## Thursday, 8 September 2016

### On This Day in Math - September 8

We Must Know, We Will Know
~David Hilbert

The 252nd day of the year; 252 is the smallest number which is the product of two distinct numbers that are reverses of each other: 252 = 12*21 *Number Gossip
(and the next would be?)

252 is a palindrome in base ten, and also in base five 20025 (How many three digit numbers are (non-trivial) palindromes in base ten and one other base less than ten)

If you flip a coin 10 times in a row, there are exactly 252 ways in which it can turn out that you get exactly 5 heads and 5 tails. That is, $252 = \binom{10}{2} = \frac{10*9*8*7*6}{5*4*3*2*1}$

EVENTS

1636 The General Court of Massachusetts Bay appropriated 400 Pounds for the "creation of a college in New Towne." Originally named Cambridge College, it was renamed in 1638 in honor of Reverend John Harvard who bequeathed the college about 800 pounds, and 300 books. The first building was called the "Indian College" and was erected in 1637. #FFF pg 155

1679 Leibniz writes to Huygens with a letter and essay which describes his analysis “situs”, a precursor of vector analysis,  *A history of vector analysis ,Michael J. Crowe; pg 3

1844 The term ABELIAN INTEGRAL seems to have first occurred in a letter of Sept. 8, 1844, from William Henry Fox Talbot: "What is the definition of an Abelian Integral? for it appears to me that most integrals possess the Abelian property." The letter was addressed to John Frederick William Herschel, who, in his reply of Sept. 13, 1844, wrote: "I suppose the most general definition of an Abelian Integral might be taken to be this that between +(x) and +(φ(x)) there shall subsist an algebraical relation between several such functions." [The Talbot letters are available here *Jeff Miller Web site

In 1854, Dr. John Snow removed the handle of the Broad Street water pump in London, thus effectively halting further spread of cholera. He had mapped the outbreaks, and thus suspected contamination of this community source of water. He was correct in this, one of the most symbolic gestures in the history of public health. Within days after the pump handle was removed, new cases of illness had ceased. Site investigation showed raw sewage from a leaking sewage cesspool that had contaminated the well water. Thus Snow, who was already a celebrated anaesthetist became a pioneer of epidemiology. The "John Snow" pub now stands beside the pink granite slab marking the site of the original pump.*TIS

1930 Hilbert’s radio broadcast in Konigsberg.  At the age of 68, Hilbert retired to conform with regulations at Gottingen.  It was the second great speech of his career. It contains the famous phrase “Wir mussen wissen. Wir werden wissen.” (We must know, we will know). These optimistic words are inscribed over Hilbert’s grave in Gottingen. A recording is available in the Gedenkband. Emil du Bois-Reymond had maintained that the nature of matter, and human consciousness would always remain unknowable. Hilbert refuted this pessimistic view with a spirit of scientific optimism.
We ought not believe those who today, with a philosophical air and a tone of superiority, prophesy the decline of culture, and are smug in their acceptance of the ignorabimus principle.... in place of this foolish Ignorabimus, let our resolution be, to the contrary: "We must know, we will know."

You can hear the four minute address, and read the English translation at the MAA website.

In 2040, the first visible conjunction during the 21st century of the crescent Moon with the five naked-eye visible planets - Mercury, Venus, Mars, Jupiter and Saturn - will occur. They will be seen clustered within a small distance of each other in the early evening sky, well east of the sun. When a similar grouping happened in the sky on 5 May 2000, the Moon and the same five planets were lost to view because of the glare of the Sun from among them.*TIS

BIRTHS

1157 Alexander Neckam (8 Sep 1157; 1217) English schoolman and scientist, who was a theology instructor at Oxford. Neckam then studied and lectured in Paris. In 1186, he returned to England, and in 1213 became abbot at Cirencester, Gloucestershire. In Paris, Neckam had learned of the mariner's compass, which the Chinese had been using for at least two centuries. In a book De utensilibus ("On Instruments") he wrote about 1180 was the first reference to the magnetic compass as being in use among the Europeans. (the Chinese encylopaedist Shen Kuo gave the first clear account of suspended magnetic compasses a hundred years earlier in 1088 AD with his book Mengxibitan, or Dream Pool Essays) His De naturis rerum ("On the Natures of Things"), a two-part introduction to a commentary on the Book of Ecclesiastes, is a miscellany of scientific information at that time novel in western Europe but already known to Greek and Muslim savants. *TIS

1584 Gregorius Saint Vincent born. His Opus geometricum (1647) contains the most beautiful frontispiece of any mathematics text. In this work, Gregorius was the ﬁrst to develop the theory of the geometric series and also the ﬁrst to show that the area under a hyperbola is a logarithm. *VFR (in the frontispiece he claims to have squared the circle) The engraved frontispiece shows sunrays inscribed in a square frame being arranged by graceful angels to produce a circle on the ground: 'mutat quadrata rotundis'. There was uneasiness in the learned world because no one in that world still believed that under the specific Greek rules the quadrature of a circle could possibly be effected, and few relished the thought of trying to locate an error, or errors, in 1200 pages of text. Four years later, in 1651, Christiaan Huygens found a serious defect in the last book of 'Opus geometricum', namely in Proposition 39 of Book X, on page 1121. This gave the book a bad reputation.*SAU

1588 Marin Mersenne born (8 September 1588 – 1 September 1648) was a French theologian, philosopher, mathematician and music theorist, and did important work in acoustics. Often called the center of the scientific world in the early 17th century for his communication with and between many of the most prominent scientific minds of the period. He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings. *Wik

1634 Hendrik van Heuraet (8 September 1634; Haarlem,Netherlands - 1600?) The dates of his birth and death are unclear as little is known of him. The birthdate is estimated from the date papers were signed for his inheritance, which had to happen on (or after) he turned twenty-one. His mother was Maria de Coninck who came from Oude Rijn, a town near to Leiden. His father was Abraham van Heuraet, an immigrant from Hamburg who had settled in Haarlem where he was a cloth merchant.
It is known is that he went with Hudde to the Protestant university in Saumur, a town on the river Loire in western France, in 1658. From Saumur he wrote a letter to van Schooten entitled Epistola de transmutatione curvarum linearum in rectas. Van Schooten published this letter in 1659. In it he gives a rectification method which reduces, for any arbitrary algebraic curve, the rectification to a quadrature of an associated curve, that is to computing the area under an associated curve. This was particularly important since at this time mathematicians believed that it was not possible to compare the length of a curved arc with a straight line segment. Van Heuraet's breakthrough is therefore significant in the development of mathematics. In particular, in the paper, he computed the integral ∫ √(1+y' 2) dx and applied his methods to the parabola. His methods of rectification of curves became part of a more general theory by Fermat which was produced independently and at about the same time. William Neile, independently of van Heuraet, had previously found the arc length of an algebraic curve in 1657 when he rectified the cubical parabola.
van Heuraet's work led to an argument with Huygens over a priority claim, suggesting that Huygens recognized the importance of the work. (most historians find little reason to side with Huygens in this claim) *SAU

1671 Pierre Polinière (8 September 1671, Coulonces, France - 9 February 1734, Coulonces, France) was an early investigator of electricity and electrical phenomena, notably "barometric light", a form of gas-discharge light, which suggested the possibility of electric lighting. He also helped to introduce the scientific method in French universities.*Wik

1861 Percy John Heawood (8 September 1861 Newport, Shropshire, England[1] - 24 January 1955 Durham, England) was a British mathematician. He devoted essentially his whole working life to the four color theorem and in 1890 he exposed a flaw in Alfred Kempe's proof, that had been considered as valid for 11 years. With the four color theorem being open again he established the five color theorem instead. The four color theorem itself was finally established by a computer-based proof in 1976. *Wik

1919 Albert H. Bowker, (8 September 1919 - 20 January 2008) Born in Winchendon MA. He received a BS in Math from MIT in 1941 and a PhD in Math-Stat from Columbia in 1949. Dr. Bowker served as founding Chairman of the Stat Dept at Stanford, being at Stanford until 1961. In 1963, he became Chancellor of the expanding City University of New York (CUNY), returning to California in 1971 to become Chancellor of the University of California at Berkeley.
Dr. Bowker was President of the Institute of Mathematical Statistics (IMS) in 1962 and President of the American Statistical Association (ASA) in 1964.
For an interesting and informative interview with Dr. Bowker conducted by Stanford's Ingram Olkin in 1987 in which Bowker told of his many interactions with well-known contributors to Statistics (including one with Fisher with reservations because of Neyman-Pearson theory) go here. *David Bee

DEATHS
1637 Robert Fludd, also known as Robertus de Fluctibus (17 January 1574; Bearsted, Kent, UK – 8 September 1637; London, UK), was a prominent English Paracelsian physician. He is remembered as an astrologer, mathematician, cosmologist, Qabalist and Rosicrucian apologist.
Fludd is best known for his compilations in occult philosophy. He had a celebrated exchange of views with Johannes Kepler concerning the scientific and hermetic approaches to knowledge.
Between 1598 and 1604, Fludd studied medicine, chemistry and hermeticism on the European mainland. His itinerary is not known in detail. On his own account he spent a winter in the Pyrenees studying theurgy with the Jesuits.

On his return to England, Fludd entered Christ Church, Oxford. In 1605 he graduated M.B. and M.D. He then moved to London, settling in Fenchurch Street, and making repeated attempts to enter the College of Physicians. Fludd encountered problems with the College examiners, both because of his unconcealed contempt for traditional medical authorities, and because of his attitude. After at least six failures, he was admitted in 1609. Subsequently both his career and his standing in the College took a turn very much for the better. He was on good terms with Sir William Paddy. Fludd was one of the first to support in print the theory of the circulation of the blood of the College's William Harvey. To what extent Fludd may have actually influenced Harvey is still debated, in the context that Harvey's discovery is hard to date precisely. The term "circulation" was certainly ambiguous at that time
Fludd's works are mainly controversial. In succession he defended the Rosicrucians against Andreas Libavius, debated with Kepler (claiming the hermetic or "chemical" approach is deeper than the mathematical), argued against French natural philosophers including Gassendi and Mersenne, and engaged in the discussion of the weapon-salve, a form of sympathetic magic, current in the 17th century in Europe, whereby a remedy was applied to the weapon that had caused a wound in the hope of healing the injury it had made. (I suspect much of the success was having the doctors focus on the weapon rather than infecting the wounded body). *Wik

1882 Joseph Liouville (24 Mar 1809, 8 Sep 1882) French mathematician who discovered transcendental numbers (those which are not the roots of algebraic equations having rational coefficients), and that there are infinitely many of them. He also did work in real and complex analysis, number theory, and differential geometry. His name is remembered in the Sturm-Liouville theory of differential equations that generalizes Joseph Fourier's ideas, and are important in mathematical physics. He studied celestial mechanics. Liouville founded in 1836, and edited for nearly four decades, the Journal de Mathématique which remains a leading French mathematical publication. He edited and published (1843) the manuscripts left behind upon the untimely death of Evariste Galois 22 years earlier.*TIS Liouville was one of Lord Kelvin's mathematical heros, and he once stopped a lecture in Glascow to ask his students, "Do you know what a mathematician is?" He then wrote on the blackboard the equation
and, pointing to the board stated, A mathematician is one to whom that is as obvious as twice two are four is to you. Liouville was a mathematician." *Walter Gratzer, Eurekas and Euphorias, pg 21

1894 Hermann Ludwig Ferdinand von Helmholtz (31 Aug 1821, 8 Sep 1894) German scientist who contributed much to physiology, optics, electrodynamics, mathematics, and meteorology, including the law of the conservation of energy (1847). He also developed thermodynamics, in particular introducing concept of free energy. In 1850, he measured the speed of a nerve impulse and, in 1851, invented the ophthalmoscope. He discovered the function of the cochlea in the inner ear and developed Thomas Young's theory of colour vision (published 1856). His study of muscle action led him to formulate a much more accurate theory concerning the conservation of energy than earlier proposed by Julius Mayer and James Joule. *TIS

1963 Robert Bell (15 Jan 1876, 8 Sept 1963) graduated from Glasgow University. He was appointed to a professorship at the University of Otago in New Zealand. He worked in Geometry and was editor of the EMS Proceedings for several years. *SAU

1969 Gordon Thomas Whyburn (January 7 1904 , September 8 1969) American mathematician who worked on the topology of point sets. *Wik

1981 Hideki Yukawa (23 Jan 1907, 8 Sep 1981) Japanese physicist who shared the 1949 Nobel Prize for Physics for "his prediction of the existence of mesons on the basis of theoretical work on nuclear forces." In his 1935 paper, On the Interaction of Elementary Particles*, he proposed a new field theory of nuclear forces that predicted the existence of the previously unknown meson. Mesons are particles heavier than electrons but lighter than protons. One type of meson was subsequently discovered in cosmic rays in 1937 by American physicists, encouraging him to further develop meson theory. From 1947, he worked mainly on the general theory of elementary particles in connection with the concept of the "non-local" field. He was the first Japanese Nobel Prize winner.*TIS Recently K Ken Nakamura ‏@KKenNakamura sent me a tweet that said,"In my generation every Japanese knew the name Yukawa; in fact Yukawa was a synonym with genius."

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
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