On This Day in Math - July 4

Things that people learn purely out of curiosity

can have a revolutionary effect on human affairs

~Frederick Seitz - born 100 years ago today


EVENTS
1045 The Crab Nebula supernova is recorded in China and Japan. *VFR U.S. president who was throughout his lifetime an extraordinarily learned man, including interests in mathematics and natural sciences. He corresponded with such men as Joseph Priestley, and sometimes contributed time and money to progress in these fields. He collected and classified fossils. He was interested in the experiments being made in ballons and submarines. While visiting Europe, he sent home various mechanical and scientific gadgets produced including a polygraph and phosphorus matches. At his Monticello estate, he practiced scientific farming, and was always on the lookout for a significant new plant or seed. Jefferson died shortly before 1pm. His old friend, John Adams, died a few hours later.*TIS

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1662 “By and by comes Mr. Cooper ... of whom I entend to learn Mathematiques; and so begin with him today ... . After an hour’s being with him at Arithmetique, my first attempt being to learn the Multiplication table, then we parted till tomorrow.” Samuel Pepys, in his diary....At the time he was something like a modern Secretary of the Navy. *VFR

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1744 Euler wrote Christian Goldbach that he has finished his book Introductio in analysin infinitorum (Lausanne 1748). In this work the trigonometric and logarithmic functions were first treated in their modern form. *VFR

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

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1819 William Herschel writes to his sister, Caroline, "Lina, there is a great comet. I want you to come and assist me. Come to dine and spend the day here.... we shall have time to prepare maps and telescopes. I saw it's situation last night, it has a long tail." He was eighty years old at the time, and he was still at work when he died, two years later. *Timothy Ferris, Coming of Age in the Milky Way

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1843 Liouville began an address to the Academy of Sciences with the words: “I hope to interest the Academy in announcing [that in] the papers of Evariste Galois I have found a solution, as precise as it is profound, of this beautiful problem: whether or not it [the general equation of fifth degree] is solvable by radicals.” This work of Galois was published in 1846. *VFR

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1862 Charles Lutwidge Dodgson, mathematics teacher at Oxford, went boating on the Isis, a tributary of the Thames, with the three daughters of Henry George Liddell, dean of Christ Church, Oxford. He was especially fond of Alice Liddell, then ten, and it was mainly for her that he began the story of another Alice’s tumble down a rabbit hole. The work was published exactly three years later as Alice’s Adventures under Ground under the pseudonym Lewis Carroll, with the famous illustrations by John Tenniel (see note). This work is a favorite of mathematicians, so if you haven’t read it recently, you should. See 26 November 1864. [Note: "When Charles Dodgson – more widely known as Lewis Carroll – made drawings in the early 1960s for his book Alice’s Adventures in Wonderland, he was disappointed with the results. He employed cartoonist John Tenniel to create the now-famous illustrations, while his original ideas were consigned to the archive of Christ Church College, Oxford, where he worked as a lecturer in mathematics until his death in 1898. TATE ETC. sent a cultural historian to view Dodgson’s rarely seen drawings which feature in Tate Liverpool’s ‘Alice in Wonderland’ exhibition. " *Tate ETC] From Nov 2011 to Jan 2012 the Tate Liverpool was showing these original works as part of the "Alice in Wonderland" exhibit. You can see some of them at the web page where I found the notes above.)

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1963 The San Francisco Chronicle carried a report entitled, “A Milestone in Math—Professor’s New Concept,” by David Perlman. This popular account of Paul J. Cohen’s proof of the independence of the axiom of choice was probably the first published. *VFR

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2011 Independence day occurs on Monday. In what year will it next appear on a Monday? And the time after that?

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BIRTHS
1790 Sir George Everest, British military engineer and geodesist, born in Gwernvale, Powys, Wales, UK. He worked on the trigonometrical survey of India (1818-43), providing the accurate mapping of the subcontinent. For more than twenty-five years and despite numerous hardships, he surveyed the longest arc of the meridian ever accomplished at the time. Everest was relentless in his pursuit of accuracy. He made countless adaptations to the surveying equipment, methods, and mathematics in order to minimize problems specific to the Great Survey: immense size and scope, the terrain, weather conditions, and the desired accuracy. Mount Everest, formerly called Peak XV, was renamed in his honour in 1865. *TIS

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1868 Henrietta Swan Leavitt American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies.*TIS

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1906 Dan Rutherford studied at St Andrews and Amsterdam. He spent most of his career in St Andrews becoming Gregory Professor of Applied Mathematics. In spite of this title most of his research was in pure mathematics and in particular in algebra. He became President of the EMS in 1940 and 1963. *SAU

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1911 Frederick Seitz American physicist who made fundamental contributions to the theory of solids, nuclear physics, fluorescence, and crystals. As Eugene Wigner's first doctoral student, late in 1932, Seitz developed the cellular method of deriving solid-state wave functions. The widespread application of this Wigner-Seitz method to the understanding of metals is regarded as the catalyst for the formation of the field of solid-state physics in the U.S. His subsequent research focused on the theory and properties of crystals. He studied dislocations and imperfections in crystal structures, the effect of irradiation on crystals, and the process of diffusion (the movement of atoms or particles caused by random collision) in crystalline materials.*TIS

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1945 John Paulos born in Denver, Colorado. Currently a professor at Temple University, he is the author of the popular book Innumeracy. *VFR American mathematician and author of books encouraging people to make sense of the statistics and figures that inform their lives. He represents that mathematics as a subject that is easy to learn and understand. Paulos argues that ignorance of basic mathematical concepts discourages critical thinking and results in costly mistakes and misguided decisions by both political leaders and ordinary people in their everyday lives.*TIS

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DEATHS
1742 Guido Grandi died. He corresponded with Leibniz on the sum of the series 1−1+1−1+1−•••. *VFR Luigi Guido Grandi (October 1, 1671 – July 4, 1742) was an Italian priest, philosopher, mathematician, and engineer born in Cremona. He was Jesuit-educated and became a member of the Camaldolese order. He became a professor of philosophy at the Camaldolese monastery in Florence in 1700 and a professor of mathematics in 1714.
In mathematics Grandi is best known for studying the rose curve, a curve which has the shape of a petalled flower, and for Grandi's series. He named the rose curve rhodonea. He also contributed to Note on the Treatise of Galileo Concerning Natural Motion in the first Florentine edition of Galileo Galilei's works and helped introduce Gottfried Leibniz's ideas on calculus to Italy. He also worked as an engineer, being superintendent of water at Tuscany, and in that capacity he was involved in the drainage of the Chiana Valley. In 1709 he visited England where he was elected a Fellow of the Royal Society.*Wik

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1826 Thomas Jefferson died and was buried at Monticello. He wrote his own epitaph: “Here was buried Thomas Jefferson, author of the Declaration of Independence, of the statute of Virginia for religious freedom, and father of the University of Virginia.” *VFR

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U.S. president who was throughout his lifetime an extraordinarily learned man, including interests in mathematics and natural sciences. He corresponded with such men as Joseph Priestley, and sometimes contributed time and money to progress in these fields. He collected and classified fossils. He was interested in the experiments being made in ballons and submarines. While visiting Europe, he sent home various mechanical and scientific gadgets produced including a polygraph and phosphorus matches. At his Monticello estate, he practiced scientific farming, and was always on the lookout for a significant new plant or seed. Jefferson died shortly before 1pm. His old friend, John Adams, died a few hours later.*TIS

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1901 Peter Guthrie Tait Scottish physicist and mathematician who helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics.*TIS Tait was a fellow-pupil of Maxwell at Edinburgh Academy and both of them went on to study at Edinburgh University and Cambridge. Tait became Professor of Mathematics at Queen's College Belfast and then moved to the Chair of Natural Philosophy at Edinburgh which he occupied for more than 40 years. With his collaborations with Maxwell, Thomson (Lord Kelvin) and Hamilton he made important contributions in both mathematics and physics. He became one of the first honorary members of the EMS in 1883. *SAU

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1910 Giovanni Virginio Schiaparelli, Italian astronomer who is remembered for his observations of Mars over seven oppositions and named the "seas" and "continents". In 1877, he saw on the surface of the planet Mars the markings that he called canali (channels), later misinterpreted as "canals." He made extensive studies, both observational and theoretical, of comets, determining from the shapes of their tails that there was a repulsive force from the sun. He showed that meteor swarms travel through space in cometary orbits. He explained the regular meteor showers as the result of the dissolution of comets and proved it for the Perseids. He suggested that Mercury and Venus rotate on their axes, discovered the asteroid Hesperia (1861) and was a major observer of double stars.*TIS

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1934 Marie Marja Sklodowska Curie was a Polish-born French chemist and physicist. In 1898, her celebrated experiments on uranium minerals led to discovery of two new elements. First she separated polonium, and then radium a few months later. The quantity of radon in radioactive equilibrium with a gram of radium was named a curie (subsequently redefined as the emission of 3.7 x 1010 alpha particles per sec.) With Henri Becquerel and her husband, Pierre Curie, she was awarded the 1903 Nobel Prize for Physics. She was then sole winner of a second Nobel Prize in 1911, this time in Chemistry. Her family won five Nobel awards in two generations. She died of radiation poisoning from her pioneering work before the need for protection was known.*TIS

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1962 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

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1986 Oscar Zariski's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties.*SAU

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1987 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

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2002 Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work (developing the theory of distributions, a new notion of generalized functions motivated by the Dirac delta-function of theoretical physics). He was the first French mathematician to receive the Fields medal. For a long time he taught at the École polytechnique. *Wik

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Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

On This Day in Math - July 3

Music is the pleasure the human mind experiences from counting

without being aware that it is counting. 

 ~Gottfried Leibniz

EVENTS
1822 Charles Babbage described his ideas for a “difference engine” to the Royal Society. *VFR

1841, John Couch Adams decided to determine the position of an unknown planet by the irregularities it causes in the motion of Uranus. He entered in his journal; "Formed a design in the beginning of this week in investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus... in orderto find out whether they may be attributed to the action of an undiscovered planet beyond it..." In Sep 1845 he gave James Challis, director of the Cambridge Observatory, accurate information on where the new planet, as yet unobserved, could be found; but unfortunately the planet was not recognized at Cambridge until much later, after its discovery at the Berlin Observatory on 23 Sep 1846. *TIS

2011  Astronomers using the Hubble Space Telescope discovered a fourth moon orbiting the icy dwarf planet Pluto. The tiny, new satellite – temporarily designated P4 -- was uncovered in a Hubble survey searching for rings around the dwarf planet.

Two labeled images of the Pluto system taken by the Hubble Space Telescope's Wide Field Camera 3 ultraviolet visible instrument with newly discovered fourth moon P4 circled. The image on the left was taken on June 28, 2011. The image of the right was taken on July 3, 2011. Credit: NASA, ESA, and M. Showalter (SETI institute)


BIRTHS
1820 Ernest de Jonquières was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU

1866 Henry Baker spent his whole life in Cambridge and worked on Geometry and Analysis and inspired a younger generation of geometers.. He was made an honorary member of the EMS in 1926. *SAU

1897 Jesse Douglas born in New York City. He did important work on Plateau’s problem, which asks for the minimal surface connecting a given boundary. For this work he received a Fields medal in 1936, the first time that they were given. *VFR ..the Plateau problem... had first been posed by the Italian-French mathematician Joseph-Louis Lagrange in 1760. The Plateau problem is one of finding the surface with minimal area determined by a fixed boundary. Experiments (1849) by the Belgian physicist Joseph Plateau demonstrated that the minimal surface can be obtained by immersing a wire frame, representing the boundaries, into soapy water. Douglas developed what is now called the Douglas functional, so that by minimizing this functional he could prove the existence of the solution to the Plateau problem. Douglas later developed an interest in group theory.*TIS

1933 Frederick Justin Almgren, Almost certainly Almgren's most impressive and important result was only published in 2000, three years after his death. Why was this? The paper was just too long to be accepted by any journal. Brian Cabell White explains the background in a review of the book published in 2000 containing the result:-
By the early 1970s, geometric analysts had made spectacular discoveries about the regularity of mass-minimizing hypersurfaces. (Mass is area counting multiplicity, so that if k sheets of a surface overlap, the overlap region is counted k times.) In particular, the singular set of an m-dimensional mass-minimizing hypersurface was known to have dimension at most m - 7. By contrast, for an m-dimensional mass-minimizing surface of codimension greater than one, the singular set was not even known to have m-measure 0. Around 1974, Almgren started on what would become his most massive project, culminating ten years later in a three-volume, 1700-page preprint containing a proof that the singular set not only has m-dimensional measure 0, but in fact has dimension at most (m - 2). This dimension is optimal, since by an earlier result of H Federer there are examples for which the dimension of the singular set is exactly (m - 2). ... Now, thanks to the efforts of editors Jean Taylor and Vladimir Scheffer, Almgren's three-volume, 1700-page typed preprint has been published as a single, attractively typeset volume of less than 1000 pages.*SAU

1933 William (Bill) Parry FRS (3 July 1934–20 August 2006) was an English mathematician. During his research career, he was highly active in the study of dynamical systems, and, in particular, ergodic theory, and made significant contributions to these fields. He is considered to have been at the forefront of the introduction of ergodic theory to the United Kingdom. He played a founding role in the study of subshifts of finite type, and his work on nilflows was highly regarded.*Wik

1945 Saharon Shelah (Hebrew: שהרן שלח‎) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Shelah is one of the most prolific contemporary mathematicians. As of 2009, he has published nearly 900 mathematical papers (together with over 200 co-authors). His main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.*Wik

DEATHS
1749 William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November, 1711 he became a Fellow of the Royal Society, and was later its Vice-President.*Wik

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1789 Jakob Bernoulli II died. *VFR 
Born in Basel in 1759 (17 October), the son of Johann (II). 1780 assistant to Daniel in experimental physics

He graduated in Jurisprudence in 1778 but also studied Maths and Physics. In 1782, he applied for Daniel's former chair but was unsuccessful.

He became secretary to an imperial representative in Venice

In 1786 he went to Petersburg, to the Academy of Science (Fuss recommended him to Dashkoff) and in 1788 became ordentlich academy member for mathematics.

He married one of Euler's granddaughters, Charlotte.

At thirty years of age, he drowned in the Neva.  *Brian Daugherty

1991 Ernst Witt (June 26, 1911-July 3, 1991) was a German mathematician born on the island of Als (German: Alsen). Shortly after his birth, he and his parents moved to China, and he did not return to Europe until he was nine.
Witt's work was mainly concerned with the theory of quadratic forms and related subjects such as algebraic function fields.*Wik

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

On This Day in Math - July 2

OOPS...

Heavier-than-air flying machines are impossible.
  I have not the smallest molecule of faith in aerial navigation other than ballooning, 

or of the expectation of good results from any of the trials we hear of. 1895

And in a Letter to Baden-Powell (1896) Radio has no future.

William Thomson, Lord Kelvin

EVENTS
1133 First trade security agreement between Pisans and Alibibn Yusof of Morocco.  Under such an agreement, Guilielmo, father of Leonardo brought his young son (who would much later be called Fibonacci) to Bugia, where he would learn of the Arabic calculation system that he would introduce to his  homeland in his Liber Abbaci in 1202.  *Devlin, The Man of Numbers

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1832   Legendre writes to Nathanial Bowditch regarding his translation of LaPlace's "Mecanique Celeste" ,"Your work is not merely a translation with a commentary; I regard it as a new edition, augmented and improved, and such a one as might have come from the hands of the author himself, ... if he had been solicitously studious of being clear."   LaPlace's classic is a very difficult book, and Biot, who helped him prepare it for printing said that Laplace himself would frequently get lost in following his own line of reasoning  and insert, "il est aise a voir" (It is easy to see).  *The Teaching and History of Mathematics in the United States, F. Cajori

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1850 Stokes’s theorem made its first appearance as a postscript to a letter from Sir William Thompson (Lord Kelvin) to Stokes. It first appeared publicly as question 8 on the Smith’s Prize exam for 1854. Stokes drew up this competitive exam, which was taken by the best mathematics students at Cambridge University. By the time Stokes died the theorem was universally known as “Stokes’s theorem.” [Spivak, Calculus on Manifolds, p. viii].

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1897 – Italian scientist Guglielmo Marconi obtains a patent for radio in London.*Wik

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1982 Science (p. 39) reported that Steven Smale had proved that the average-case behavior of the simplex algorithm for linear programming is far better than the worse-case behavior, which is exponential. [Mathematics Magazine 56 (1983), p. 55]. *VFR

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2011 Simon Chua, 58, received Australia's B. H. Neumann Award for pioneering efforts in training and honing the talent of young Filipino mathematicians for the past 15 years.

The Australian Mathematics Trust (AMT) bestowed the award to Chua on July 2, 2011. The B. H. Neumann Awards are presented annually for "important contributions over many years to the enrichment of mathematics learning in Australia and its region," according to the AMT.

The award is named in honor of Bernhard H. Neumann, the so-called father of Australian mathematics, who “provided outstanding leadership, support and encouragement for mathematics and the teaching of mathematics at all levels."

Chua, who is president and cofounder of the Mathematics Trainers Guild-Philippines (MTG), is the first Asian to receive the award.

Through the MTG, Filipino students have won numerous medals in math competitions abroad including in China, United States, Singapore, Thailand, Hong Kong and Indonesia.

In 2006, Chua became the first Filipino to win the Paul Erdos Award from the World Federation of National Mathematics Competitions. *MathDL

BIRTHS
1622 Rene-Francoise de Sluse born. 1830 “It is true that Fourier is of the opinion that the principle object of mathematics is the public utility and the explanation of natural phenomena; but a scientist like him ought to know that the unique object of science is the honor of the human spirit and on this basis a question of [the theory of] numbers is worth as much as a question about the planetary system.” Jacobi to Legendre. Big Kline, p. 1037. VFR

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1842 George Thom graduated from Aberdeen and then became Principal of Doveton College in Madras, India. He returned to Scotland as Vice-Principal of Chanonry School Aberdeen and then became Rector of Dollar Institution (later to become Dollar Academy). He held this post for 24 years. He was a founder member of the EMS and became the fifth President in 1886. *SAU

1847 Andrew Gray graduated from Glasgow University and was appointed assistant and secretary to Lord Kelvin. He became Professor of Physics at University College Bangor and then returned to Glasgow as Kelvin's successor. He produced many books and papers in both mathematics and physics.*SAU

1852 Birthdate of William Burnside, whose Theory of Groups (1897, 1911) is now a classic. His suspicion that every group of odd order is solvable was proved in 1962 by Walter Feit and John G. Thompson. *VFR

1862 Sir William Henry Bragg was a pioneer British scientist in solid-state physics who was a joint winner (with his son Sir Lawrence Bragg) of the Nobel Prize for Physics in 1915 for research on the determination of crystal structures. During the WW I, Bragg was put in charge of research on the detection and measurement of underwater sounds in connection with the location of submarines. He also constructed an X-ray spectrometer for measuring the wavelengths of X-rays. In the 1920s, while director of the Royal Institution in London, he initiated X-ray diffraction studies of organic molecules. Bragg was knighted in 1920. *TIS

1906 Hans Beth, German-born American theoretical physicist who helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. Bethe did work relating to armour penetration and the theory of shock waves of a projectile moving through air. He studied nuclear reactions and reaction cross sections (1935-38). In 1943, Oppenheimer asked Bethe to be the head of the Theoretical Division at Los Alamos on the Manhattan Project. After returning to Cornell University in 1946, Bethe became a leader promoting the social responsibility of science. He received the Nobel Prize for Physics (1967) for his work on the production of energy in stars. *TIS



DEATHS

1566  Nostradamus, French astrologer died on this day  (b. 1503). I wonder if he predicted THIS in his prophacies.

1591 Vincenzo Galilei Italian music theorist, lutenist and composer, who as the father of Galileo Galilei, adopted experimentation to prove aspects of acoustics, and may thus have influenced his son, Galileo, away from pure, abstract mathematics and towards making experiments and investigation. Vincenzo's discoveries in acoustics included some of the physics of vibrating strings and columns of air. In particular he was the first to show that the ratio of an interval was proportional to string lengths but varied as the square of the tension applied to the strings and as the cubes of volumes of air. He recognized the superiority of equal tempered tuning and compiled a codex of pieces illustrating the use of all 24 major and minor keys as early as 1584.*TIS

1613 Bartholomeo Pitiscus was a Polish theologian who first coined the word Trigonometry. *SAU Pitiscus achieved fame with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introduced the word "trigonometry" to the English and French languages, translations of which had appeared in 1614 and 1619, respectively. It consists of five books on plane and spherical trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619).*Wik

1621 Thomas Harriot died of a cancerous ulcer on his left nostril. While in America in 1586 he learned to “drink” tobacco smoke from the Indians. This probably makes him the earliest recorded tobacco fatality. He is best known for his contributions to algebra, including the invention of the symbol for less than. He might have adopted this symbol from a decoration on an Indian’s back. See C. L. Smith, “On the origin of ‘<’ and ‘>’,” The Mathematics Teacher, 57(1964), 479–481 for a picture of this Indian.*VFR His executors posthumously published his Artis Analyticae Praxis on algebra in 1631; Nathaniel Torporley was the intended executor of Harriot's wishes, but Walter Warner in the end pulled the book into shape. It may be a compendium of some of his works but does not represent all that he left unpublished (more than 400 sheets of annotated writing). It isn't directed in a way that follows the manuscripts and it fails to give the full significance of Harriot's writings.*Wik He introduced a simplified notation for algebra and his fundamental research on the theory of equations was far ahead of its time. He was able to solve equations, even with negative or complex roots. However, he published no mathematical work in his lifetime. (Artes analyticae praxis, posthumous, 1631). Especially early in his career, he worked on navigation for his patron Walter Raleigh. Harriot carried out extensive telescopic observations of the satellites of Jupiter and of sunspots. When investigating optics, he discovered the sine law and measured the refractive indices of 13 different substances. He investigated free motion and motion resisted in air, and ballistic curves.*TIS Thomas Harriot was an English mathematician who did outstanding work on the solution of equations, recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution.*SAU
The solution of quadratic equations by the method of factoring was often referred to as Harriot's method because of his introduction of the method in his writing.

It is not possible today to find Harriot's grave. Although he was buried near the altar of St Christopher le Stocks in London, the church was destroyed in the great fire of 1666. There is a plaque in the entrance hall of the Bank of England, which is close to the site of Harriot's grave. It reproduces the original Latin wording of his epitaph.(p474) An English translation would read:

Stay, traveler, lightly tread;
Near this spot lies all that was mortal
Of that most celebrated man Thomas Harriot.
He was that most learned Harriot . . .
Who cultivated all the sciences and excelled in all . . .
A most studious searcher after truth . . .

1874 Gouverneur Emerson American physician, statistician and agriculturalist who prepared a series of tables of deaths and causes in Philadelphia, during thirty years from 1807. These showed, for example, the excessive mortality of males during childhood. He began practice in Philadelphia on 4 Aug 1820, where yellow fever broke out a few weeks later, with 73 deaths by that fall. Emerson recorded cases, dates, locations, and outcomes. He concluded no current medical treatments was especially effective. When smallpox reappeared there, with 325 deaths in 1824, Emerson drafted a bill for control measures. There were only 6 cases of smallpox in the city in 1825, and 3 in 1826. In retirement, he turned to peach culture, and studied phosphate and guano fertilizers. *TIS

1947 Nikolai Grigorievich Chebotaryov proved his density theorem generalising Dirichlet's theorem on primes in an arithmetical progression*SAU

1963 Seth Barnes Nicholson was an American astronomer best known for discovering four satellites of Jupiter. As a graduate student at the University of California, while photographing the recently- discovered 8th moon of Jupiter with the 36-inch Crossley reflector, he discovered a 9th (1914). During his life career at Mt.Wilson Observatory, he discovered two more Jovian satellites (1938) and the 12th (1951), as well as a Trojan asteroid, and computed orbits of several comets and of Pluto. His main assignment at Mt. Wilson was observing the sun with the 150-foot solar tower telescope, and he produced annual reports on sunspot activity and magnetism for decades. With Edison Pettit, he measured the temperatures of the moon, planets, sunspots, and stars in the early 1920s. *TIS

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2002 Daniel Chonghan Hong (3 Mar 1956; 2 Jul 2002 at age 46)
Korean theoretical physicist specializing in statistical physics and nonlinear dynamic physics, who with colleague Hugo Caram, originated the void diffusing-void model of granular flow, which is recognized as an effective theoretical treatment for a broad range of dynamical phenomena in granular media. In general, his work ranged from percolation network, viscous fingering, granular flows to traffic equations. He studied and taught in America from 1981, and wrote articles for popular magazines on various topics. He died at the young age of 46 of cardiac arrest. *TIS

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Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

On This Day in Math - July 1

Mathematics, rightly viewed, possesses not only truth, but supreme beauty

a beauty cold and austere, like that of sculpture, 

without appeal to any part of our weaker nature,

without the gorgeous trappings of painting or music, 

yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. 

 The true spirit of delight, the exaltation, the sense of being more than Man, 

which is the touchstone of the highest excellence, 

is to be found in mathematics as surely as in poetry.

--BERTRAND RUSSELL,

EVENTS
1349 Sometimes, a little astronomical knowledge can be a dangerous thing, even to those who possess it. A tale from medieval England is passed down from the chronicles of the scholar Thomas Bradwardine of a witch who attempted to force her will on the people through knowledge of an impending eclipse. Bradwardine, who had studied astronomical predictions of Arabian astronomers, saw through the ruse, and matched the prediction of the July 01, 1349 A.D. lunar eclipse with a more precise one of his own. No word survives as to the fate of the accused, but one can only suspect banishment or worse.*listosaur.com

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1694 Opening of the University of Halle in Germany. Georg Cantor later taught there. *VFR

1798 Napoleon’s fleet reached Alexandria, bearing Monge and Fourier.*VFR

1818 William George Horner’s (1786–1837) method of solving equations is presented to the Royal Society.*VFR  In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form. Horner's method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini's rule. Student's often learn this process as synthetic division.  *Wik

1847 The United States issued its first two postage stamps. They pictured Benjamin Franklin and George Washington respectively [Scott #1-2]. *VFR

1852 Dirichlet delivers a memorial lecture at the Berlin Academy in honor of his close friend Jacobi, calling him the greatest member of the Academy since Lagrange. *VFR

1856 Weierstrass appointed Professor of Mathematics at the Royal Polytechnic School in Berlin. *VFR

In 1858, the Wallace-Darwin theory of evolution was first published at the Linnaean Society in London*. The previous month Charles Darwin received a letter from Alfred Wallace, who was collecting specimens in the East Indies. Wallace had independently developed a theory of natural selection - which was almost identical to Darwin's. The letter asked Darwin to evaluate the theory, and if worthy of publication, to forward the manuscript to Charles Lyell. Darwin did so, almost giving up his clear priority for he had not yet published his masterwork The Origin of Species. Neither Darwin nor Wallace were present for the oral presentation at the Linnaean Society, where geologist Charles Lyell and botanist Joseph Hooker presented both Wallace's paper and excerpts from Darwin's unpublished 1844 essay.*TIS

1873 From a letter dated July 1, 1873, in the Coast Survey files in the National Archives in Washington. Peirce writes, "Newcomb, in a paper .... says he finds that pendulums hung by springs twist and untwist as they oscillate and says this will affect the time of oscillation."The Charles S. Peirce-Simon Newcomb Correspondence by Carolyn Eisele.

1894 The New York Mathematical Society changed its name to the American Mathematical Society to reflect its national charter. [AMS Semicentennial Publications, vol. 1, p. 74]. *VFR

1908 International agreement to use SOS for distress signal signed. An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

1918 Florian Cajori (1859–1930) appointed professor of the history of mathematics at the University of California, Berkeley, one of the few such chairs in the the world. During the next twelve years he published 159 papers on the history of mathematics. *VFR

1964 The New York Times, in a full page ad, announced that Paul Newman and Joanne Woodward would play a game on an elliptical pool table. It had a pocket at one focus so that if the ball passed over the other focus it would bank off the rail into the pocket. [UMAP Journal, 4(1983), p. 176; Recreational Mathematics Magazine, no. 14, January-February 1964] *VFR

BIRTHS
1646 Gottfried Wilhelm Leibniz born in Leipzig, Germany. Leibniz occupies a prominent place in the history of mathematics and the history of philosophy. He developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685[4] and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers. In philosophy, Leibniz is mostly noted for his optimism, e.g. his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or a priori definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He wrote works on politics, law, ethics, theology, history, philosophy, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. As of 2010, there is no complete gathering of the writings of Leibniz.*Wik

1779 John Farrar born at Lincoln, Massachusetts. As Hollis professor of mathematics and natural philosophy at Harvard, he was responsible for a sweeping modernization of the science and mathematics curriculum, including the change from Newton’s to Leibniz’s notation for the calculus. *VFR

1788 Jean Victor Poncelet born in Metz, France. He taught engineering and mechanics, but had a hobby of much greater interest—projective geometry. *VFR French mathematician and engineer whose study of the pole and polar lines associated with conic led to the principle of duality. While serving as an engineer in Napoleon's 1812 Russian campaign as an engineer, he was left for dead at Krasnoy, but then captured. During his imprisonment he studied projective geometry and wrote a treatise on analytic geometry. Released in 1814, he returned to France, and in 1822 published Traité des propriétés projectives des figures in which he presented his fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity. As a professor of mechanics (1825-35), he applied mechanics to improve waterwheels and was able to double their efficiency.*TIS

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

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1906 Jean Dieudonn´e born. *VFR French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS

DEATHS

1749 William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November, 1711 he became a Fellow of the Royal Society, and was later its Vice-President.[1]*Wik

1957 Donald McIntosh graduated from the University of Aberdeen and taught at George Watson's Ladies College in Edinburgh. He was appointed a Director of Education. He became Secretary of the EMS in 1899 and President in 1905. *SAU

1963 Bevan Braithwaite Baker graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London. *SAU

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1971 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

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1983 Richard Buckminster Fuller was a U.S. engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). Fuller also invented a wide range of other paradigm-shifting machines and structural systems. He was especially interested in high-strength-to-weight designs, with a maximum of utility for minimum of material. His designs and engineering philosophy are part of the foundation of contemporary high-tech design aesthetics. He held over 2000 patents.*TIS  This is another one who died within two weeks of his date of birth. I must organize data on this...

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Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History