
Isaac Barrow, Trinity College Cambridge 
No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.~George Boole
The 286th day of the year; 286 is a tetrahedral number (
a triangular pyramid, note that 285 was a square pyramidal number, how often can they occur in sequence?) It is the sum of the first eleven triangular numbers, 286 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66
And to top yesterday's curiosity, here are four squares with the same digits 286^{2}=81796, 137^{2}=18769, 133^{2} = 17 689, 281^{2} =78961
And 286 is a concatenation of the first two perfect numbers 6, and 28
EVENTS
2128 B.C. In China the earliest record of solar eclipse was made.*VFR (This date seems to have been computed back by a Buddhist astronomer,IHang in about 720 AD based on the year of the Dynasty for which it was recorded.)
1597 Kepler replied to Galileo’s letter of 4 August 1597 urging him to be bold and proceed openly in his advocacy of Copernicanism. [Eves, Circles, 159◦] *VFR
1729 Euler mentioned the gamma function in a letter to Goldbach. In 1826 Legendre gave the function its symbol and name. [Cajori, History of Mathematical Notations, vol. 2, p. 271] (the Oct 13 date is for the Julian Calendar still used in Russia when Euler wrote from there. It was the 24th in most of the rest of the world using the Gregorian Calendar.) In the letter Euler writes \(\Gamma{x} = \lim_{r\to\infty} \frac{r!r^x}{x(1+x)(2+x)\dots(r+x)}\)<br />
In this same letter, Euler gives the relation we would now write as \(\frac{1}{2}! = \frac{\sqrt {\pi}}{2}\) and points out many other fractional relations. *Detlef Gronau Why the Gamma Function So As It Is <br />

Sketch of M51 by Lord Rosse in 1845, *Wik 
1773 What later became known as the Whirlpool Galaxy was discovered on October 13, 1773 by Charles Messier while hunting for objects that could confuse comet hunters, and was designated in Messier's catalog as M51. *David Dickinson @Astroguyz
1860 The earliest surviving aerial photograph is titled 'Boston, as the Eagle and the Wild Goose See It.' Taken by James Wallace Black and Samuel Archer King on October 13, 1860, it depicts Boston from a height of 630m. Aerial photography was first practiced by the French photographer and balloonist GaspardFĂ©lix Tournachon, known as "Nadar", in 1858 over Paris, France. The photographs he produced no longer exist. *Smithsonian *Wik
1884 An international conference in Washington D. C. decided “to adopt the meridian passing through the center of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.” Greenwich Mean Time, or GMT, was born. If someone ever asked you what President Chester Arthur did for us (don't say "Who?") simply say he pushed for the International Meridian Conference in Washington.
Addendum: I have been gently corrected by Rebekah Higgitt @beckyfh and Thony Christie @rmathematicus that in fact "The resolutions from the conference were only proposals – it was up to the respective governments to show political will and implement them ..." and that happened slowly. I am also aware that GMT was widely used in the UK before this conference to standardize railway time tables. A good source on a little more detail is at the
Greenwich Meridian Org
1893 The term "Diophantine equation" appears in English in 1893 in Eliakim Hastings Moore (18621932), "A DoublyInfinite System of Simple Groups," Bulletin of the New York Mathematical Society, *Jef Miller, Earliest Known Uses of Some of the Words of Mathematics
1904 Clever Hans, The horse that could do math is investigated by Oskar Pfungst. The investigation will continue for six weeks.
Hans was a horse owned by Wilhelm von Osten, who was a gymnasium mathematics teacher, an amateur horse trainer, phrenologist, and something of a mystic. Hans was said to have been taught to add, subtract, multiply, divide, work with fractions, tell time, keep track of the calendar, differentiate musical tones, and read, spell, and understand German. Von Osten would ask Hans, "If the eighth day of the month comes on a Tuesday, what is the date of the following Friday?” Hans would answer by tapping his hoof. Questions could be asked both orally, and in written form. Von Osten exhibited Hans throughout Germany, and never charged admission. Hans's abilities were reported in The New York Times in 1904. After von Osten died in 1909, Hans was acquired by several owners. After 1916, there is no record of him and his fate remains unknown.
psychologist Oskar Pfungst demonstrated that the horse was not actually performing these mental tasks, but was watching the reaction of his human observers.*Wik
1915 "Precision Computer"  The issue of the Engineering and Contracting journal for this date, in addition to details of a new threeton worm drive contractors truck, advised of the availability of the new Ross Precision Computer. This circular slide rule consists of a silvercolored metal dial, 81/2" wide, mounted on a silvercolored metal disc. Three oblong holes on the base disc permit the reading of trigonometric scales on a white celluloid and cardboard disc that is between the metal discs. (HT to JF Ptak @ptak)
In 1985, at the Fermi National Accelerator Laboratory in Illinois, the first observation was made of protonantiproton collisions by the Collider Detector at Fermilab (CDF) with 1.6 TeV centerofmass energy. In all, 23 of collisions were detected in Oct 1985. The Tevatron, four miles in circumference (originally named the Energy Doubler), is the world's highestenergy particle accelerator. Its lowtemperature cooling system was the largest ever built when it was placed in operation in 1983. Its 1,000 superconducting magnets are cooled by liquid helium to 268 deg C (450 deg F). Fermilab (originally named the National Accelerator Laboratory) was commissioned by the U.S. Atomic Energy Commission, in a bill signed by President Johnson on 21 Nov 1967. *TIS
BIRTHS1734 William Small (13 October 1734; Carmyllie, Angus, Scotland – 25 February 1775; Birmingham, England). He attended Dundee Grammar School, and Marischal College, Aberdeen where he received an MA in 1755. In 1758, he was appointed Professor of Natural Philosophy at the College of William and Mary in Virginia, then one of Britain’s American colonies.
Small is known for being Thomas Jefferson's professor at William and Mary, and for having an influence on the young Jefferson. Small introduced him to members of Virginia society who were to have an important role in Jefferson's life, including George Wythe a leading jurist in the colonies and Francis Fauquier, the Governor of Virginia.
Recalling his years as a student, Thomas Jefferson described Small as:
"a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and a large and liberal mind... from his conversation I got my first views of the expansion of science and of the system of things in which we are placed."
In 1764 Small returned to Britain, with a letter of introduction to Matthew Boulton from Benjamin Franklin. Through this connection Small was elected to the Lunar Society, a prestigious club of scientists and industrialists.
In 1765 he received his MD and established a medical practice in Birmingham, and shared a house with John Ash, a leading physician in the city. Small was Boulton's doctor and became a close friend of Erasmus Darwin, Thomas Day, James Keir, James Watt, Anna Seward and others connected with the Lunar Society. He was one of the bestliked members of the society and an active contributor to their debates.
Small died in Birmingham on 25 February 1775 from malaria contracted during his stay in Virginia. He is buried in St. Philips Church Yard, Birmingham.
The William Small Physical Laboratory, which houses the Physics department at the College of William & Mary, is named in his honor. *Wik
1776 Peter Barlow (13 Oct 1776; 1 Mar 1862) English mathematician and engineer who invented two varieties of achromatic (noncolourdistorting) telescope lenses. In 1819, Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal. In 1822, he built a device which is to be considered one of the first models of an electric motor supplied by continuous current. He also worked on the design of bridges, in particular working (181926) with Thomas Telford on the design of the bridge over the Menai Strait, the first major modern suspension bridge. Barlow was active during the period of railway building in Britain.*TISThe Menai Suspension Bridge viewed from the Anglesey side

*Wik 
1885 Viggo Brun (13 October 1885, Lier – 15 August 1978, DrĂ¸bak) was a Norwegian mathematician.
He studied at the University of Oslo and began research at the University of GĂ¶ttingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors (9almost primes); and that all large even integers are the sum of two 9 (or smaller)almost primes.
In 1919 Brun proved that the sum of the reciprocals of the twin primes converges to Brun’s constant:
1⁄3 + 1 ⁄5 + 1⁄ 5 + 1⁄7 + 1 ⁄11 + 1⁄ 13 + 1⁄17 + 1 ⁄19 + . . . = 1.9021605 . . .by contrast, the sum of the reciprocals of all primes is divergent. He developed a multidimensional continued fraction algorithm in 1919/20 and applied this to problems in musical theory.
He also served as praeses of the Royal Norwegian Society of Sciences and Letters in 1946.
It was in 1994, while he was trying to calculate Brun’s constant,
that Thomas R. Nicely discovered a famous flaw in the Intel Pentium
microprocessor. The Pentium chip occasionally gave wrong answers
to a floatingpoint (decimal) division calculations due to errors in five
entries in a lookup table on the chip. Intel spent millions of dollars
replacing the faulty chips.
More recently, Nicely has calculated that the value of Brun’s constant
1s 1.902160582582 _ 0.000000001620.
*Wik
1890 Georg Feigel (13 October 1890 – 20 April 1945) was a German mathematician. At the University of Berlin he developed an introductory course, Einf¨uhrung in die H¨ohere Mathematik (published, posthumously, 1953) which was responsible for introducing the new fundamental concepts of mathematics based on axioms and structures into the universities. *VFR
Feigl's main areas of work were the foundations of geometry and topology, where he studied fixed point theorems for ndimensional manifolds.
Feigl was one of the initial authors of the Mathematisches WĂ¶rterbuch ("Mathematical dictionary"). Because of the impending siege by the Red Army he was forced to leave Breslau in January 1945 with his family and other members of the Mathematical Institute. His wife Maria was distantly related to the lord of the manor of Wechselburg castle and prepared the castle to receive the mathematicians. Feigl brought his previously developed materials for the Mathematisches WĂ¶rterbuch and asked his students to further refine it in the castle. They did not have access to books, lecture notes, calculators, or typewriters in the castle. Johann Radon (1887–1956) and Feigl were willing and able to continue lectures started in Breslau for one hour a day at Wechselburg castle, without any documents. Feigl had a severe stomach ailment and died after a few months without medication in Wechselburg. The Mathematisches WĂ¶rterbuch did not appear until 1961, when Hermann Ludwig Schmid (1908–1956) and Joseph Naas (1906–1993) published it.
1893 Kurt Werner Friedrich Reidemeister (13 Oct 1893, 8 July 1971) Reidemeister was a pioneer of knot theory and his work had a great influence on Group Theory. Reidemeister's other interests included the philosophy and the foundations of mathematics. He also wrote about poets and was a poet himself. He translated MallarmĂ©. *SAU
1915 Arthur Burks (October 13, 1915 – May 14, 2008) was a principal designer of the ENIAC. Burks  who was born in Duluth, Minn., and educated at DePauw University and the University of Michigan  did extensive work on the ENIAC, the machine designed at the University of Pennsylvania’s Moore School and completed in 1946. After working with J. Presper Eckert and John Mauchly on the ENIAC, Burks moved on to Princeton University, where he helped John von Neumann develop his computer at the Institute for Advanced Studies.*CHM
1932 John Griggs Thompson (13 Oct 1932, )American mathematician who was awarded the Fields Medal in 1970 for his work in group theory, solving (with Walter Feit) one of its thorniest problems, the socalled "odd order" problem. (Group theory is a branch of mathematics that focuses on the study of symmetries  such as the symmetries of a geometric figure, or symmetries that arise in solutions to algebraic equations.) Thompson's proof, with 253 pages of equations, filled an entire issue of the Pacific Journal of Mathematics. It stands out as one of math’s longest and most complex. Thompson also collaborated on the classification of the finite simple groups, the building blocks of more general groups. Group theory has important applications in physics, chemistry and other fields.*TIS
DEATHS
1715 Nicolas Malebranche CO ( 6 August 1638 – 13 October 1715) was a major French philosopher and follower of Descartes whose ideas he developed to bring them more in line with standard Roman Catholic orthodox belief.*SAU In his works, he sought to synthesise the thought of St. Augustine and Descartes, in order to demonstrate the active role of God in every aspect of the world. Malebranche is best known for his doctrines of vision in God, occasionalism and ontologism. *Wik
1793 William Hopkins FRS (2 February 1793 – 13 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the seniorwrangler maker.
Before graduation, Hopkins had married Caroline Frances Boys (1799–1881) and was, therefore, ineligible for a fellowship. He instead maintained himself as a private tutor, coaching the young mathematicians who sought the prestigious distinction of Senior Wrangler. He was enormously successful in the role, earning the sobriquet senior wrangler maker and grossing £700800 annually. By 1849, he had coached almost 200 wranglers, of whom 17 were senior wranglers including Arthur Cayley and G. G. Stokes. Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter.
He also made important contributions in asserting a solid, rather than fluid, interior for the Earth and explaining many geological phenomena in terms of his model. However, though his conclusions proved to be correct, his mathematical and physical reasoning were subsequently seen as unsound.In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge.
There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins. Subsequently, Lord Kelvin helped to make Green's 1828 work famous according to the book "George Green" written by D.M. Cannell. *Wik
1913 Gyula VĂˇlyi (5 January 1855  13 October 1913) was a Hungarian mathematician and theoretical physicist, a member of the Hungarian Academy of Sciences, known for his work on mathematical analysis, geometry, and number theory.*Wik
1987 Walter H. Brattain (10 Feb 1902, 13 Oct 1987) Walter Houser Brattain was an American scientist born in China who, with John Bardeen and William B. Shockley, won the Nobel Prize for Physics in 1956 for investigating semiconductors (materials of which transistors are made) and for the development of the transistor. At college, he said, he majored in physics and math because they were the only subjects he was good at. He became a solid physicist with a good understanding of theory, but his strength was in physically constructing experiments. Working with the ideas of Shockley and Bardeen, Brattain's hands built the first transistor. Shortly, the transistor replaced the bulkier vacuum tube for many uses and was the forerunner of microminiature electronic parts.*TIS
1990 Hans Freudenthal, . *VFR (September 17, 1905, Luckenwalde, Brandenburg – October 13, 1990) was a Dutch mathematician. He was Professor Emeritus at Utrecht University when he died at age 85. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education. *Wik
2001 Olga Arsenevna Oleinik (2 July 1925, 13 Oct 2001) Oleinik wrote over 370 published papers and eight books. Her main research was concerned with algebraic geometry, partial differential equations, and mathematical physics. Winner of numerous prizes including the 1952 Chebotarev Prize for her research on elliptic equations with a small parameter in the highest derivative, the 1964 Lomonosov Prize for research on asymptotic properties of the solutions of problems of mathematical physics, and the 1988 State Prize for her series of papers on the investigation of boundaryvalue problems for differential operators and theirs applications in mathematical physics. In 1985 she was awarded the honorary title of Honored Scientist of the Russian Federation for her achievements in research and teaching, and in 1995 was awarded the Order of Honor by the president of the Russian Federation. She was also the 1996 AWM Noether Lecturer.*Agnes Scott College,
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