On This Day in Math - July 8

I never came across one of Laplace's "Thus it plainly appears"

without feeling sure that I have hours of hard work before me to fill up the chasm

and find out and show how it plainly appears.

Nathanial Bowditch, Quoted in F Cajori, The Teaching and History of Mathematics in the United States
(LaPlace's classic, "Mecanique Celeste", 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".
 Bowditch translated the work and Legendre wrote of the translation, "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." )


The 189th day of the year; the product of the primes in a prime quadruplet always end in 189, except for the very first quadruplet 3x5x7x11.(A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form {p, p+2, p+6, p+8} you can see some of the smaller ones listed here

There are 14 prime years in the 21st Century (2017 will be the third), but the 189th century would be the first to contain as few as five prime years (18803, 18839, 18859, 18869 and 18899).

Narayana, an Indian mathematician in the 14th century, came up with an interesting Fibonacci-like series: A cow produces one calf every year. Beginning in its fourth year, each calf produces one calf at the beginning of each year. How many cows and calves are there altogether after n years? For the 15th year, the total is 189. (How many mature and immature?)

2357 is a prime number. 23357 is also prime.  233357 is also prime but 2333357 is not, and then 23333357 is; and yes, this is somehow related to the number 189. I came across a sequence on OEIS  which gave "Numbers k such that (7*10^k + 71)/3 is prime." Like you may have, I wondered, "Why would someone search for primes of so unusual a sequence?" Well, if you take those prime numbers, and subtract 2 from them, you get the number of threes that when placed between the digit 2 and the digits 57, will produce a prime. So I can inform you today that not only is (7*10¹⁸⁹ +71 )/3 a prime number, but that prime number is a 2 followed by 187 threes followed by 57.  And you thought 189 was just some hum-drum number!!!!!

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EVENTS

1672 Newton's first publication is in a letter to the Philosophical Transactions: “A Serie’s of Quere’s Propounded by Mr. Isaac Newton, to be Determin’d by Experiments, Positively and Directly Concluding His New Theory of Light and Colours; and Here Recommended to the Industry of the Lovers of Experimental Philosophy, as they Were Generously Imparted to the Publisher in a Letter of the Said Mr. Newtons of July 8.1672” (Thanks to Thony Christie) *Philosophical Transactions

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1680 Hooke demonstrates sound vibration. This was done by putting flour on a glass plate, and bowing on the edge of glass. Hooke had observed that the motion of the glass was vibrate perpendicular to the surface of the glass, and that the circular figure of the flour changed into an oval one way, and the reciprocation of it changed it into an oval the other way. This phenomenon was rediscovered by Chladni in the eighteenth century, and given his name "Chladni figures". *Daniel P McVeigh, "An Early History of the Telephone 1664-1865"

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1706 de Moivre wrote to Johann Bernoulli on 8 July 1706 telling him about Machin's series for π he suggested that Johann Bernoulli might tell Jakob Hermann about Machin's unproved result. He did so and Hermann quickly discovered a proof that Machin's series converges to π. He produced techniques that show other similar series also converge rapidly to π and he wrote on 21 August 1706 to Leibniz giving details. Two years later, on 6 July 1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π.
In 1706 William Jones published a work Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners. (This is the book in which Jones first uses Pi in the mathematical sens it is now used) This contains on page 243 the following passage:-
There are various other ways of finding the lengths or areas of particular curve lines, or planes, which may very much facilitate the practice; as for instance, in the circle, the diameter is to the circumference as 1 to (16/5- 4/239) - 1/3(16/53- 4/2393) &c. = 3.14159 &c. = π. This series (among others for the same purpose, and drawn from the same principle) I received from the excellent analyst, and my much esteemed friend Mr John Machin; and by means thereof, van Ceulen's number, or that in Art. 64.38 may be examined with all desirable ease and dispatch.
Jones also reports that this formula allows π be calculated:-
... to above 100 places; as computed by the accurate and ready pen of the truly ingenious Mr John Machin. No indication is given in Jones's work, however, as to how Machin discovered his series expansion for π.

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1831 Quetelet officially uses the term, "l'homme moyen" in an article about the different ages at which men commit crimes. *Statistics on the Table: The History of Statistical Concepts and Methods By Stephen M. Stigler

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1835 Liberty bell cracked. *VFR Or maybe not In the 1830s, the bell was adopted as a symbol by abolitionist societies, who dubbed it the "Liberty Bell". It acquired its distinctive large crack sometime in the early 19th century—a widespread story claims it cracked while ringing after the death of Chief Justice John Marshall in 1835.*Wik

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1842 Francis Baily (1774-1844) UK, at an eclipse in Italy, focuses attention on the corona and prominences and identifies them as part of the Sun's atmosphere. *NSEC

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1842 Dominique Francois Jean Arago (1786-1853), French astronomer. Studied solar eclipse of July 08, 1842 and concluded the sun exist of gas.*NSEC

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1881, a patron came into Edward Berner's drug store in Two Rivers, Wisconsin, and sat down at the soda-fountain counter. Since it was the Sabbath, the customer couldn't have the desirable, but scandalous, flavored soda water. Berner compromised by putting ice cream in a dish and poured over it the chocolate syrup that was previously only served as flavoring in ice-cream sodas. That was an ice cream Sunday! The name became "sundae", after the day on which Berner served it. TIS

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1933 Jansky announced detection of radio radiation from galactic center.*VFR Before Jansky observed the Milky Way in the 1930s, physicists speculated that radio waves could be observed from astronomical sources. In the 1860s, James Clerk Maxwell's equations had shown that electromagnetic radiation is associated with electricity and magnetism, and could exist at any wavelength. Several attempts were made to detect radio emission from the Sun by experimenters such as Nikola Tesla and Oliver Lodge, but those attempts were unable to detect any emission due to technical limitations of their instruments.
Karl Jansky made the discovery of the first astronomical radio source serendipitously in the early 1930s. As an engineer with Bell Telephone Laboratories, he was investigating static that interfered with short wave transatlantic voice transmissions. Using a large directional antenna, Jansky noticed that his analog pen-and-paper recording system kept recording a repeating signal of unknown origin. Since the signal peaked about every 24 hours. *Wik

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2002 Well into his mid-nineties, Donald Coxeter gives the keynote address at the Janos Bolyai Conference on Hyperbolic Geometry with a new paper on the Descartes circle theorem as extended by Phillip Beecroft. His Opening remarks:

The Absolute property of four mutally tangent circles that I am describing seems to have been discovered by Mr. Phillip Beecroft, of Hyde Academy, Cheshire, England, and published in The Lady and Gentleman's Dairy... In Beecroft's own words, "If any four circles be described to touch each other mutually, another set of four circles of mutual contact may be described whose points of contach shall coincide with those of the first four." He then proceeded to give a new and elegant proof of the 1842 theorem, which extended the four circle theorem of Descartes to be, in essence, an eight circle theorem.

*Siobhan Roberts, King of Infinite Space

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BIRTHS

1760 Christian Kramp (July 8, 1760 – May 13, 1826) was a French mathematician, who worked primarily with factorials.
As Bessel, Legendre and Gauss did, Kramp worked on the generalised factorial function which applied to non-integers. His work on factorials is independent of that of James Stirling and Vandermonde. He was the first to use the notation n! (Elements d'arithmétique universelle, 1808). In fact, the more general concept of factorial was found at the same time by Arbogast.*TIS For more on the symbols and history of the factorial see here.

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1777 Daniel Friedrich Hecht (8 July 1777 in Sosa – 13 March 1833 in Saxony) was a German mathematician. He was a mine manager, then a teacher and finally a professor of mathematics. He is most notable for writing high school textbooks on maths and geometry. *Wik

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1838 Count Ferdinand von Zeppelin Germany aviation pioneer who built the first rigid dirigible airships, named Zeppelins. He patented his idea on 31 Aug 1895 and formed a company to build airships in 1898. Many thought his invention incredible, and called him "Foolish Count". His first airship took off in 2 Jul 1900 at Lake Constance, where it had been assembled in a floating assembly shed. He continued to improve the design and built a fleet of airships for commercial passenger service. During WW I, Zeppelins were used to bomb Britain beginning 19 Jan 1915 with attacks on Great Yarmouth and King's Lynn. After the war, passenger service included transatlantic flights. Zeppelin use ended after the 6 May 1937 Hindenburg fire disaster at Lakehurst, N.J., U.S.A.*TIS

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1895 Igor Yevgenyevich Tamm (8 July 1895 – 12 April 1971) Soviet physicist who shared the 1958 Nobel Prize for Physics with Pavel A. Cherenkov and Ilya M. Frank for his efforts in explaining Cherenkov radiation. Tamm was an outstanding theoretical physicist, after early researches in crystallo-optics, he evolved a method for interpreting the interaction of nuclear particles. Together with I. M. Frank, he developed the theoretical interpretation of the radiation of electrons moving through matter faster than the speed of light (the Cerenkov effect), and the theory of showers in cosmic rays. He has also contributed towards methods for the control of thermonuclear reactions. *TIS
one of my favorite math stories is from George Gamow's autobiography and is about Tamm.

"Here is a story told to me by one of my friends who was at that time
a young professor of physics in Odessa. His name was Igor Tamm (Nobel
Prize laureate in Physics, 1958). Once when he arrived in a neighboring
village, at that period when Odessa was occupied by the Reds, and was
negotiating with a villager as to how many chickens he could get for
half a dozen silver spoons, the village was captured by one of the
Makhno bands, who were roaming the country, harassing the Reds. Seeing
his city clothes (or what was left of them), the capturers [sic]
brought him to the Ataman, a bearded fellow in a tall black fur
hat with machine-gun cartridge ribbons crossed on his broad chest and
a couple of hand grenades hanging on the belt.

'You son-of-a-bitch, you Communist agitator, undermining our Mother
Ukraine! The punishment is death.'

'But no,' answered Tamm, 'I am a professor at the University of Odessa
and have come here only to get some food.'

'Rubbish!' retorted the leader. 'What kind of professor are you ?'

'I teach mathematics.'

'Mathematics?' said the Ataman. 'All right! Then give me an estimate of
the error one makes by cutting off Maclaurin's series at the nth term.
Do this, and you will go free. Fail, and you will be shot!'

Tamm could not believe his ears, since this problem belongs to a rather
special branch of higher mathematics. With a shaking hand, and under
the muzzle of the gun, he managed to work out the solution and handed
it to the Ataman.

'Correct!' said the Ataman. 'Now I see that you really are a professor.
Go home!'

Who was this man? No one will ever know. If he was not killed later, he
may well be lecturing now on higher mathematics in some Ukrainian
university."

I tell this story every other year or so to my physics students when
they cannot be bothered to remember the form of the remainder in Taylor
expansions....

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1904 Henri (-Paul) Cartan, (July 8, 1904 – August 13, 2008) mathematician born in Nancy, France. His father, Elie Cartan, was also a mathematician. Henri made fundamental advances in the theory of analytic functions, worked on the theory of sheaves, homological theory, algebraic topology and potential theory. Along with others, such as Weil and Dieudonné, Henri Cartan wrote under the name Bourbaki. Bourbaki's Eléments de mathématique contains more than 30 volumes and aims to present mathematics so as to illustrate the axiomatic structure of modern mathematics. *TIS

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1915 Kenneth O. May (July 8, 1915, Portland, Or. – December 1,1977) was an American mathematician and historian of mathematics, who developed May's theorem. The Kenneth O. May Prize is awarded for outstanding contributions to the history of mathematics. Ken May established Historia Mathematica, and preserved it by separating it from its creator, "The distinguished predecessors of HM were associated with their founders and died with them.  If HM is to avoid this fate, we must prepare and carry through a prompt transfer of editorial responsibility to younger hands." His list of publications numbers above 300.  *Henry S. Tropp, E'loge, Isis 70, Sept 1979, Pgs 419-422

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DEATHS

1390 Albert of Saxony died. He wrote an excellent logic text and published two works on squaring the circle. *VFR ert was born at Rickensdorf near Helmstedt, the son of a farmer in a small village; but because of his talent, he was sent to study at the University of Prague and the University of Paris.
At Paris, he became a master of arts (a professor), and held this post from 1351 until 1362. In 1353, he was rector of the University of Paris. After 1362, Albert went to the court of Pope Urban V in Avignon as an envoy of Rudolf IV, Duke of Austria, in order to negotiate the founding of the University of Vienna. The negotiations were successful, and Albert became the first rector of this University in 1365.
In 1366, Albert was elected bishop of Halberstadt (counted as Albert III), Halberstadt being the diocese in which he was born. As Bishop of Halberstadt, he allied himself with Magnus with the Necklace, Duke of Brunswick-Lüneburg, against Gebhard of Berg, Bishop of Hildesheim, and was taken prisoner by Gebhard in the battle of Dinckler in 1367.
He died at Halberstadt in 1390.*Wik

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1695 Christiaan Huygens (14 April 1629 – 8 July 1695) Dutch mathematician, astronomer, and physicist, who founded the wave theory of light, discovered the true shape of the rings of Saturn, and contributed to the science of dynamics - the study of the action of forces on bodies. Using a lens he ground for himself, on 25 Mar 1655, he discovered the first moon of Saturn, later named Titan. In 1656, he patented the first pendulum clock, which he developed to enable exact time measurement while observing the heavens. Huygens studied the relation of the length of a pendulum to its period of oscillation (1673) and stated theories on centrifugal force in circular motion which influenced Sir Isaac Newton in formulating his Law of Gravity. Huygens also studied and drew the first maps of Mars. On 14 Jan 2005, a NASA space probe, named after Huygens, landed on Titan. *TIS

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1902 John Daniel Runkle (October 11, 1822 – July 8, 1902) was a U.S. educator and mathematician. B.S. in mathematics, 1851, Harvard College, second president of the Massachusetts Institute of Technology, was associated with the Nautical Almanac computation project from 1849 to 1884. In 1858 he founded the journal Mathematical Monthly and edited it for three years, when publication ceased. In 1860 he was a member of the committee that prepared the “Objects and Plan of an Institute of Technology” which led to the establishment of MIT. In 1862 he became MIT’s first secretary, and in 1865 he joined the new faculty as professor of mathematics, where he remained until 1902. He served as president pro-tem, 1868-1870, and was MIT’s second president, 1870-1878. He was married to Catherine Robbins Bird Runkle. *MIT History

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1971 Kurt Werner Friedrich Reidemeister (October 13, 1893 – July 8, 1971) was a mathematician born in Braunschweig (Brunswick), Germany.
He received his doctorate in 1921 with a thesis in algebraic number theory at the University of Hamburg under the supervision of Erich Hecke. In 1923 he was appointed assistant professor at the University of Vienna. While there he became familiar with the work of Hans Hahn and Wilhelm Wirtinger. In 1925 he became full professor at University of Königsberg, where he stayed until 1933, when he was forced to leave because of his opposition of the Nazis.
Reidemeister's interests were mainly in combinatorial group theory, combinatorial topology, geometric group theory, and the foundations of geometry. His books include Knoten und Gruppen (1926), Einführung in die kombinatorische Topologie (1932), and Knotentheorie (1932). He was the brother of Marie Neurath.*Wik

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1979 Shin'ichiro Tomonaga (March 31, 1906 – July 8, 1979) Japanese physicist who shared the Nobel Prize for Physics in 1965 (with Richard P. Feynman and Julian S. Schwinger of the U.S.) for independently developing basic principles of quantum electrodynamics. He was one of the first to apply quantum theory to subatomic particles with very high energies. Tomonaga began with an analysis of intermediate coupling - the idea that interactions between two particles take place through the exchange of a third (virtual particle), like one ship affecting another by firing a cannonball. He used this concept to develop a quantum field theory (1941-43) that was consistent with the theory of special relativity. WW II delayed news of his work. Meanwhile, Feynman and Schwinger published their own independent solutions.

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2008 Sixto Ríos García (January 4, 1913; Pelahustán, Toledo - July 8, 2008; Madrid,) was a Spanish mathematician, known as the father of Spanish statistics.
He has held the positions of Director of the School of Statistics at the University of Madrid, Director of the Institute for Operations Research and Statistics CSIC, Director, Department of Statistics, Faculty of Mathematical Sciences at the Complutense University and President of the Spanish Society Operational Research, Statistics and Information. It was academic correspondent of the National Academy of Sciences of Buenos Aires, and organizer and founder, commissioned by Unesco, School of Statistics, University of Caracas. He was a member of the drafting committee of Statistical Abstracts and fellow of the International Statistical Institute and the Institute of Mathematical Statistics. Wik-ES

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2010 David Harold Blackwell (April 24, 1919 – July 8, 2010) was Professor Emeritus of Statistics at the University of California, Berkeley, and is one of the eponyms of the Rao–Blackwell theorem. Born in Centralia, Illinois, he was the first African American inducted into the National Academy of Sciences, and the first black tenured faculty member at UC Berkeley.*Wik

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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

On This Day in Math - July 7

Probability is a mathematical discipline whose aims are akin to those, 

for example, of geometry of analytical mechanics.

In each field we must carefully distinguish three aspects of the theory:
(a) the formal logical content,
(b) the intuitive background,
(c) the applications.
The character, and the charm, of the whole structure cannot be appreciated without 

considering all three aspects in their proper relation.

William Feller, An Introduction to Probability Theory and its Applications

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The 188th day of the year; 188 is the largest known even number that can be expressed as the sum of two (distinct) primes in exactly five ways. *Prime Curios Students might seek smaller numbers that can be so expressed..

Neither 188²  nor 188³ contain a one or an eight. *@Derektionary

There are 188 11 bead necklaces using two colors, if the necklace can not be turned over.

188 is a Happy number: trajectory under iteration of sum of squares of digits map to 1.

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EVENTS

1339 There was an annular-total eclipse, with the total part of the track finding its way between the Orkney and Shetland Islands without touching either. At this location the track of totality was only 1 km wide, with a duration of 1 second! Presuming that you could position a boat to an accuracy of 1 km, totality must have been a ring of Baily's Beads. *NSEC

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1637 In 1625 (Christen Sørensen) Longomontanus suggested to the King, Christian IV, that he should build an observatory to replace Tycho’s Stjerneborg, which had been demolished in 1601. The observatory, the Rundetaarn (Round Tower), was conceived as part of the Trinitatis Complex: a university church, a library and the observatory. The foundation stone was laid on 7 July 1637 and the tower was finished in 1642. Longomontanus was appointed the first director of the observatory, after Leiden 1632 only the second national observatory in Europe. The church and Library were finished in 1657. *RMAT, Tycho’s last bastion

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1668, Sir Isaac Newton received his M.A. from Trinity College in Cambridge.*TIS

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1742 Goldbach's conjecture was sent in a letter to Leonhard Euler on 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 10¹⁴ - but still remains unproved. *TIS

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1747 Johann Sebastian Bach dedicated his Musikalisches Opfer (Musical Offering) to Frederick the Great. For a discussion of the mathematical significance of this cerebral music, see Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. *VFR

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1777 Johan Bernoulli, then astronomer Royal, Berlin, is paid a sum of 84 pounds for the Sexcentenary tables.  "To Mr. John Hyacinth Magellan....for the use of Mr. Bournoulli .. as a reward for his care and trouble in constructing a manuscript Book of Tables for facilita."
Two years later they would pay 28.35 pounds to Dr. Charles Hutton for translating the preface of the tables.

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1788 Caroline Herschel's nebula discovery,* History of Astronomy ‏@HistAstro

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1823 William Rowan Hamilton passed into Trinity College, Dublin. He was easily first out of the 100 candidates. *VFR

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1847 Lassel discovered a satellite of Neptune. *VFR (this date does not concur with other dates on these discoveries) In 1846 Lassell discovered Triton, the largest moon of Neptune, just 17 days after the discovery of Neptune itself by German astronomer Johann Gottfried Galle. In 1848 he independently co-discovered Hyperion, a moon of Saturn. In 1851 he discovered Ariel and Umbriel, two new moons of Uranus.*Wik

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1855, a letter from Michael Faraday in The Times newspaper, London, described the polluted state of the River Thames he had observed on a boat trip: "The whole of the river was an opaque pale brown fluid. In order to test the degree of opacity, I ... dropped [pieces of card] into the water at every pier the boat came to; before they had sunk an inch below the surface they were indistinguishable, though the sun shone brightly at the time." His words, he said, were no exaggeration, they were "the simple truth." He asserted, "If there be sufficient authority to remove a putrescent pond from the neighborhood of a few simple dwellings, surely the river which flows for so many miles through London ought not to be allowed to become a fermenting sewer." *TIS  I wrote a few years ago about the return of the seahorse to the muddy waters of the Thames. 

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1960 Press conference announces discovery of laser to the world. "VoilÁ. that Was It! The Laser was Born!" *Hughes Research Lab Web page.

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BIRTHS

1638 Francois or Francois Bertrand Barrême Barrême,(7 July 1638, Tarascon, France - 1703, Paris France) is considered one of the founders of accounting . After having engaged in trading in Italy , he moved to Paris where he gave lessons in bookkeeping and became a protégé of Colbert . Expert for the accounts of the Accounting Chamber of Paris and King's ordinary arithmetician, he is the author of books of mathematical conversions. His books were so common that today his name is used for what was once in English called a "ready reckoner", a table of numbers used to facilitate simple calculations, esp one for applying rates of discount, interest, charging, etc, to different sums . *Wik

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1746 Giuseppe Piazzi (July 7, 1746 - July 22, 1826) an Italian mathematician and astronomer. He discovered the asteroid Ceres and established an observatory at Palermo, now the Osservatorio Astronomico di Palermo – Giuseppe S. Vaiana. (for more detail see the source article) *Today in Astronomy

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*Wik

1752 Joseph-Marie Jacquard born (7 July 1752 – 7 August 1834). *VFR French silk weaver, (born Lyons), inventor of the Jacquard programmable power loom for brocaded fabric. His loom would mechanically produce any pattern, controlled by perforated control cards (1805). This served as the impetus for the technological revolution of the textile industry and is the basis of the modern automatic loom. The concept of using punched cards was later applied by Hollerith to keeping track of the 1890 US census data. The idea futher evolved to computer input punched cards. *TIS

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1816 Rudolf Wolf Swiss (7 July 1816 – 6 December 1893) astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte Carlo methods.*TIS

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1888 Archibald Goldie (7 July 1888 in Glenisla, Angus, Scotland - 24 Jan 1964 in London, England) studied at the universities of St Andrews and Cambridge. He served in the Meteorological Service of the British Army in World War I and continued to work in various branches of the Meteorological Office.*SAU

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1906 William Feller (July 7, 1906 – January 14, 1970). He once said that multiplication, especially before breakfast, is seldom commutative. He died in 1970. *VFR
Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators".*Wik

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DEATHS

1900 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *VFR

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1927 Magnus Gustaf Mittag-Leffler died (16 March 1846 – 7 July 1927) . Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem.*TIS

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1930 Sir Arthur Conan Doyle (22 May 1859 – 7 July 1930) Scottish novelist, physician, spiritualist. His fictional detective, Sherlock Holmes, emulates the scientist, diligently searching through data and to make sense of it. "It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." *TIS

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1942 William Henry Young (London, 20 October 1863 - Lausanne, 7 July 1942) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.*SAU

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1975 William Hodge (17 June 1903 – 7 July 1975) studied at Edinburgh and Cambridge Universities. After some time at Bristol and in the USA he returned to Cambridge and became Lowndean Professor of Astronomy and Geometry. His main interests were in Algebraic Geometry and Differential Geometry. He became an honorary member of the EMS in 1954. He was knighted in 1959. *SAU His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry. *Wik

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2014 Klaus Peters,( --, July 7, 2014) mathematician and STEM Publisher for over 50 years, passed away on July 7, 2014. Klaus, who received his doctorate from University of Erlangen in 1962, became well-known in the mathematical community largely through A.K. Peters Ltd, publisher of scientific and technical books, specializing in mathematics and computer science, as well as journals Experimental Mathematics, Internet Mathematics, and the Journal of Graphics Tools. Klaus was a familiar face at mathematics meetings around the world, and recently consulted with the AMS publishing division on a number of different projects, including Really Big Numbers. He was a strong and eloquent advocate for scholarly publishing. *AMS

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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

On This Day in Math - July 6

You, who wish to study great and wonderful things, 

who wonder about the movement of the stars, 

must read these theorems about triangles. 

Knowing these ideas will open the door to all of astronomy

and to certain geometric problems.

Johann Regiomontanus De Tringulis Omnimodis




The 187th day of the year; 187^(1*8*7)+1+8+7 is prime. There are only two such (non-zero) numbers. Students might search for the other.

The 187th prime is 1117. 11*17 = 187

& 187² and 187³ don't have 1, 7, or 8.
*Math Year-Round ‏@MathYearRound

With 187 people in a room, there's a 50% chance that 4 share the same birthday *Derek Orr

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EVENTS

1656 Huygen, in a letter to Carcavi, gives the solution, without proof, to a dice throwing probability problem posed by Fermat. (If A wins for Throwing a six, and B wins by throwing a seven, and after A throws once, B and A each roll twice in turns. What are the odds of A winning?) *A History of Probability and Statistics and Their Applications Before 1750 By Anders Hald

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1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π. In 1706 William Jones had published a work Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners. (This is the book in which Jones first uses Pi in the mathematical sense it is now used)  This contains on page 243 the following passage:-
There are various other ways of finding the lengths or areas of particular curve lines, or planes, which may very much facilitate the practice; as for instance, in the circle, the diameter is to the circumference as 1 to (16/5- 4/239) - 1/3(16/53- 4/2393) &c. = 3.14159 &c. = π. This series (among others for the same purpose, and drawn from the same principle) I received from the excellent analyst, and my much esteemed friend Mr John Machin; and by means thereof, van Ceulen's number, or that in Art. 64.38 may be examined with all desirable ease and dispatch.
Jones also reports that this formula allows π be calculated:-
... to above 100 places; as computed by the accurate and ready pen of the truly ingenious Mr John Machin.
No indication is given in Jones's work, however, as to how Machin discovered his series expansion for π so when de Moivre wrote to Johann Bernoulli on 8 July 1706 telling him about Machin's series for π he suggested that Johann Bernoulli might tell Jakob Hermann about Machin's unproved result. He did so and Hermann quickly discovered a proof that Machin's series converges to π. He produced techniques that show other similar series also converge rapidly to π and he wrote on 21 August 1706 to Leibniz giving details.  Two years later, on 6 July 1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π.

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1785 The Continental Congress of the United States adopted the decimal system of money with the dollar as unit.

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1815 Total solar eclipse on the North Pole. (Ok, I admit, I wouldn't have thought that could happen!)

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1819 When Marie Madeleine Sopie Blanchard ascended in her hydrogen balloon to watch a firework,  she would become the first woman to lose her life while flying. Her craft crashed on the roof of a house and she fell to her death. *yovisto.

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1909 Einstein resigns his position at the Bern Patent Office to move to Zurich to take up his first full-time academic position in the newly established chair of theoretical physics at the University of Zurich. His lectures were extremely popular due to his humor, unusual presentations, patience and accommodation to his students to make sure they understood. *Brody & Brody, The Science Class You Wish You Had

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In 1920, a radio compass was used for first time for aircraft navigation. In a test of the radio compass as an aid to navigation, an F5L left Hampton Roads and flew directly to the battleship Ohio (BB 12), 94 miles at sea in a position unknown to the pilot. Without landing, the plane made the return trip to Hampton Roads, this time navigating by signals from Norfolk. *TIS

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2016 Astronomy Magazine announces that China has completed the world's largest radio telescope.

E.T. may be easier to find now that China has just finished installation of the 4,450 triangular panels on the world's largest radio telescope, the Five Hundred Meter Aperture Spherical Telescope (FAST). The telescope was finished nearly three months ahead of schedule, with the original ETA in September. With its enormous size of 30 soccer fields, FAST has taken nearly five years and $180 million to build.
So how big is it? One of the scientists that worked on building FAST told Xinhua that if the dish were to be completely filled with wine, there would be enough to give five bottles to all seven billion people on Earth.
The next largest radio telescope is the 305-meter-wide Arecibo Telescope in Puerto Rico, which was completed in 1963. The Arecibo Telescope has held the crown of largest radio telescope for 53 years. FAST is 64 percent larger.

*Astronomy Magazine

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BIRTHS

1849  Alfred Bray Kempe (6 July 1849, Kensington, London – 21 April 1922, London) published a false "proof" of the four color theorem in 1879 which stood until Heawood showed the mistake 11 years later. The 'proof' is however still the basis for the computer aided proof discovered 100 years later.*SAU

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1883 Ernst Arnold Kohlschütter (July 6, 1883 – May 28, 1969) a German astronomer and astrophysicist from Halle.
In 1908 he was awarded his Ph.D. from the University of Göttingen.
In 1911 he began working at the Mount Wilson Observatory, studying the spectra of the Sun and stars. In collaboration with Walter Sidney Adams, and in 1914 they discovered that the absolute luminosity of a star was proportional to the relative intensity of the lines in the spectrum. This allowed astronomers to determine the distance of stars, including main sequence and giants, using the spectroscope.
He became the director of the Bonn observatory in 1925. Therein he was dedicated to astrometric studies.
The crater Kohlschütter on the Moon is named in his honor. *Today in Astronomy

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1910 Lothar Collatz  (July 6, 1910, Arnsberg, Westphalia – September 26, 1990, Varna, Bulgaria) was a German mathematician. In 1937 he posed the famous Collatz conjecture, which remains unsolved.
The Collatz conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.
Take any natural number n. If n is even, divide it by 2 to get n / 2, if n is odd multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called "Half Or Triple Plus One", or HOTPO indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.

Paul Erdős said about the Collatz conjecture: "Mathematics is not yet ready for such problems." and also offered $500 for its solution.
In 2006, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s, proved that a natural generalization of the Collatz problem is undecidable. However, as this proof depends upon the generalization, it cannot be applied to the original Collatz problem. *Wik

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DEATHS

1476 Regiomontanus, aka Johann Mueller, (6 Jun 1436, 6 Jul 1476 at age 40)the father of trigonometry as a science independent of astronomy. According to a rumor repeated by Gassendi in his Regiomontanus biography he was assassinated by relatives of George of Trebizond whom he had criticized in his writings. More likely he died in an epidemic raging in Rome at the time.The ideas behind the law of sines, like those of the law of cosines, predate the word sine by over a thousand years. Theorems in Euclid on lengths of chords are essentially the same ideas we now call the law of sines. The law of sines for plane triangles was known to Ptolemy and by the tenth century Abu'l Wefa had clearly expounded the spherical law of sines. It seems that the term "law of sines" was applied sometime near 1850, but I am unsure of the origin of the phrase.
The spherical law of sines was first presented by Johann Muller in his De Triangulis Omnimodis in 1464. This was the first book devoted wholly to trigonometry (a word not then invented). David E. Smith suggests that the theorem was Muller's invention.
The German astronomer and mathematician who was chiefly responsible for the revival and advancement of trigonometry in Europe. His book De triangulis omnimodis (1464) is a systematic account of methods for solving triangles. Much of the material on spherical trigonometry in Regiomontanus' On Triangles was taken directly and without credit from the twelfth-century work of Jabir ibn Aflah otherwise known as Geber, as noted in the sixteenth century by Gerolamo Cardano.
In Jan 1472 Muller made observations of a comet which were accurate enough to allow it to be identified with Halley's comet 210 years later (being three returns of the 70 year period comet). He also observed several eclipses of the Moon. His interest in the motion of the Moon led him to make the important observation that the method of lunar distances could be used to determine longitude at sea. However, instruments of the time lacked the necessary accuracy to use the method at sea. *TIS
Thony C who writes the excellent history blog, The Renaissance Mathematicus, noted, "However at least in the case of Regiomontanus appearances are deceptive; what we have here is a date of death that is anything but certain.".  See his explanation of the remark here.
The  title page of "On Triangles" by Regiomontanus  is here.  Although the work was written in 1464, it was not published until 1533.

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1854  Georg Simon Ohm (17 March 1789 – 6 July 1854) was a German physicist. As a high school teacher, Ohm began his research with the recently invented electrochemical cell, invented by Italian Count Alessandro Volta. Using equipment of his own creation, Ohm determined that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current. This relationship is now known as Ohm's law.*Wik

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1915 Lawrence Hargrave(29 Jan 1850, 6 Jul 1915 at age 65) Australian aeronaut and inventor best known for his invention of the box kite. Hargrave “flew” on 12 Nov 1894, by attaching himself to a huge four kite construction attached to the ground by piano wire. Due to their abilities to carry heavy payloads, steady flight, and capacity for high altitude flight, these kites have had many industrial and military uses in the past. Box kites were used until the 1930's to carry meteorological equipment for high altitude weather studies and by the Royal Air Force as sea rescue equipment to deliver radio aerials. Hargrave also made important studies of wing surfaces and worked with rotary engines and gliders. *TIS

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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

On This Day in Math - July 5

There is no smallest among the small and no largest among the large,

But always something still smaller and something still larger.

Quoted in E Maor, To Infinity and Beyond: a Cultural History of the Infinite


The 186th day of the year;  186 is the product of the first four primes less; the product of the first four positive integers (7 x 5 x 3 x 2 - 4 x 3 x 2 x 1 = 186) . *Prime Curios

186 is the sum of consecutive primes, 186 = = 89 + 97,

186 is a sphenic (wedge) number, product of 3 distinct primes: 186 = 2*3*31

and from Jim Wilder @wilderlab An equation for July 4th: 7⁴ = 2401 = (2 + 4 + 0 + 1)⁴   And a followup from World Observer@WKryst2011 points out that there are only two other such year dates. (student's should find both)

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EVENTS

In 1643, an exceptionally strong wind occurred in Essex County, Mass. The description by Governor John Winthrop is the first record suggestive of a tornado in the U.S.: "There arose a sudden gust so violent for one-half hour as it blew down multitudes of trees. It lifted up their meeting house at Newbury, the people being in it. It darkened the air with dust, yet through God’s great mercy it did no hurt, but only killed one Indian with the fall of a tree." However, no tornado-like funnel shape - so likely to be noted, if seen - was not included in his log. So, it was likely not a tornado, in fact, but a severe straight-line squall with strong downburst winds. Reverend Increase Mather cited a likely tornado in Jul 1680 storm at Cambridge, Mass*TIS

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1687 Halley wrote to Newton that his Principia was finally published. [Westfall, p. 468] *VFR 1687 – ushering in a tidal wave of changes in thought that would significantly accelerate the already ongoing scientific revolution by giving it tools that produced technologically valuable results, which had theretofore been otherwise unobtainable. (Thony Christie has pointed out that the use of "published" may give a false impression to the modern reader, even though this is the date printed on the title page of the document. The actual words, used by Halley were, "I have at length brought your Book to an end, and hope it will please you. the last errata came just in time to be inserted. I will present from you the books you desire to...." )

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1698 Johann Bernoulli, in a letter to Leibniz, defined the notion of a function. The term “function” is due to Leibniz. [Cajori, Historical Introduction to the Mathematical Literature, p. 96]*VFR

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1766 Ben Franklin writes from England to Rev Ezra Stiles, "I have lately propos’d our ingenious and learned Contriman Mr: Winthorp, as a Member of the Royal Society." On Feb 20, 1766. John Winthrop Esqr. Hollisian Professor of Mathematics and Natural Philosophy was unanimously elected Fellow of the Royal Society in London. *Franklin Papers, Natl Archives

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1951 – William Shockley invents the junction transistor. *Wik

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2012  Gresham College  announces the appointment of Raymond Flood, Fellow of Kellogg College, Oxford, as Professor of Geometry and Other Mathematical Sciences. The Geometry chair at Gresham College is the oldest in England, dating back to the College’s founding in 1597. Gresham College was the first higher education institution in England besides the Universities of Oxford and Cambridge, and it was created with the guiding principle of providing free education to the traders and people of London so that England could maintain a position at the forefront of a global economy. Gresham College’s central position in science and mathematics has seen the Royal Society formed within the College, and past luminaries including Henry Briggs, Sir Christopher Wren, Robert Hooke, Sir Christopher Zeeman and Sir Roger Penrose. *Gresham Press Release

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BIRTHS

1820 William John Macquorn Rankine, (5 July 1820 – 24 December 1872) Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. As the chair (1855) of civil engineering and mechanics at Glasgow, he developed methods to solve the force distribution in frame structures. Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853. Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. *TIS While many students never encounter it, there is a temperature scale named after Rankine. It is the Fahrenheit scale equivalent of the Kelvin scale for Celsius.

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1867 Andrew Ellicott Douglass (July 5, 1867, Windsor, Vermont – March 20, 1962, Tucson, Arizona) American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS

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1888 Louise Freeland Jenkins (July 5, 1888 – May 9, 1970) was an American astronomer.
She was born in Fitchburg, Massachusetts. In 1911 she graduated from Mount Holyoke College, then she received a Master's degree in astronomy in 1917 from the same institution. From 1913 to 1915 she worked at the Allegheny Observatory in Pittsburgh.
About 1921 she moved to Japan, becoming a teacher at the Women's Christian College, a missionary school. She returned to the United States in 1925 after her father died. A year later she returned to teach at a school in Himeji. (Hinomoto Gakuen girl's high school.)
In 1932 she returned to the US and became a staff member at Yale University Observatory. She was co-editor of the Astronomical Journal starting in 1942, and continued in this post until 1958. She would return to visit Japan later in her life.
She was noted for her research into the trigonometric parallax of nearby stars. She also studied variable stars.
The crater Jenkins on the Moon is named in her honor. *Today in Astronomy

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1946 Gerardus (Gerard) 't Hooft (July 5, 1946 - ) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions".
His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization, and the holographic principle. *Wik

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DEATHS

1865 Oskar Bolza died (12 May 1857–5 July 1942). Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Bolza published The elliptic s-functions considered as a special case of the hyperelliptic s-functions in 1900 which related to work he had been studying for his doctorate under Klein. However, he worked on the calculus of variations from 1901. Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907). His text Lectures on the Calculus of Variations published by the University of Chicago Press in 1904,[3] became a classic in its field and was republished in 1961 and 2005.[4] After the death of his friend Maschke in 1908, Bolza became unhappy in the United States and, in 1910, he and his wife returned to Freiburg in Germany where he was appointed as an honorary professor. Chicago gave him the title of 'non-resident professor of mathematics' which he retained for the rest of his life.*Wik He returned to Germany in 1910, where he researched function theory, integral equations and the calculus of variations. In 1913, he published a paper presenting a new type of variational problem now called "the problem of Bolza." The next year, he wrote about variations for an integral problem involving inequalities, which later become important in control theory. Bolza ceased his mathematical research work at the outbreak of WW I in 1914.*TIS

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1911 George Johnstone Stoney (15 February 1826 – 5 July 1911) Irish physicist who introduced the term electron for the fundamental unit of electricity. At the Belfast meeting of the British Association in Aug 1874, in a paper: On the Physical Units of Nature, Stoney called attention to a minimum quantity of electricity. He wrote, "I shall express 'Faraday's Law' in the following terms ... For each chemical bond which is ruptured within an electrolyte a certain quantity of electricity traverses the electrolyte which is the same in all cases." Stoney offered the name electron for this minimum electric charge. When J.J. Thomson identified cathode rays as streams of negative particles, each carrying probably Stoney's minimum quantity of charge, the name was applied to the particle rather than the quantity of charge.*TIS

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1926 Peter Scott Lang graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

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1932 Rene Louis Baire died (21 January 1874 – 5 July 1932) a French mathematician most famous for his Baire category theorem, which helped to generalize and prove future theorems. His theory was published originally in his dissertation Sur les fonctions de variable réelles ("On the Functions of Real Variables") in 1899.*Wik French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

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1977 Henry Scheffé (New York City, USA, 11 April 1907 – Berkeley, California, USA, 5 July 1977) worked in several different areas of Statistics, including linear models, analysis of variance and nonparametrics.*SAU He is known for the Lehmann–Scheffé theorem and Scheffé's method.

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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