The 97th day of the year; The number formed by the concatenation of odd numbers from one to 97 is prime. (1+3+5+7+9+11+13+15+17+... 93+95+97 quick students, how many digits will it have?) *Prime Curios
And from Cliff Pickover, 97 is the largest prime that we can ever find that is less than the sum of square of its digits 92 + 72 > 97
There are 97 leap days every 400 years in the Gregorian Calendar
97 is the smallest prime that has a prime alphabetical value in its Roman numerals-based representation (XCVII): 24 + 3 + 22 + 9 + 9 = 67 *Number Gossip
The longest whole-number name consisting entirely of alternating consonants and vowels is NINETY-SEVEN. However, if all integers are allowed, NEGATIVE NINETY-SEVEN would qualify.
Several more number facts about 97 at the Extended Number Facts pages.
EVENTS
1646 Torricelli sends "The geometry of indivisibles" To Michelangelo Ricci. He communicated the “universal theorem,” still considered the most general possible even today, which allows determination of the center of gravity of any figure through the relation between two integrals. *Encylopedia.com (Torricelli would use this method to find the volume of Torricelli's Trumpet (today often called Gabriel's Horn). A finite solid volume with an infinite surface area.
*Weisstein, Eric W. "Gabriel's Horn." From MathWorld
1666 Perhaps the kindest rejection letter ever, John Pell to Samuel Morland. British Polymath Morland had considered writing a book on the "quadrature of curvlinear spaces" and sent a sample to Pell, who responded:
*A brief account of the life, writings, and inventions of Sir. S. Morland
1696 John Bernoulli, in a letter to Leibniz, becomes the first to use the term "integral". Bernoulli had preferred the letter I for the integration symbol, but deferred to Leibniz preference, and adopted the script s, \( \int \) . Florian Cajori, The History of Notation in the Calculus (However.. I found this citation also credited to Cajori, :The word INTEGRAL first appeared in print by Jacob Bernoulli (1654-1705) in May 1690 in Acta eruditorum, page 218. He wrote, "Ergo et horum Integralia aequantur" (Cajori vol. 2, page 182; Ball). According to the DSB this represents the first use of integral "in its present mathematical sense."
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| Jacob Bernoulli |
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| Johann (John) Bernoulli |
1794 Joseph Priestley forever left England and traveled to the United States. Only a few years before, on 14 Jul 1791, his laboratory, home and library were burned to destruction by a mob of people angry at his support of the French Revolution. His French colleague, Lavoisier, was executed a week after Priestley left England. Priestley's discovery of oxygen was 20 years earlier, on 1 Aug 1774. During the last years of his life in America he spent his time quietly writing, and furthering the cause of Unitarianism in the new nation.
Thomas Jefferson to Joseph Priestley on 21 March 1801
Dear Sir
I learnt some time ago that you were in Philadelphia, but that it was only for a fortnight, & supposed you were gone. it was not till yesterday I rec would write eived information that you were still there, had been very ill but were on the recovery. I sincerely rejoice that you are so. yours is one of the few lives precious to mankind, & for the continuance of which every thinking man is solicitous.
Priestly is buried in Riverview Cemetery Northumberland, Northumberland County, Pennsylvania, USA
1794 On March 28, 1794, the president of the French commission that developed the metric system, Joseph Louis Lagrange, proposed using the day (French jour) as the base unit of time, with divisions déci-jour and centi-jour.
In 1795, the French National Convention passed a law introducing the metric system, putting Legendre in charge of the transition to the new system. The final system, as introduced in 1795, included units for length, area, dry volume, liquid capacity, weight or mass, and currency, but not time. Decimal time of day had been introduced in France two years earlier, but was set aside at the same time the metric system was inaugurated, and did not follow the metric pattern of a base unit and prefixed units.
On 22nd July 1799 the definitive standards of the metric system, the platinum metre and the platinum kilogramme, were ceremonially deposited in the French National Archives, and on 10th December 1799 a law was passed confirming their status as the only legal standards for measuring length and mass in France.
(The combination metric and decimal clock is at the Fitzwilliam Museum in Cambridge, U.K. The metric is on the outside scale, the duodecimal is on the small enamel dial inset above the center
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| *thepainterflynn |
Two and a half years after Walker's invention was made public, Isaac Holden arrived, independently, at the same idea of coating wooden splinters with Sulphur. The exact date of his discovery, according to his own statement, was October 1829. Previously to this date, Walker's sales-book contains an account of no fewer than 250 sales of friction matches, the first entry bearing the date 7 April 1827. Already comfortably well off, he refused to patent his invention, despite being encouraged to by Michael Faraday and others, making it freely available for anyone to make. He received neither fame nor wealth for his invention, although he was able to retire some years later. The credit for his invention was attributed only after his death.
Following the ideas laid out by the French chemist, Charles Sauria, who in 1830 invented the first phosphorus-based match by replacing the antimony sulfide in Walker’s matches with white phosphorus, matches were first patented in the United States in 1836, in Massachusetts, being smaller in size and safer to use. White phosphorus was later banned for public usage because of its toxicity. Today's modern matches were created by the Swedish chemist, Gustaf Erik Pasch.*Wik
1795, France adopted by law, the metre as the unit of length and the base of the metric system. Since there had been no uniformity of French weights and measures prior to the Revolution, the Academy of Sciences had been charged on 8 May 1790 to organise a better system. Delambre and Méchain measured an arc of the meridian from Dunkirk to Barcelona, so that the metre could be defined as one ten-millionth part of the distance between the poles and the equator. *TIS
One of the last remaining ‘mètre étalons’, or standard metre bars, can be found below a ground-floor window on the Ministry of Justice in Paris (Credit: PjrTravel/Alamy)
1880 Charles Darwin sent a letter to Francis Galton to call his attention to a letter and circular on “a queer subject” (fingerprinting) from Henry Faulds. Darwin suggests that Galton might want to present it at the Anthropological Institute, which he did. In his response the next day Galton says that he had taken several thumb prints several years before after “having heard of the Chinese plan with criminals.”. *Karl Pearson, The Life, Letters and Labours of Francis Galton
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| Galton |
1921 Albert Einstein attended a lecture on relativity at City College, New York. The speaker was Edward Kasner, the mathematician who introduced the term "Googol" (10^100).
Einstein praised Kasner's talk and spoke for 20 minutes afterward. *Paul Halpern
1940 Booker T. Washington becomes the first African American to be depicted on a United States postage stamp.
*The Painter Flynn
1953 IBM 701 formally dedicated at a luncheon at which Oppenheimer was the principal speaker. It used electrostatic storage tubes, a magnetic drum, and magnetic tapes. In all, 19 of these machines were built, and IBM was launched into the new world of electronic computers. [Goldstein, The Computer from Pascal to von Neumann, p. 328]*VFR
IBM 701 operator's console
1964 IBM Announces "System 360" Computer Family:
IBM announces the release of its "System 360" mainframe computer architecture--embodied in five new models--launching its most successful computer system of all time. Called the "360" because it was meant to address all possible sizes and types of customer with one unified software-compatible architecture, the 360 family of machines generated in excess of $100 billion in revenue for IBM.*CHM
1970 The Netherlands issued a set of five stamps designed with the aid of a computer. Journal of Recreational Mathematics, 4(1971), 20–23, . *VFR
1978 An editorial in the Pensacola Journal on minimum competency in English and mathematics stated, “After all, if you give the test to four students and four flunk, that’s a 50 percent failure rate.” [The AMATYC Journal, 13(1979), 59]
1981 The fastest computation of the 13th root of a 100-digit number is in 1 minute and 28.8 seconds by Willem Klein. [Guinness]
1989 To start his after-dinner remarks at a meeting of the Ohio Section of the MAA, Gerald Alexanderson told the following story that he had heard from Polya, who heard it from Lebesgue: At the coliseum in Rome the emperor ordered a lion to be brought into the arena with a Christian. The Christian whispered something in the lion’s ear and the lion became meek and whimpered away. This scene was repeated with increasingly ferocious lions. Finally the emperor told the Christian that he could go free if he would tell him what he was saying to the lion. The response was truly frightening: “After dinner you have to give a speech.”
BIRTHS
1768 François Joseph Français (7 April 1768 in Saverne, Bas-Rhin, France - 30 Oct 1810 in Mainz, Germany) Much of François Français's work was published after his death by his brother who added to it in a way to make the contribution of each hard to distinguish. François worked on partial differential equations and his memoir of 1795 on this topic was developed further and presented to the Académie des Sciences in 1797. Lacroix praised Français' work and described it as making a major contribution to the study of partial differential equations; however, it was not published.*SAU
1809 James Glaisher FRS (7 April 1809 – 7 February 1903) was an English meteorologist, aeronaut and astronomer.
Born in Rotherhithe, the son of a London watchmaker, Glaisher was a junior assistant at the Cambridge Observatory from 1833 to 1835[2] before moving to the Royal Observatory, Greenwich, where he served as Superintendent of the Department of Meteorology and Magnetism at Greenwich for 34 years.
In 1845, Glaisher published his dew point tables for the measurement of humidity. He was elected a Fellow of the Royal Society in June 1849.
He was a founding member of the Meteorological Society (1850) and the Aeronautical Society of Great Britain (1866). He was president of the Royal Meteorological Society from 1867 to 1868. Glaisher was elected a member of The Photographic Society, later the Royal Photographic Society, in 1854 and served as the society's president for 1869–1874 and 1875–1892. He remained a member until his death. He was also President of the Royal Microscopical Society. He is most famous as a pioneering balloonist. Between 1862 and 1866, usually with Henry Tracey Coxwell as his co-pilot, Glaisher made numerous ascents to measure the temperature and humidity of the atmosphere at the greatest altitudes attainable at that time.
Their ascent on 5 September 1862 broke the world record for altitude but he passed out around 8,800 metres (28,900 feet) before a reading could be taken. One of the pigeons making the trip with him died. Estimates suggest that he rose to more than 9,500 metres (31,200 feet) and as much as 10,900 metres (35,800 feet) above sea level. Glaisher lost consciousness during the ascent and Coxwell lost all sensation in his hands. The valve-line had become entangled so he was unable to release the mechanism; with great effort, he climbed onto the rigging and was finally able to release the vent before losing consciousness. This allowed the balloon to descend to a lower altitude.
The two made additional flights. According to the Smithsonian Institution, Glaisher "brought along delicate instruments to measure the temperature, barometric pressure and chemical composition of the air. He even recorded his own pulse at various altitudes".
In 1871, Glaisher arranged for the publication of his book about the balloon flights, Travels in the Air, a collection of reports from his experiments. To ensure that numerous members of the general public would learn from his experiences, he included "detailed drawings and maps, colorful accounts of his adventures and vivid descriptions of his precise observations", according to one report.
He died in Croydon, Surrey in 1903, aged 93. *Wik
James Glaisher (left) and Henry Tracey Coxwell Ballooning in 1864
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1823 Guillaume-Jules Hoüel (April 7, 1823 in Thaon; June 14, 1886 in Périers) was a French mathematician. He entered the École Normale Supérieure in 1843. He originally did research on celestial mechanics, but later became interested in Non-Euclidean geometry and corresponded with Joseph Tilly.*Wik
Hoüel became interested in non-euclidean geometry once he had been made aware of the work of Bolyai and Lobachevsky. He published translations of many important works by Bolyai, Beltrami, Helmholtz and Riemann. He corresponded with Tilly on non-euclidean geometry. *SAU
Hoüel became interested in non-euclidean geometry once he had been made aware of the work of Bolyai and Lobachevsky. He published translations of many important works by Bolyai, Beltrami, Helmholtz and Riemann. He corresponded with Tilly on non-euclidean geometry. *SAU
1866 Erik Ivar Fredholm (April 7, 1866 – August 17, 1927) Swedish mathematician who is remembered for Fredholm integral equations with applications in mathematical physics and actuarial science. His first paper (1890) was on a special class of functions inspired by the heat equation. His 1898 doctoral dissertation involved a study of partial differential equations motivated by an equilibrium problem in elasticity. Fredhlom also had a career in actuarial science and from 1902 onwards he studyied various questions in this area, including an elegant formula he proposed to determine the surrender value of a life insurance policy. He built a machine to solve differential equations. David Hilbert extended one of Fredholm's integral equations discoving Hilbert spaces on which would be built the quantum theory.*TIS
1897 Tatsujiro Shimizu (清水 辰次郎, Shimizu Tatsujirō, 7 April 1897 – 8 November 1992) was a Japanese mathematician working in the field of complex analysis. He was the founder of the Japanese Association of Mathematical Sciences.
Shimizu graduated from the Department of Mathematics, School of Science, Tokyo Imperial University in 1924, and stayed there working as a staff member. In 1932 he moved to Osaka Imperial University and became a professor. He made contributions to the establishment of the Department of Mathematics there. In 1949, Shimizu left Osaka and took up a professorship at Kobe University. After two years, he moved again to Osaka Prefectural University. From 1961 he was a professor at the Tokyo University of Science.[2][3]
In 1948, seeing the difficulty in publication of paper in mathematics, Shimizu started a new journal Mathematica Japonicae, for papers of pure and applied mathematics in general, on his own funds. The journal served as the foundation of the Japanese Association of Mathematical Sciences.
Shimizu remained active in mathematics into old age. He gave talks at the meeting of the Mathematical Society of Japan until 90 years old. He died in Uji City, Kyoto Prefecture, on November 8, 1992, at the age 95. *Wik
1923 Peter John Hilton (7 April 1923 – 6 November 2010) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War. Hilton's principal research interests were in algebraic topology, homological algebra, categorical algebra, and mathematics education. He published 15 books and over 600 articles in these areas, some jointly with colleagues.*Wik
1959 Leopoldo Luis Cabo Penna Franca (7 April 1959, 19 September 2012) was a Brazilian mathematician who had a major impact in the development and analysis of innovative finite element methods. He worked mainly on stabilised methods for fluids, acoustics and solids, residual-free methods, and enriched methods for transport equations.
After the award of his Master's Degree, Franca wished to continue to study for a Ph.D. supported by CAPES and was able to undertake research at Stanford University in California. Before the award of his Ph.D., Franca had over ten papers in print. His early papers were written with several fellow students and staff in the Division of Applied Mechanics, Durand Building, Stanford University. These included Franca's thesis advisor Thomas J R Hughes and Michel Mallet, Marc Balestra, Isaac Harari, together with the Brazilian post-doctoral student Abimael Fernando Dourado Loula who had been awarded his doctorate by the Federal University in Rio de Janeiro in 1979.
In 2011 he briefly joined National Laboratory for Scientific Computing at the Ministério da Ciência e Tecnologia but, later in the same year, he joined the new IBM Research Laboratory in Brazil, the first IBM Research Laboratory in the Southern Hemisphere. It was established in June 2010, with locations in São Paulo and Rio de Janeiro. Ulisses Mello, engineer and associate director at IBM Research, Brazil, led the Smarter Natural Resources & Discovery strategic group and it was this group that Franca joined as a senior research scientist. He worked on projects involving applications of computational mathematics and mechanics to the oil industry. While working for IBM, Franca was one of six members of staff who applied for a patent for Method to assess the impact of existing fractures and faults for reservoir management on 9 November 2012. Sadly Franca had died two months before the application for the patent was filed. *SAU
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DEATHS
1823 Jacques-Alexandre-César Charles (12 Nov 1746, 7 Apr 1823 at age 76) French mathematician, physicist, and inventor. When Benjamin Franklin visited France in 1779, Charles was inspired to study physics. He soon became an eloquent speaker to non-scientific audiences. His lectures and demonstrations attracted notable patrons and helped popularize Franklin's theory of electricity and other new scientific concepts. With Nicolas and Anne-Jean Robert, he made several balloon ascents, and was the first to use hydrogen for balloon inflation (1783). Charles invented most of the equipment that is still used in today's balloons.
About 1787 he developed Charles's law concerning the thermal expansion of gases that for a gas at constant pressure, its volume is directly proportional to its absolute temperature. *TIS
Charles's law (also known as the law of volumes), describing how gases tend to expand when heated, was first published by natural philosopher Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Charles, and named the law in his honor.
Around 1787 Charles did an experiment where he filled five balloons to the same volume with different gases. He then raised the temperature of the balloons to 80 °C (not at constant temperature) and noticed that they all increased in volume by the same amount. This experiment was referenced by Gay-Lussac in 1802 when he published a paper on the precise relationship between the volume and temperature of a gas. Charles' law states that under constant pressure, an ideal gas' volume is proportional to its absolute temperature. The volume of a gas at constant pressure increases linearly with the absolute temperature of the gas. The formula he created was V1/T1 = V2/T2.
*Wik
1889 Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg. He was the brother of Emil du Bois-Reymond.
His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent (more specifically, that diverges at every point). His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.
Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function.
He developed a theory of infinitesimals in Über die Paradoxen des Infinitär-Calcüls ("On the paradoxes of the infinitary calculus") in 1877. He wrote,
The infinitely small is a mathematical quantity and has all its properties in common with the finite ... A belief in the infinitely small does not triumph easily. Yet when one thinks boldly and freely, the initial distrust will soon mellow into a pleasant certainty ... A majority of educated people will admit an infinite in space and time, and not just an "unboundedly large". But they will only with difficulty believe in the infinitely small, despite the fact that the infinitely small has the same right to existence as the infinitely large ...
*Wik
1889 Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg. He was the brother of Emil du Bois-Reymond.
His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent (more specifically, that diverges at every point). His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.
Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function.
He developed a theory of infinitesimals in Über die Paradoxen des Infinitär-Calcüls ("On the paradoxes of the infinitary calculus") in 1877. He wrote,
The infinitely small is a mathematical quantity and has all its properties in common with the finite ... A belief in the infinitely small does not triumph easily. Yet when one thinks boldly and freely, the initial distrust will soon mellow into a pleasant certainty ... A majority of educated people will admit an infinite in space and time, and not just an "unboundedly large". But they will only with difficulty believe in the infinitely small, despite the fact that the infinitely small has the same right to existence as the infinitely large ...
*Wik
1933 Raymond Edward Alan Christopher Paley,(7 January 1907 – 7 April 1933) was killed at age 26 in an avalanche while skiing near Banff, Alberta, Canada. G. H. Hardy wrote of this young analyst: “There is something very intimidating to an older man in such youthful quickness and power, and of all the people who frightened me when I came back to Cambridge, Paley was the man who frightened me the most.” [Collected Papers of G. H. Hardy, vol. 7, p. 745.]*VFR (He was buried in Banff)
His contributions include the Paley construction for Hadamard matrices (closely related to the Paley graphs in graph theory) and his collaboration with Norbert Wiener in the Paley–Wiener theorem (harmonic analysis). He collaborated with A. Zygmund on Fourier series (see also Paley–Zygmund inequality) and worked with J. E. Littlewood on what became known as Littlewood–Paley theory, an application of real-variable techniques in complex analysis.
Paley graphs are an important family of graphs in combinatorics and graph theory. They are examples of quasi-random graphs: explicit, deterministic networks exhibiting properties we typically expect to see asymptotically in random graphs.
Consider a prime power p congruent to 1 (mod 4), and let vertices be the elements of the finite field of order p. Two distinct vertices are adjacent if their difference is a non-zero square in the field. This is the p–Paley graph.
For example, in the case of p = 5, the finite field has elements 0, 1, 2, 3, and 4, and the non-zero squares are 1 and 4 (which equals -1 (mod 5)). So differences should be 1 or -1. Thus, in the 5-Paley graph each vertex i is adjacent to i+1 and i-1 (mod 5). This is just the 5-cycle, as depicted below. *Wik
1934 Ernst Paul Heinz Prüfer (10 Nov 1896 in Wilhelmshaven, Germany - 7 April 1934 in Münster, Germany)proved important results about abelian groups.*SAU
He worked on abelian groups, algebraic numbers, knot theory and Sturm-Liouville theory. His advisor was Issai Schur.
He is remembered for the Prüfer sequence (also known as a Prüfer code; it has broad applications in graph theory and network theory).*Wik
1986 : Leonid Vitalyevich Kantorovich (19 Jan 1912, 7 Apr 1986 at age 74) Soviet mathematician and economist who shared the 1975 Nobel Prize for Economics with Tjalling Koopmans for their work on the optimal allocation of scarce resources. Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication Mathematical methods of organising and planning production which he published in 1939. The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed *TIS
2014 James Alexander "Sandy" Green FRS (26 February 1926 – 7 April 2014) was a mathematician and Professor at the Mathematics Institute at the University of Warwick, who worked in the field of representation theory.
He was born in February 1926 in Rochester, New York, but moved to Toronto with his emigrant Scottish parents later that year. The family returned to Britain in May 1935 when his father, Frederick C. Green, took up the Drapers Professorship of French at the University of Cambridge.
He won a scholarship to the University of St Andrews and matriculated aged 16 in 1942. He took an ordinary BSc in 1944, and then, after scientific service in the war, was awarded a BSc Honours in 1947. He gained his PhD at St John's College, Cambridge in 1951, under the supervision of Philip Hall and David Rees.
In the summer of 1944, he was conscripted for national scientific service at the age of eighteen, and was he was assigned to work at Bletchley Park, where he acted as a human "computer" carrying out calculations in Hut F, the "Newmanry", a department led by Max Newman, which used special-purpose Colossus computers to assist in breaking German naval codes.
His first lecturing post (1950) was at the University of Manchester, where Newman was his Head of department. In 1964 he became a Reader at the University of Sussex, and then in 1965 was appointed as a professor at the newly formed Mathematics Institute at Warwick University, where he led the algebra group. He spent several periods as a visiting academic in the United States, beginning with a year at the Institute for Advanced Study in Princeton, New Jersey in 1960–61, as well as similar visits to universities in France, Germany and Portugal.[citation needed] After retiring from Warwick he became a member of the faculty and Professor Emeritus at the Mathematics Institute of the University of Oxford, in whose meetings he participated actively. His final publication was produced at the age of eighty.
Green found all the characters of general linear groups over finite fields (Green 1955) and invented the Green correspondence in modular representation theory. Both Green functions in the representation theory of groups of Lie type and Green's relations in the area of semigroups are named after him. His final publication (2007) was a revised and augmented edition of his 1980 work, Polynomial Representations of GL(n).
Green met his wife, Margaret Lord, at Bletchley Park, where she worked as a Colossus operator, also in the Newmanry section (Hut F). The couple married in August 1950, and have two daughters and a son. Up to his death, he lived in Oxford.
He was elected to the Royal Society of Edinburgh in 1968 and the Royal Society in 1987 and was awarded two London Mathematical Society prizes: the Senior Berwick Prize in 1984 and the de Morgan Medal in 2001.
*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
