On This Day in Math - June 5

Don't worry about people stealing your ideas. 

If your ideas are any good,

you'll have to ram them down people's throats. 

~Howard Aiken

The 157th day of the year; 2¹⁵⁷ is the smallest "apocalyptic number," i.e., a number of the form 2ⁿ that contains '666'. *Prime Curios (Can you find an apocalyptic number of the form 3ⁿ)

157 is also the largest solution I know for a prime, p, such that \( \frac{p^p-p!}{p} \) is prime.

The number 157 in base ten is equal to \(31_{[52]}\), but don't worry if you get that backwards,
\(52_{[31]}\) is also equal to 157 in decimal. Can you find other examples of reversible numeral/base that give the same decimal value?

EVENTS

1661 Newton admitted to Trinity College.  He was admitted as a "sizar", which meant he earned part of the cost of his education by doing menial chores.  His mother was quite wealthy enough to pay his tuition, but was unsure about his prospects at college since he seemed to be such a poor farmer. Mama and Junior seemed to have an unsteady relationship. He once admitted to his diary in a list of sins, "Threatening my father and mother Smith to burn them and the house over them." 

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1828 The final meeting of the Board of Longitude in Greenwich. This was the 243rd meeting of the Board since it's creation in 1714. John Barrow, Second Secretary of the Admiralty chaired the meeting. On July 15th the Board was dissolved by Parliament.

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1833 Ada Lovelace first meets Charles Babbage at the home of Mary Sommerville. She is known to have assisted Charles Babbage in the design of an "analytical engine", an early mechanical computing device. She is often credited with writing the first computer program.
Ada's mother, Lady Byron, had intentionally schooled Ada in the Sciences and Mathematics to counteract the "poetic tendencies" she might have inherited fom her father. Ada knew Mary Somerville and Augustus de Morgan socially and received some math instruction from both. She died of cancer in the womb in November of 1852, only 36 years of age, and was buried beside Lord Byron, the father she never knew, in the parish church of St. Mary Magdalene, Hucknall in the UK.
In 1980, 165th years after Ada's birth, the US Defense Department announced a powerful new computer language. They named it Ada in honour of the Countess of Lovelace's important role in the history of computing. It may be of interest to students of mathematics and computer science that Ada Lovelace husband,also named William, was the Baron of Ockham (ancestor of 14th century William of Occam, for whom Occam’s Razor is named) in the 19th century.

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1873 The term “radian” first appeared in print. Some suggest it may have been intended as an abbreviation for "RADIus ANgle".
Here is a quote from Cajori's History of Mathematical Notations, vol 2 (1929) as provided by Julio Cabellion to the Historia-Matematica Newsgroup:
"An isolated matter of interest is the origin of the term 'radian', used with trigonometric functions. It first appeared in print on June 5, 1873, in examination questions set by James Thomson at Queen's College, Belfast. James Thomson was a brother of Lord Kelvin. He used the term as early as 1871, while in 1869 Thomas Muir, then of St. Andrew's University, hesitated between 'rad', 'radial' and 'radian'. In 1874, T. Muir adopted 'radian' after a consultation with James Thomson. (+)" (+) _Nature_, Vol. 83, pp. 156, 217, 459, 460.
The concept of a radian measure, as opposed to the degree of an angle, should probably be credited to Roger Cotes. According to a recent post to a math history newsgroup by Bob Stein; "He then calculated this as approximately 57.295 degrees. He had the radian in everything but name, and he recognized its naturalness as a unit of angular measure."

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1929 The US Post Office issued a 2 cent stamp commemorating the Golden Jubilee of Edison's electric Lamp. On Dec 31, 1879 Edison gave the first public demonstration of his new incandescent lamp when he lit up a street in Menlo Park, New Jersey. The Pennsylvania Railroad Company ran special trains to Menlo Park on the day of the demonstration in response to public enthusiasm over the event.
Although the first incandescent lamp had been produced 40 years earlier, no inventor had been able to come up with a practical design until Edison embraced the challenge in the late 1870s. His patent would be approved on January 27, 1880. *.history.com

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1943 Contract signed to develop ENIAC with the Moore School at the University of Pennsylvania.

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 1977, first personal computer, the Apple II, went on sale. They were the invention of Steve Wozniak and Steve Jobs. They have the 6502 microprocessor, ability to do Hi-res and Lo-res color graphics, sound, joystick input, and casette tape I/O. They have a total of eight expansion Slots for adding peripherials. Clock speed is 1MHz and, with Apple's Language Card installed, standard memory size is 64kB. (The Apple I designation referred to an earlier computer that was not much more than a board. You had to supply your own keyboard, monitor and case.) The Apple II was one of three prominent personal computers that came out in 1977. Despite its higher price, it quickly pulled ahead of the TRS-80 and the Commodore Pet. *TIS Model pictured must be after 1979 when the floppy disk drive (1978) and spreadsheet program VisiCalc (1979) made it a blockbuster.

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1995 The first gaseous condensate was produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder NIST–JILA lab, using a gas of rubidium atoms cooled to 170 nanokelvin (nK) [6] (1.7×10−7 K). For their achievements Cornell, Wieman, and Wolfgang Ketterle at MIT received the 2001 Nobel Prize in Physics. This Bose–Einstein condensate was first predicted by Satyendra Nath Bose and Albert Einstein in 1924–25. Interestingly, Bose first letter to Einstein was written on June 4,1924 so the discovery was one day over exactly 71 years later. *Wik

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BIRTHS

1819 John Couch Adams (5 June 1819 – 21 January 1892); In 1878 he published his calculation of Euler’s constant (Euler-Mascheronie constant) to 263 decimal places. (he also calculated the Bernoulli numbers up to the 62 nd) *VFR The Euler-Mascheronie constant is the limiting value of the difference between the sum of the first n values in the harmonic series and the natural log of n. (not 263 places, but the approximate value is 0.5772156649015328606065...)
He also predicted the location of the then unkown planet of Neptune, but it seems he failed to convince Airy to search for the planet. Independently, Urbanne LeVerrier predicted its locatin in Germany, and then assisted Galle in the Berlin Observatory in locating the planet on 23 September 1846. As a side note, when he was appointed to a Regius position at St. Andrews in Scotland, he was the last professor ever to have to swear and oath of “abjuration and allegience”, swearing fealty to Queen Victoria, and abjuring the Jacobite succession. The need for the oath was removed by the 1858 Universities Scotland Act. Adams made many other contributions to astronomy, notably his studies of the Leonid meteor shower (1866) where he showed that the orbit of the meteor shower was very similar to that of a comet. He was able to correctly conclude that the meteor shower was associated with the comet.

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1883 John Maynard Keynes born. (5 June, 1883–21 April, 1946) a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments. He greatly refined earlier work on the causes of business cycles, and advocated the use of fiscal and monetary measures to mitigate the adverse effects of economic recessions and depressions. His ideas are the basis for the school of thought known as Keynesian economics, as well as its various offshoots. *Wik In one logic class of Whitehead he was the only student. Keynes worked on the foundations of probability.

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1888 Gregor Michailowitch Fichtenholz, ( 5 June 1888 in Odessa; 25 June 1959 in Leningrad)who was the founder of the Leningrad school of function theory. *VFR
1900 Dennis Gabor (5 Jun 1900, 8 Feb 1979 at age 78) Hungarian-born British electrical engineer who won the Nobel Prize for Physics in 1971 for his invention of holography, a system of lensless, three-dimensional photography that has many applications. He first conceived the idea of holography in 1947 using conventional filtered-light sources. Because such sources had limitations of either too little light or too diffuse, holography was not commercially feasible until the invention of the laser (1960), which amplifies the intensity of light waves. He also did research on high-speed oscilloscopes, communication theory, physical optics, and television. Gabor held more than 100 patents. *TIS

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1904 George McVittie studied at Edinburgh and Cambridge. He then held posts at Leeds, Edinburgh and London and became Professor of Astronomy at the University of Illinois. His main work was in Relativity and Cosmology. *SAU More detail of his life can be found in this obituary.

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DEATHS

1716 Roger Cotes (10 July 1682 — 5 June 1716) died at age 33 of a violent fever. Sir Isaac Newton, speaking of Mr. Cotes, said, “If he had lived we might have known something.” See Ronald Gowing’s Roger Cotes, Natural Philosopher, pp. 136 and 142. *VFR
A really nice bio about Cotes is at the Renaissance Mathematicus blog by Thony Christie.

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1940 Augustus Edward Hough Love (17 April 1863, Weston-super-Mare – 5 June 1940, Oxford), British geophysicist and mathematician who discovered a major type of earthquake wave that was subsequently named for him. Love assumed that the Earth consists of concentric layers that differ in density and postulated the occurrence of a seismic wave confined to the surface layer (crust) of the Earth which propagated between the crust and underlying mantle. His prediction was confirmed by recordings of the behaviour of waves in the surface layer of the Earth. He proposed a method, based on measurements of Love waves, to measure the thickness of the Earth's crust. In addition to his work on geophysical theory, Love studied elasticity and wrote A Treatise on the Mathematical Theory of Elasticity, 2 vol. (1892-93). *TIS

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1965 Tadashi Nakayama or Tadasi Nakayama (July 26, 1912 – June 5, 1964) was a mathematician who made important contributions to representation theory. He received his degrees from Tokyo University and Osaka University and held permanent positions at Osaka University and Nagoya University. He had visiting positions at Princeton University, Illinois University, and Hamburg University. Nakayama's lemma and Nakayama algebras and Nakayama's conjecture are named after him.

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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 - June 4

First public demonstration in Annonay, 4 June 1783

We may always depend on it that algebra,

which cannot be translated into good English

and sound common sense, 

is bad algebra.

~W. K. Clifford Common Sense in the Exact Sciences

The 156th day of the year; 156 is the number of graphs with six vertices. *What's So Special About This Number.

\( ( \pi(1)+\pi(5)+\pi(6)) * (p_1 + p_5 + p_6) = 156 \). 156 is the smallest number for which this is true, and the only even number for which it is true. (The symbols \( \pi(n)\) and \(p_n \) represent the number of primes less than or equal to n, and the nth prime respectively)

156 is evenly divisible by 12, the sum of its digits. Numbers which are divisible by the sum of their digits are usually called Niven Numbers.

According to an article in the Journal of Recreational Mathematics the origin of the name is as follows. In 1977, Ivan Niven, a famous number theorist presented a talk at a conference in which he mentioned integers which are twice the sum of their digits. Then in an article by Kennedy appearing in 1982, and in honor of Niven, he christened numbers which are divisible by their digital sum “Niven numbers.” One might try to find the smallest strings of consecutive Niven Numbers with more than a single digit. *http://trottermath.net/niven-numbers/

I wonder about the relative order of the classes of numbers which are n times their digit sum for various n.

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EVENTS

780 B.C. First reliable record of a total solar eclipse is made, China. *VFR   A clay tablet retrieved from the ancient city of Ugarit, Syria (as it is now) gives the oldest eclipse record, with two interpretations of the date being regarded as plausible. The date most favored by recent authors on the subject is 5 Mar 1223 BC, although alternatively 3 May 1375 BC has also been proposed as plausible.

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1656 Fr Kaspar Schotts writes to Otto von Gericke on June 4th 1656, seeking clarification of the working of the vacuum pump Gericke had invented and sold to Elector of Mainz and Bishop of Würzburg, Johann Phillip von Schönborn who had passed it on to the Jesuit College. For the next decade, until his death in May 1666, Schotts was a phenomenally industrious and prolific disseminator of scientific and technological developments, writing no fewer than eleven works, totaling more than 7000 pages. *culturesofknowledge.org
Schott's book was the first written account of the Gericke pump.
Agnes M. Clerke writes, :Reading in 1687 in Schott's Mechanica hydraulico-pneumatica of Guerieke's invention of exhausting the air in a closed vessel, Robert Boyle set Robert Hooke to contrive a method less clumsy, and the result was the so-called machinea Boyleana, completed towards 1659. " * Bibliotheca Chemico-Mathematica (Volume I), 1921

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1679 Hannah Newton Smith, mother of Isaac Newton is buried. Exactly what she died of is not known. It was a contagious disease with symptoms that included blisters and a high fever. She contracted the illness while tending to a younger son, Benjamin Smith, at Stamford. He recovered, but she became gravely ill. Newton hurried from Cambridge, and personally attended his mother until her death in late May or early June of 1779. She was buried in Colsteworth. *Isaac Newton Fun facts.

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1734 The Dublin Journal advertised as “just published” bishop-elect George Berkeley’s The Analyst or a Discourse Addressed to an Infidel Mathematician, a work sharply critical of the foundations of the calculus. It had the positive effect of making mathematicians think about how to justify their work. [Works of George Berkeley, IV, 55] *VFR
The infidel mathematician in question is believed to have been either Edmond Halley, or Isaac Newton himself—though if to the latter, the discourse was then posthumously addressed, as Newton died in 1727. The most frequently quoted passage from The Analyst refers to the use of infinitesimals in the method of finding derivativ:"And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?"

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1769 June 04, 1769 Six hours after the transit of Venus there was a total solar eclipse. This solar eclipse was total in Scandinavia. Venus should have been projected in the corona of the sun. The planet was about one solar diameter from the edge of the sun. The next corona transit of Venus will be June 6, 2263. *NSEC

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1783 The brothers Montgolfier made their first public attempt to rise in a balloon at the marketplace in Annonay, near Lyons. In September, Euler, who was then 76, succeeded in integrating the difficult differential equations governing the motion of the balloon. In the course of the work he suffered several spells of dizziness; he died September 18, 1783. [Tietze, 290] *VFR
The Montgolfier Company still exists in Annonay (Ardèche, France). In 1799, Etienne de Montgolfier died. His son-in-law, Barthélémy Barou de la Lombardière de Canson (1774–1859), succeeded him as the head of the company, thanks to his marriage with Alexandrine de Montgolfier. The company became "Montgolfier et Canson" in 1801, then "Canson-Montgolfier" in 1807. Nowadays, Canson still produces fine art papers, school drawing papers and digital fine art and photography papers and is sold in 120 countries. *Wik

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1784 The very first woman to fly in a balloon followed only 8 months after the first manned flight, when opera singer Élisabeth Thible took her place with Mr. Fleurant on board a hot air balloon christened La Gustave in honour of King Gustav III of Sweden. Another early woman balloonist was Jeanne Geneviève Labrosse, who became the first woman to ascend solo in 1798 and, on October 12, 1799, the first woman to make a parachute descent (in the gondola), from an altitude of 900 meters. But also disaster is not far ahead. Ballooning was a risky business for the pioneers. When Marie Madeleine Sopie Blanchard ascended in her hydrogen balloon to watch a firework on July 6, 1819, she should 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. On May 20, 1784, the Marchioness and Countess of Montalembert, the Countess of Podenas and a Miss de Lagarde had taken a trip on a tethered balloon in Paris, but Elisabeth Thible was the first woman in the world to free float in a hot air balloon. *windows to world history

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1794 Joseph Priestley (1733-1804), chemist and natural philosopher, arrived at New York in the United States, having emigrated from England. Soon thereafter, he settled at Northumberland, Pennsylvania. Although now remembered for his scientific work (including the discovery of oxygen and other gases), in his time he became unpopular in England for his political opinions and support of the French Revolution. His home and laboratory were set on fire in 1791, and by 1794 he decided to leave his home country and pursue his scientific studies in America. *TIS

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1874 Mathematician William Kingdom Clifford elected to the Royal Society of London. He was one of the best known English scientists of his day because of his popular writings. [p. 16 of A Guide to Francis Galton’s English Men of Science, by Victor L. Hilts, Transactions of the American
Philosophical Society, volume 65, part 5, 1975] *VFR Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics and geometry. He was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression "mind-stuff". *Wik

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 1903 One of the world’s first hackers used Morse code insults to disrupt a public demo of Marconi's wireless telegraph. A demonstration of the Marconi radio communications system at the Royal Institution, London, was hacked by Nevil Maskelyne (His family claimed relation to the former Astronomer Royal, a claim historians dispute.  His father invented the pay toilet, a claim historians accept). Physicist John Ambrose Fleming was lecturing to give the public their first demonstration of wireless communication. Italian radio pioneer Guglielmo Marconi was at his clifftop radio station in Poldhu, Cornwall, 300 miles away, preparing to send a Morse code signal. Though the audience was unaware of it, the assistant tending the receiving apparatus found it was already tapping out the word "Rats", repeatedly. Then it mocked, “There was a young fellow of Itally, who diddled the public quite prettily...” and more. An adversary, music hall magician Neville Maskelyne was interrupting using a transmitter in a nearby hall, to make the point of security flaws in radio messaging.*TIS An entertaining presentation of the events in some detail are provided by The New Scientist

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1919 Emmy Noether received the right to teach at Gottingen.*VFR
also on June 4, 1919, Congress, by joint resolution, approved the woman's suffrage amendment and sent it to the states for ratification. The House of Representatives had voted 304-89 and the Senate 56-25 in favor of the amendment. (Library of Congress)... an odd coincidence?

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1924 Dissatisfied with the existing derivations of plank’s radiation law, Satyendra Nath Bose developed a logically satisfactory derivation based entirely on Einstein’s photon concept. Bose in his letter to Einstein wrote:

“I have ventured to send you the accompanying article for your perusal and opinion. I am anxious to know what you think of it. You will see that I have tried to deduce the coefficient 8p v2/c3 in Plank’s Law independent of classical electrodynamics, only assuming that the elementary regions in the phase-space has the content h3. I do not know sufficient German to translate the paper. If you think the paper worth publication I shall be grateful if you arrange for its publication in Zeitschrift für Physic. Though a complete stranger to you, I do not feel any hesitation in making such a request. Because we are all your pupils though profiting only by your teachings through your writings. I do not know whether you still remember that somebody from Calcutta asked your permission to translate your papers on Relativity in English. You acceded to the request. The book has since published. I was the one who translated your paper on Generalised Relativity.”

Einstein not only acknowledged the receipt of Bose’s letter but also assured Bose that he would have it published as he regarded it as an important contribution. Einstein applied Bose’s method to give the theory of the ideal quantum gas, and predicted the phenomenon of Bose-Einstein condensation.*Vigyan Prasar Science Portal
The class of particles that obey Bose–Einstein statistics, bosons, was named after Bose by Paul Dirac *Wik

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1925 “No one shall expel us from the paradise which Cantor created for us,” said David Hilbert in an address to the Westphalian Mathematical Society in Munster in honor of Karl Weierstrass. *VFR  The speech is online at the Dartmouth Math Site

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1934 Stanley Jashemski, 19, of Youngstown, Ohio is credited with what might be the shortest and most elegant proof of the Pythagorean theorem. A proof that Eli Maor has dubbed "The Folding Bag Proof."

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In 1963, six-year-old Robert Patch received a U.S. patent for a "Toy Truck" (No. 3,091,888). The toy separated into a chassis, driver's cab, truck body, wheels and four axles so it could be reassembled in either a closed van body or dump truck form. When the wheel axles were put into place, they also held the also cab and body to the chassis. The truck body can be turned upside down and end for end in order to mount as either a van body, or a dump truck body with a swinging back end. As a dump truck, the body pivots on the wheel axles to tip its load, and the back wall swings open on its own pivots at the top of the wall.*TIS  As with many school projects, Dad may have helped a little.

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1966 To commemorate the 300th anniversary of the Academie des Sciences, France issued a stamp picturing Bernard Le Bovier de Fontenelle and the 1666 meeting room of the Academie. [Scott #1159]. *VFR

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1982 Hungary issued a stamp picturing Rubik’s cube to celebrate the beginning of the First Rubik’s Cube World Championship, which began in Budapest the next day. [Scott #2752].

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1983   Commodore announces a reduced dealer price of US$200 for the Commodore 64 (C-64) computer at the Consumer Electronics Show (CES) in Chicago. They also announce an expanded software library of seventy new titles selling at prices of about half of the common price of software currently on the market. (*The Great Geek Manual)

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BIRTHS

1754 Franz Xaver von Zach (baron) (June 4, 1754 – September 2, 1832) German-Hungarian astronomer patronized by Duke Ernst of Saxe-Gotha-Altenburg. Director of observatory near Gotha (1787-1806). There he organized in 1798 the first congress of astronomers with Josef Lalande (1732-1807) as celebrated guest. In last years of the 18th century he formed a group of 24 astronomers chosen from throughout Europe to track down a "missing" planet between the orbits of Mars and Jupiter, where they instead discovered the asteroids. His greatest contribution was in the organizational area, for he maintained an enormous correspondence with all the astronomers of his time, and edited 28 volumes of Monatliche Korrespondenz zur Beforderung der Erd- und Himmelskunde (1800-13).*TIS

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1889 Beno Gutenberg (4 Jun 1889, 25 Jan 1960) American seismologist noted for his analyses of earthquake waves and the information they furnish about the physical properties of the Earth's interior. With Charles Richter, he developed a method of determining the intensity of earthquakes. Calculating the energy released by present-day shallow earthquakes, they showed that three-quarters of that energy occurs in the Circum-Pacific belt. *TIS

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1966 Vladimir Voevodsky (4 June 1966, ) is a Russian mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. *Wik

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DEATHS

1946 Ernst Leonard Lindelöf, (7 March 1870, Helsinki (in Swedish: Helsingfors)–4 June 1946, Helsinki) was a Finnish topologist after whom Lindelöf spaces are named; he was the son of Leonard Lorenz Lindelöf and brother of the philologist Uno Lorenz Lindelöf.
Lindelöf studied at the University of Helsinki, where he completed his Ph.D. in 1893, became a docent in 1895 and professor of Mathematics in 1903. He was a member of the Finnish Society of Sciences and Letters.
In addition to working on mathematical topics as diverse as differential equations and the gamma function, Lindelöf actively promoted the study of the history of Finnish mathematics.*Wik

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1973  Maurice René Fréchet ( September 2, 1878 – June 4, 1973) was a French mathematician known chiefly for his contribution to real analysis. He is credited with being the founder of the theory of abstract spaces, which generalized the traditional mathematical definition of space as a locus for the comparison of figures; in Fréchet's terms, space is defined as a set of points and the set of relations. In his dissertation of 1906, he investigated functionals on a metric space and formulated the abstract notion of compactness. In 1907, he discovered an integral representation theorem for functionals on the space of quadratic Lebesgue integrable functions. He also made important contributions to statistics, probability and calculus. *TIS

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Lloyd Viel Berkner (1 Feb 1905; 4 Jun 1967) American physicist and engineer who first measured the extent, including height and density, of the ionosphere (ionized layers of the Earth's atmosphere), leading to a complete understanding of radio wave propagation and he helped develop radar systems, especially the Distant Early Warning system. He later investigated the origin and development of the Earth's atmosphere. Early in his career, he worked on radio navigation beacons for the Airways division of the Bureau of Lighthouses (1927-28), as radio engineer on the Byrd Antarctic expedition (1928-30). Returning to the U.S. Bureau of Standards (1930-33) he studied the ionosphere using radio-pulse transmissions, then terrestial magnetism with the Carnegie Institution (1933-51). *TIS

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2008  Brian Griffiths, (26 Sept 1927 in Horwich, Lancashire, England - 4 June 2008 in Southampton, England) was an outstandingly able mathematician, whose career was devoted to helping others share his appreciation and love of the subject. What made Griffiths special among mathematics professors was his interest in education, the place of mathematics in society, what mathematics should be taught to whom, and how to teach the subject effectively. He also wrote or co-authored numerous books on topology, surfaces, analysis and mathematical models that provided teachers and others with accessible explanations of what was happening within university mathematics. *SAU

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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 - June 3

1908 article discussing the return of the comet in 1910

Whenever two unknown magnitudes appear
in a final equation, we have a locus,
the extremity of one of the unknown magnitudes

describing a straight line or a curve.

~Fermat Introduction to Plane and Solid Loci

The 155th day of the year; 155 is the sum of the primes between its smallest and largest prime factor. 155 = 5 x 31 and (5+ 7 + 11 + 13 + 17 + 19 + 23 + 29 +31 = 155) *Prime Curios
Can you find another such number? ***( Stijn Dierckx @Stanny1990 sent a link to a list of them)



Fun with primes: 2^2 + 3! + 5! + 7^2 - 11 - 13 = 155.

And from Math Year-Round ‏@MathYearRound 155² +155 ± 1 are twin primes. Students (and teachers) may be surprised how frequently x²2 + x ± 1 forms twin primes.

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EVENT

1636  In a letter to Fr. Marin Mersenne, Fermat describes the spiral with polar equation r²=a² x. 

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1696 Halley finds "his" comet; Entered in the Journal of the Royal Society on this day:

"Halley produced the Elements of the Calculation of the Motion of the two Comets that Appear'd in the years 1607 and 1682, which are in all respects alike, as to the place of their Nodes and Perihelia, their Inclinations to the sun.."

; *Lisa Jardine, Ingenious Pursuits pg37-38

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1769 Capt. James Cook pauses on his first circumnavigation of the globe to observe the transit of Venus in Tahiti. Cook and his ninety-eight foot bark, Endeavour, carried the Venus transit observation crew mounted by the Royal Society, led by a future Royal Soc. President, Joseph Banks. They would erect an observation station at Point Venus in Tahiti to observe the June 3, 1769 observation under clear blue skys. *Timothy Ferris, Coming of Age in the Milky Way
Banks himself never observed the transit. His journal records, "I then wishd success to the observers Msrs Gore and Monkhouse and repaird to the Island, where I could do the double service of examining the natural produce and buying provisions for my companions who were engagd in so usefull a work." *Captain Cook's Endeavour Journal website
For those who could not make such trips for the viewing, a fold-out view was in Benjamin Martin's 1773s "Institutions of Astronomical Calculations"

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1796 The first observatory in the U S was built by David Rittenhouse at his family farm in Norriton, Pa. in order to observe the transit of Venus across the sun on this date. He made the telescope and quadrant used for the observation. Rittenhouse was the first American astronomer to acquire international fame. He invented the first light diffraction grating, and discovered a comet. *Kane, Famous First Facts, pg 535

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1856 Lewis Carroll took his first photo of Alice Liddel.

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1880   Alexander Graham Bell transmitted the first wireless telephone message on his newly invented photophone from the top of the Franklin School in Washington, D.C. Bell believed that the photophone was his most important invention. The device allowed the transmission of sound on a beam of light. Of the eighteen patents granted in Bell's name alone, and the twelve that he shared with his collaborators, four were for the photophone.
Bell's photophone worked by projecting the voice through an instrument toward a mirror. Vibrations in the voice caused similar vibrations in the mirror. Bell directed sunlight into the mirror, which captured and projected the mirror's vibrations. The vibrations were transformed back into sound at the receiving end of the projection. The photophone functioned similarly to the telephone, except that the photophone used light as a means of projecting the information and the telephone relied on electricity. (Library of Congress)

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In 1965, the first American astronaut to make a spacewalk was Major Edward White II,  when he spent 20 minutes outside the Gemini 4 capsule during Earth orbit at an altitude of 120 miles. A tether and 25 foot airline were wrapped in gold tape to form a single, thick cord. He used a hand-held 7.5 pound oxygen jet propulsion gun to maneuver. The launch had taken place a few hours earlier on the same day. During the remainder of the flight, pilot White and his crewmate commander McDivitt completed 12 scientific and medical experiments. The total time in orbit was almost 98 hours, making 62 orbits. Soviet cosmonaut Aleksei A. Leonov, had made the first ever spacewalk for 10 minutes about three months earlier. *TIS

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1983 The Movie Wargames was released. It had the first use of the term "firewall" to appear in the movies.

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BIRTHS

1659 David Gregory (3 June 1659 – 10 October 1708) Scottish mathematician and astronomer. In 1702 he published a book Astronomiae physicae et geometricae elementa, an effort in the popularization of Newtonian science. However, in the matter of chromatic aberration, Gregory noted something that Newton had missed. Different kinds of glass spread the colours of the spectrum by different amounts. He suggested a suitable combination of two different kinds of glass might eliminate chromatic aberration. (A half century later, Dollond accomplished this result. (see below)) Telescopes were a special interest of his, and Gregory also experimented with making an achromatic telescope. *TIS  He was the nephew of astronomer and mathematician James Gregory.  (Thanks to ThonyC for calling my attention to an error of omission in the note above. Here, I hope, is the corrected history of the development of the achromatic lense)  [Credit for the invention of the first achromatic doublet is often given to an English barrister and amateur optician named Chester Moore Hall. Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses to two different opticians, Edward Scarlett and James Mann. They in turn sub-contracted the work to the same person, George Bass. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall failed to appreciate the importance of his invention, and it remained known to only a few opticians.
In the late 1750s, Bass mentioned Hall's lenses to John Dollond, who understood their potential and was able to reproduce their design. Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets.]

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1726 James Hutton (Edinburgh, 3 June 1726 OS (14 June 1726 NS) – 26 March 1797) Scottish geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

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DEATHS

1657 William Harvey (1 April 1578 – 3 June 1657) English physician and discoverer of the true nature of the circulation of the blood and of the function of the heart as a pump. Functional knowledge of the heart and the circulation had remained almost at a standstill ever since the time of the Greco-Roman physician Galen - 1,400 years earlier. Harvey's courage, penetrating intelligence, and precise methods were to set the pattern for research in biology and other sciences for succeeding generations, so that he shares with William Gilbert, investigator of the magnet, the credit for initiating accurate experimental research throughout the world.*TIS

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1903 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π² for the number of square-free integers not exceeding n.*SAU

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1925 Nicolas Camille Flammarion (26 Feb 1842; 3 Jun 1925 at age 83) was a French astronomer who studied double and multiple stars, the moon and Mars. He is best known as the author of popular, lavishly illustrated, books on astronomy, including Popular Astronomy (1880) and The Atmosphere (1871). In 1873, Flammarion (wrongly) attributed the red color of Mars to vegetation when he wrote “May we attribute to the color of the herbage and plants which no doubt clothe the plains of Mars, the characteristic hue of that planet...” He supported the idea of canals on Mars, and intelligent life, perhaps more advanced than earth's. Flammarion reported changes in one of the craters of the moon, which he attributed to growth of vegetation. He also wrote novels, and late in life he turned to psychic research. *TIS

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1971 Heinz Hopf  (19 November 1894 – 3 June 1971)  topologist   He studied under Ludwig Bieberbach, receiving his doctorate in 1925. In his dissertation, Connections between topology and metric of manifolds (German Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten), he proved that any simply connected complete Riemannian 3-manifold of constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space. He also studied the indices of zeros of vector fields on hypersurfaces, and connected their sum to curvature. Some six months later he gave a new proof that the sum of the indices of the zeros of a vector field on a manifold is independent of the choice of vector field and equal to the Euler characteristic of the manifold. This theorem is now called the Poincaré-Hopf theorem.*Wik

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1980 Naum Ilyich Akhiezer (6 March 1901 – 3 June 1980) was a Soviet mathematician of Jewish origin, known for his works in approximation theory and the theory of differential and integral operators. He is also known as the author of classical books on various subjects in analysis, and for his work on the history of mathematics. He is the brother of the theoretical physicist Aleksander Akhiezer.*Wik

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1990  Robert (Norton) Noyce was a U.S. engineer and coinventor (1959), with Jack Kilby, of the integrated circuit, a system of interconnected transistors on a single silicon microchip. He held sixteen patents for semiconductor devices, methods, and structures. In 1968, he and colleague Gordon E. Moore cofounded N.M. Electronics, which later was renamed Intel Corporation. Noyce served as Intel's president and chairman (1968-75), then as vice chairman until 1979. *TIS

1995  J(ohn) Presper Eckert, Jr. was an American engineer and coinventor of the first general-purpose electronic computer, a digital machine that was the prototype for most computers in use today.  In 1946, Eckert with John W. Mauchly fulfilled a government contract to build a digital computer to be used by the U.S. Army for military calculations. They named it ENIAC for Electronic Numerical Integrator and Computer. By 1949, they had started a manufacturing company for their BINAC computer. This was followed by a business oriented computer, UNIVAC (1951), which was put to many uses and spurred the growth of the computer industry. By 1966 Eckert held 85 patents, mostly for electronic inventions. *TIS

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2010   Vladimir Arnold (12 June 1937 – 3 June 2010) won a Wolf prize for his work on dynamical systems, differential equations, and singularity theory.    *SAU  Another who died within weeks of their birtdate; he was born on June 12. 

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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 - June 2

 I learned to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics. 

~ Paul Dirac

The 154th day of the year; 154 is the smallest number which is a palindrome in base 6, [444]₆ ; base 8 ,[242]₈; and base 9 ,[181]₉ all three.  Student's might search for a number that is a palindrome in other simple bases.

154 also has an interesting property with appropriate powers, 1+5⁶+4²= 15642. What other day numbers can you find with similar properties?

EVENTS

1661 An eager Isaac Newton departs his farm home at Woolsthorpe for Trinity College, Cambridge, although the term would not begin until September. He would remain at Trinity for thirty-five years. He took almost nothing with him. *Thomas Levenson, Newton and The Counterfeiter

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In 1686, the publication of Newton's Principia was arranged in London at the Royal Society. The minutes of the meeting record that the astronomer Edmund Halley would "undertake the business of looking after it and printing it at his own charge."

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1692 – Bridget Bishop is the first person to go to trial in the Salem witch trials in Salem, Massachusetts. Found guilty, she is hanged on June 10.

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In 1858, the Donati Comet was first seen and named after its discoverer, Giovanni Battista Donati, at Florence. It was the second-brightest comet of the nineteenth century It reached perihelion on 30 Sep 1858. When nearest the earth on 9 Oct 1858, it was about 0.5 AU away, and had developed a scimitar-shaped triple tail. At that time, its very prominent dust tail had with an apparent length of 50°, more than half the distance from the horizon to the zenith, a linear distance of over 72 million km (about 45 million mi). It was the first comet to be photographed. With an orbital period estimated at more than 2000 years, it will not return until about the year 4000. An astronomical unit, AU, equals 93 million miles, the Sun-Earth distance.

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1913 Millikan announced the results of his experiment to measure the electron charge. *VFR

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1924 – U.S. President Calvin Coolidge signs the Indian Citizenship Act into law, granting citizenship to all Native Americans born within the territorial limits of the United States.

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1925 – Because of a lineup revision by Miller Huggins, Wally Pipp is replaced by Lou Gehrig at first base for the New York Yankees, beginning a streak of 2,130 consecutive games played, topped only by Cal Ripken, Jr. in 1995. Exactly 16 years later to the day, in 1941, Gehrig dies from Amyotropic lateral sclerosis (ALS).

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1963 Between May 11 and June 2, Donald B. Gillies found three new primes. When the primes were confirmed the UIUC Math dept (which has a postal branch) used this cancellation stamp on all mail from roughly 1964 - 1976, when Appel and Haken proved the four color theorem ("Four Colors Suffice") and a new stamp was created. Trivia question : how far away from Gillies did Appel live in Urbana Illinois ??
Answer : He lived 3 houses away. *Wik

*Wik courtesy of Chris Caldwell

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1966 Surveyor 1 Makes soft-landing on the moon. It was the first lunar soft-lander in the unmanned Surveyor program of the National Aeronautics and Space Administration (NASA, United States). It gathered data about the lunar surface that would be needed for the manned Apollo Moon landings that began in 1969. The successful soft landing of Surveyor 1 on the Ocean of Storms was the first by an American space probe onto any extraterrestrial body, and it occurred just four months after the first Moon landing by the Soviet Union's Luna 9 probe.

Surveyor 1 was launched May 30, 1966 and landed on the Moon on June 2, 1966. It transmitted 11,237 still photos of the lunar surface to the Earth by using a television camera and a sophisticated radio-telemetry system. *Wik

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BIRTHS

1884  Henry Thomas Herbert Piaggio(2 June 1884–26 June 1967) graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations.

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1895 Tibor Radó (June 2, 1895 – December 29, 1965) was a Hungarian mathematician who moved to the USA after World War I. He was born in Budapest and between 1913 and 1915 attended the Polytechnic Institute. In World War I, he became a First Lieutenant in the Hungarian Army and was captured on the Russian Front. He escaped from a Siberian prisoner camp and, traveling thousands of miles across Arctic wasteland, managed to return to Hungary.
He received a doctorate from the University of Szeged in 1923. He taught briefly at the university and then became a research fellow in Germany for the Rockefeller Foundation. In 1929, he moved to the United States and lectured at Harvard University and the Rice Institute before obtaining a faculty position in the Department of Mathematics at Ohio State University in 1930. In 1935 he was granted American citizenship.
In the 1920s, he proved that surfaces have an essentially unique triangulation.
In 1933, Radó published "On the Problem of Plateau" in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions".
In World War II he was science consultant to the United States government, interrupting his academic career.
He became Chairman of the Department of Mathematics at Ohio State University in 1948.
His work focused on computer science in the last decade of his life and in May 1962 he published one of his most famous results in the Bell System Technical Journal: the Busy Beaver function and its non-computability ("On Non-Computable Functions").
In computability theory, a busy beaver (from the colloquial expression for an "industrious person") is a Turing machine that attains the maximum "operational busyness" (such as measured by the number of steps performed, or the number of nonblank symbols finally on the tape) among all the Turing machines in a certain class. The Turing machines in this class must meet certain design specifications and are required to eventually halt after being started with a blank tape. *Wik

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1916 Abraham Seidenbergwas  (June 2, 1916 – May 3, 1988)  known for his research to commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several important papers.*Wik

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DEATHS

1785 Jean Paul de Gua de Malves, (1713, Carcassonne – June 2, 1785, Paris) In 1740 he published a work on analytic geometry which, without the differential calculus, he found tangents, asymptotes, and various singular points of an algebraic function. He gave the proof of Descartes rule of signs which is found in modern texts. It is not known if Descartes ever proved it, and Newton seemed to think it was "obvious". (A short account of the history of mathematics By Walter William Rouse Ball)

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1917 William Henry Besant FRS (1 November 1828, Portsea, Portsmouth – 2 June 1917, Cambridge) was a British mathematician, brother of novelist Walter Besant.
In a competition, William won a scholarship to Corpus Christi College, Cambridge in 1844. He took part in Cambridge Mathematical Tripos in 1850, gaining the title of Senior Wrangler. He was also winner of Smith's Prize.
In 1853 William became a Fellow of Saint John's College, Cambridge where he was a lecturer in mathematics until 1889. His pupils included William Burnside, A. W. Flux and G. B. Mathews. Besant served as an examiner for Tripos in 1856, 1857, and 1885. He was also an examiner for University of London from 1859 to 1864. Besant was also a coach for students taking the Tripos; twenty-one of his students placed in the ranks of top ten wranglers. According to Mathews, "he had the great advantage (for a coach) of being equally good in geometry, analysis, and dynamics."
In 1859 Besant vacated his Fellowship with Saint John's college to marry Margaret Elizabeth Willis, daughter of Rev. Robert Willis, a professor of natural philosophy at Cambridge. They had two sons and a daughter. In 1863 Besant published Elementary Hydrostatics, a textbook on fluid statics containing mathematical exercises such as students might face in examination. The book was reprinted several times, and revised in 1892. He also wrote Treatise on Hydromechanics (1867) covering fluid mechanics. His book Elementary Conics came out in 1901.
Besant was a Fellow of the Royal Astronomical Society from 10 February 1854. He became a Fellow of the Royal Society in 1871. In 1883 Cambridge University bestowed upon him, and Edward Routh, the degree Sc.D.. He died on 2 June 1917 and is buried at the Parish of the Ascension Burial Ground in Cambridge.

He created the term Glissettes for his studies on the objects for Notes on Roulettes and Glissettes(1871). He writes in the preface:

*Wik

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1929 Otto Schreier (3 March 1901 in Vienna, Austria - 2 June 1929 in Hamburg, Germany) He will be best remembered for his work on subgroups of free groups which he studied in his habilitation thesis. He published the results in 1927 in the paper Die Untergruppen der freien Gruppe which is described as "... one of the most important papers ever published on combinatorial group theory. It took a long time for all its aspects to become effective, and it contains much more than the title indicates. "
In January 1926 Schreier attended a lecture given by Reidemeister in Hamburg on finding presentations for normal subgroups of finitely presented groups. Reidemeister published his method later in 1926. Schreier, who took a more algebraic approach compared to Reidemeister's geometrical approach, was able to extend Reidemeister's method to arbitrary subgroups and, by cleverly choosing generators for the subgroup, was able to greatly simplify the presentation obtained. Schreier published his method in his 1927 paper Die Untergruppen der freien Gruppe.
Other work of Schreier is described as follows:

... Schreier made important contributions to other parts of group theory. The classical Lie groups ... can be considered as topological spaces. Schreier (1927) showed that the fundamental group of such a space is always abelian. Schreier (1928) found an important refinement of the fundamental Jordan-Hölder theorem, 39 years after the publication of Hölder's paper. It is rare that such a widely used and basic theorem can be deepened after such a long time. (In this case, something even more unusual happened. Zassenhaus (1934) discovered a second improvement of the theorem.)

*SAU

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1942 Andrew Russell Forsyth (18 June 1858, Glasgow – 2 June 1942, South Kensington)   was a Scottish mathematician. He worked in differential equations, and function theory.
He studied at Liverpool College and was tutored by Richard Pendlebury before entering Trinity College, Cambridge, graduating senior wrangler in 1881.[1] He was elected a fellow of Trinity and then appointed to the chair of mathematics at the University of Liverpool at the age of 24. He returned to Cambridge as a lecturer in 1884 and became Sadleirian Professor of Pure Mathematics in 1895. He resigned his chair in 1910 after an affair with Marion Amelia Boys, the wife of C. V. Boys, who divorced her husband to marry him: this was unacceptable in Edwardian Cambridge. He became professor at the Imperial College of Science in 1913 and retired in 1923, remaining mathematically active into his seventies. He was elected a Fellow of the Royal Society in 1886 and won its Royal Medal in 1897.
He is now remembered much more as an author of treatises, than as an original researcher. His books have, however, often been criticized (for example by J. E. Littlewood, in his Mathematician's Miscellany). E. T. Whittaker was his only official student, according to the Mathematical Genealogy site. *Wik

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1946 William Peddie (31 May 1861 in Papa Westray, Orkney, Scotland - 2 June 1946 in Ninewells, Dundee, Scotland) graduated from Edinburgh University and then lectured in Physics. He was appointed Professor of Physics at Queen's College Dundee and held this post for 37 years. He was a founder member of the EMS and became President in 1895 and 1932. *SAU

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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