardson) was the corecipient of the 1996 Nobel Prize for Physics for their discoveryof superfluidity in the isotope helium-3. As helium is reduced in temperature toward almost absolute zero, a strange phase transition occurs, and the helium takes on the form of a superfluid. The atoms had until that point had moved with random speeds and directions. But as a superfluid, the atoms then move in a co-ordinated manner! *TiS, *Wik

1955 Bernadette Perrin-Riou (August 1, 1955 - ) was awarded the 1999 Ruth Lyttle Satter Prize in recognition of her number theoretical research on p-adic L-functions and Iwasawa theory.

1970 Elon Lindenstrauss (August 1, 1970 - ) was the first Israeli to be awarded the Fields Medal, for his results on measure rigidity in ergodic theory, and their applications to number theory.
Since 2004, he has been a professor at Princeton University. In 2009, he was appointed to Professor at the Mathematics Institute at the Hebrew University.
Lindenstrauss is the son of the mathematician Joram Lindenstrauss, the namesake of the Johnson–Lindenstrauss lemma, and computer scientist Naomi Lindenstrauss, both professors at the Hebrew University.
Lindenstrauss was awarded the Erdős Prize and the Fermat Prize in 2009. *Wik

DEATHS

1630 Federico Cesi (13 Mar 1585; 1 Aug 1630 at age 45) Italian scientist who founded the Accademia dei Lincei (1603, Academy of Linceans or Lynxes), often cited as the first modern scientific society, and of which Galileo was the sixth member (1611). Cesi first announced the word telescope for Galileo's instrument. At an early age, while being privately educated, Cesi became interested in natural history and that believed it should be studied directly, not philosophically. The name of the Academy, which he founded at age 18, was taken from Lynceus of Greek mythology, the animal Lynx with sharp sight. He devoted the rest of his life to recording, illustrating and an early classification of nature, especially botany. The Academy was dissolved when its funding by Cesi ceased upon his sudden death(at age 45). *TIS It was revived in its currently well known form of the Pontifical Academy of Sciences, by the Vatican, Pope Pius IX in 1847.

1896 Sir William Robert Grove, (11 July 1811 – 1 August 1896) British physicist and a justice of Britain's high court (from 1880), who first offered proof of the thermal dissociation of atoms within a molecule. He showed that steam in contact with a strongly heated platinum wire is decomposed into hydrogen and oxygen in a reversible reaction. In 1839, Grove mixed hydrogen and oxygen in the presence of an electrolyte, and produced electricity and water. This Grove Cell was the invention of the fuel cell. The technology was not seriously revisited until the1960s. Through the electrochemical process, the energy stored in a fuel is converted - without combusting fuel - directly into DC electricity.*TIS

1920 Bal Gangadhar Tilak (23 July 1856 – 1 August 1920, age 64), scholar, mathematician, philosopher, and militant nationalist who helped lay the foundation for India's independence. He founded (1914) and served as president of the Indian Home Rule League and, in 1916, concluded the Lucknow Pact with Mohammed Ali Jinnah, which provided for Hindu-Muslim unity in the struggle for independence. *TIS

1904 Adolf Lindenbaum (12 June 1904 – ? August 1941) was a Polish-Jewish logician and mathematician best known for Lindenbaum's lemma and Lindenbaum–Tarski algebras.

He was born and brought up in Warsaw. He earned a Ph.D. in 1928 under Wacław Sierpiński and habilitated at the University of Warsaw in 1934. He published works on mathematical logic, set theory, cardinal and ordinal arithmetic, the axiom of choice, the continuum hypothesis, theory of functions, measure theory, point-set topology, geometry and real analysis. He served as an assistant professor at the University of Warsaw from 1935 until the outbreak of war in September 1939. He was Alfred Tarski's closest collaborator of the inter-war period. Around the end of October or beginning of November 1935 he married Janina Hosiasson, a fellow logician of the Lwow–Warsaw school. He and his wife were adherents of logical empiricism, participated in and contributed to the international unity of science movement, and were members of the original Vienna Circle. Sometime before the middle of August 1941 he and his sister Stefanja were shot to death in Naujoji Vilnia (Nowa Wilejka), 7 km east of Vilnius, by the occupying German forces or Lithuanian collaborators

1987 Evelyn Merle Nelson (November 25, 1943 – August 1, 1987), born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science. Nelson's teaching record was, according to one colleague, "invariably of the highest order". However, before earning a faculty position at McMaster, prejudice against her lead to doubts about her teaching ability. Nelson published over 40 papers during her 20-year career before she died from cancer in 1987.
She, along with Cecilia Krieger, is the namesake of the Krieger–Nelson Prize, awarded by the Canadian Mathematical Society for outstanding research by a female mathematician. *Wik

1992 Leslie Fox (September 1918 Dewsbury, Yorkshire-1 August 1992 Oxford) was a British Mathematician noted for his contribution to numerical analysis.
Fox studied mathematics as a Scholar of Christ Church, Oxford graduating with a First in 1939 and continued to undertake research in the engineering department. While working on his D.Phil. in computational and engineering mathematics under the supervision of Sir Richard Southwell he was also engaged in highly secret war work. He worked on the numerical solution of partial differential equations at a time when numerical linear algebra was performed on a desk calculator. Computational efficiency and accuracy was thus even more important than in the days of electronic computers. Some of this work was published after the end of the Second World War jointly with his supervisor Richard Southwell.
On gaining his doctorate in 1942 Fox joined the Admiralty Computing service. Following the war, in 1945 he went to work in the mathematics division of the National Physical Laboratory. He left the National Physical Laboratory in 1956 and spent a year at the University of California. In 1957 Fox took up an appointment at Oxford University where he set up the Computing Laboratory. In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford and Fellow of Balliol College, Oxford.
Fox's laboratory at Oxford was one of the founding organisations of the Numerical Algorithms Group, and Fox was also a dedicated supporter of the Institute of Mathematics and its Applications (IMA). The Leslie Fox Prize for Numerical Analysis of the IMA is named in his honour.*Wik

1996 Tadeusz Reichstein (20 July 1897 – 1 August 1996) was a Polish-born Swiss chemist, botanist and Nobel laureate.

Reichstein, with Philip S. Hench and Edward C. Kendall, received the Nobel Prize for Physiology or Medicine in 1950 for his discoveries concerning hormones of the adrenal cortex, their structure and biological effects. With his co-workers, Reichstein accomplished the first isolation of four active hormones from the adrenal cortex, the first synthesis of one of them, the proof of the steroid nature of said hormones, and numerous details on the structure and properties of these important bodies. This made synthesis possible, leading to the creation of new medications *TiS *Wik

1999 Marie Paris Pişmiş de Recillas (30 January 1911 – 1 August 1999) was an Armenian-Mexican astronomer.

Pişmiş was born Mari Sukiasian (Armenian: Մարի Սուքիասեան) in 1911, in Ortaköy, Istanbul. She completed her high school studies at Üsküdar American Academy. In 1937, she became the first woman to get a Ph.D. from the Science Faculty of Istanbul University. Her advisor was Erwin Finlay Freundlich. Later, she went to Harvard University where she met her future husband Félix Recillas, a Mexican mathematician. They settled in Mexico, and she became the first professional astronomer in Mexico. According to Dorrit Hoffleit, "she is the one person most influential in establishing Mexico’s importance in astronomical education and research".

For more than 50 years she worked at UNAM which awarded her a number of prizes including the "Science Teaching Prize". She was a member of the Mexican Academy of Sciences.

Pişmiş studied among others the kinematics of galaxies, H II nebulae, the structure of open star clusters and planetary nebulae. She compiled the catalogue Pismis of 24 open clusters and 2 globular clusters in the southern hemisphere.

In 1998, she published an autobiography entitled "Reminiscences in the Life of Paris Pişmiş: a Woman Astronomer". She died in 1999. According to her wish, she was cremated. Her daughter Elsa Recillas Pishmish, son-in-law Carlos Cruz-González, and grand-daughter Irene Cruz-González also became astronomers. *Wik

2004 Philip Hauge Abelson (April 27, 1913 – August 1, 2004) was an American physicist, scientific editor and science writer. He proposed the gas diffusion process for separating uranium-235 from uranium-238 which was essential to the development of the atomic bomb. In collaboration with the U.S. physicist Edwin M. McMillan, he discovered a new element, later named neptunium, produced by irradiating uranium with neutrons. At the end WW II, his report on the feasibility of building a nuclear-powered submarine gave birth to the U.S. program in that field. In 1946, Abelson returned to the Carnegie Institution and pioneered in utilizing radioactive isotopes. As director of the Geophysics Laboratory of the Carnegie Institution (1953-71), he found amino acids in fossils, and fatty acids in rocks more than 1,000,000,000 years old. *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