**[The infinitesimals] neither have nor can have theory; in practise it is a dangerous instrument in the hands of beginners ... anticipating, for my part, the judgement of posterity, I would predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.**

~Francois Servois

The 201st day of the year; 201 is a harshad number... A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997. (Can you find the string of three consecutive Harshad numbers smaller than 201?)

**EVENTS**

**418**First report of a comet discovered during a solar eclipse, seen by the historian Philostorgius in Asia Minor. Many chronicles do mention this observation (12 western, 3 Byzantine). Philostorgius mentions that the sun was eclipsed at the 8th hour of the day. In his sketch there is a comet. This Total Solar Eclipse was from the Caribbean, Bay of Bengal, north Spain, central Italy, little Asia and ends in the north of India. *NSEC

**1595**“God in creating the universe and regulating the order of the cosmos had in view the ﬁve regular bodies of geometry as known since the days of Pythagoras and Plato.” So did Kepler record his discovery that the universe was based on the Platonic solids, a conjecture he published in 1596. *VFR "as I was showing in my class how the great conjunctions [of Saturn and Jupiter] occur successively eight zodiacal signs later, and how they gradually pass from one trine to another, that I inscribed within a circle many triangles, or quasi-triangles such that the end of one was the beginning of the next. In this manner a smaller circle was outlined by the points where the line of the triangles crossed each other.

The proportion between the circles struck Kepler’s eye as almost identical with that between Saturn and Jupiter, and he immediately initiated a vain search for similar geometrical relations.

And then again it struck me: why have plane figures among three-dimensional orbits? Behold, reader, the invention and whole substance of this little book! In memory of the event, I am writing down for you the sentence in the words from that moment of conception: The earth’s orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing this will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe within the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of planets.

Kepler of course based his argument on the fact that there are five and only five regular polyhedrons. *encyclopedia.com

**1676**Flamsteed began living at the Observatory with his two servants on July 10. On 19 July, his long series of Greenwich observations began? *Rebekah Higgitt, Teleskopos

**1799**The Rosetta stone was found by Napoleon’s troops in the Nile delta. It attracted the interest of the learned men with Napoleon, which included several mathematicians, and copies were circulated to scholars. The text is in Greek, hieroglyphics and demotic Egyptian scripts and was deciphered by Thomas Young and Fran¸cois Champollion. The cartouches on the stone, which contained royal names, were the key to decipherment. It is now a prized possession of the British Museum.*VFR

**1819**Poisson submitted a paper on the solution of the wave equation. He used the method of power series, but the techniques advocated by Cauchy and Fourier using complex variables and “Fourier analysis” won out. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, pp. 682, 687ﬀ, 1393] *VFR

**1895**George Cantor, first uses Aleph-null in a letter to Felix Klein. Prior to this he had use aleph-one for the first infinite cardinal. The first part of his Bietrage was already in print, so his letter to Klein is added, almost verbatim, to explain the changes with the publication date still showing March of that year. *From the Calculus to Set Theory, 1630-1910: An Introductory History, By I. Grattan-Guinness

**1983**The first three-dimensional reconstruction of a human head via computed tomography (CT) is published. Michael W. Vannier (Mallinckrodt Institute of Radiology, St. Louis) and his co-workers J. Marsh (Cleft Palate and Craniofacial Deformities Institute, St. Louis Children's Hospital) and J. Warren (McDonnell Aircraft Company) published the first three-dimensional reconstruction of single computed tomography (CT) slices of the human head. Computer-aided aircraft design techniques were adapted to make the cranial imaging possible. Since then, CT imaging has become a cornerstone of the medical profession.*CHM

**1767 Francois-Joseph Servois**born (19 July 1768 in Mont-de-Laval (N of Morteau), Doubs, France - 17 April 1847 in Mont-de-Laval, Doubs, France). He worked in projective geometry, functional equations and complex numbers. He introduced the word pole in projective geometry. He also came close to discovering the quaternions before Hamilton.

Servois introduced the terms "commutative" and "distributive" in a paper describing properties of operators, and he also gave some examples of noncommutativity. Although he does not use the concept of a ring explicitly, he does verify that linear commutative operators satisfy the ring axioms. In doing so he showed why operators could be manipulated like algebraic magnitudes. This work initiates the algebraic theory of operators.

Servois was critical of Argand's geometric interpretation of the complex numbers. He wrote to Gergonne telling him so in November 1813 and Gergonne published the letter in the Annales de mathématiques in January 1814. Servois wrote:- I confess that I do not yet see in this notation anything but a geometric mask applied to analytic forms the direct use of which seems to me simple and more expeditious.

Considered as a leading expert by many mathematicians of his day, he was consulted on many occasions by Poncelet while he was writing his book on projective geometry Traité des propriétés projective. *SAU

**1817 Charles Auguste Briot**(July 19, 1817 - September 20, 1882) undertook research on analysis, heat, light and electricity. His first major work on analysis was Recherches sur la théorie des fonctions which he published in the Journal of the École Polytechnique in 1859, and he also published this work as a treatise in the same year. His researches on heat, light and electricity was all based on his theories of the aether. He was strongly influenced in developing these theories by Louis Pasteur, the famous chemist. Of course Pasteur was a great scientist, but Briot had an additional reason to hold him in high esteem for, like himself and his friend Bouquet, Pasteur was brought up in the Doubs region of France.

In 1859 Briot and Bouquet published their important two volume treatise on doubly periodic functions. They published another joint effort in 1875 when their treatise on elliptic functions appeared. In this same year they published a second edition to their two volume work of 1859. In 1879 Briot, this time in a single author work, produced his treatise on abelian functions. The physical motivation for the mathematical theories which gave rise to this work in analysis was published by Briot in 1864 when he published his work on light, Essai sur la théorie mathématique de la lumière and five years later when he published his work on heat, Théorie mécanique de la chaleur.

We noted above that Briot was a dedicated teacher and as such he wrote a great number of textbooks for his students. This was certainly a tradition in France at this time and it was natural for a teacher of Briot's quality to write up his courses as textbooks. He wrote textbooks which covered most of the topics from a mathematics course: arithmetic, algebra, calculus, geometry, analytic geometry, and mechanics. For his outstanding contributions to mathematics the Académie des Sciences in Paris awarded Briot their Poncelet Prize in 1882 shortly before he died. *SAU

**1846 Edward Charles Pickering,**(July 19, 1846–February 3, 1919)was born Boston, Mass., U.S. physicist and astronomer. After graduating from Harvard, he taught physics for ten years at MIT where he built the first instructional physics laboratory in the United States. At age 30, he directed the Harvard College Observatory for 42 years. His observations were assisted by a staff of women, including Annie Jump Cannon. He introduced the use of the meridian photometer to measure the magnitude of stars, and established the Harvard Photometry (1884), the first great photometric catalog. By establishing a station in Peru (1891) to make the southern photographs, he published the first all-sky photographic map (1903).*TIS

**1894 Aleksandr Yakovlevich Khinchin**July 19, 1894 – November 18, 1959) was a Russian mathematician who contributed to many fields including number theory and probability.Khinchin's book Mathematical Foundations of Information Theory, translated into English from the original Russian in 1957, is important. It consists of English translations of two articles: The entropy concept in probability theory and On the basic theorems of information theory which were both published earlier in Russian. The second of these articles provides a refinement of Shannon's concepts of the capacity of a noisy channel and the entropy of a source. Khinchin generalised some of Shannon's results in this book which was written in an elementary style yet gave a comprehensive account with full details of all the results.*SAU

**1913 Mary Cannell**(19 July 1913 in Liverpool, England - 18 April 2000) It was the work which she undertook after she retired which earns her a place as a highly respected historian of mathematics. Her work stemmed from the fact that George Green had worked as a miller near Nottingham. Green was a mathematician who was well known to almost all students of mathematics around the world, yet little was known of his life. Flauvel writes:- ... widespread knowledge of Green himself dates only from the 1970s when Cannell and other Nottingham colleagues worked to restore his windmill and his memory...When I first visited Green's windmill in Nottingham the booklet which I purchased was George Green Miller and Mathematician written in 1988 by Mary Cannell. She produced a major biography of Green, George Green : Mathematician and Physicist 1793-1841 : The Background to His Life and Work in 1993. In addition she wrote research articles on Green's life and work bringing to the world of mathematics an understanding of Green's remarkable life.

Flauvel writes:- She charmed audiences on several continents, promoting interest in Green and early 19th-century mathematical physics, in the clear tones and pure vowels of pre-war English, somewhere between Miss Marple and Dame Peggy Ashcroft. ... Mary Cannell was working on projects of one sort or another - the Green website, the revised edition of the biography, research papers, the catalogue in the university of Nottingham library - right to the end, in days filled with her characteristic energy and enthusiasm. *SAU

**DEATHS**

**1878 Egor Ivanovich Zolotarev**(March 31, 1847, Saint Petersburg – July 19, 1878, Saint Petersburg) produced fundamental work on analysis and number theory. *SAU

**1947 John Clark**graduated from Edinburgh University and became a teacher at George Heriot's School in Edinburgh. He went on to become Rector of this school. He became Secretary of the EMS in 1891 and President in 1897. *SAU

**Hugh Everett III**(November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.

Discouraged by the scorn

^{}of other physicists for MWI, Everett ended his physics career after completing his Ph.D. Afterwards, he developed the use of generalized Lagrange multipliers for operations research and applied this commercially as a defense analyst and a consultant. He was married to Nancy Everett née Gore. They had two children: Elizabeth Everett and Mark Oliver Everett, who became frontman of the musical band Eels.

**1992 Allen Newell**(March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *Wik

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