Sunday 4 June 2023

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 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 x2+ x ± 1 forms twin primes.

155 is also a pentagonal number, n*(3*n-1)/2, n=0, +- 1, +- 2, +- 3, ..... Euler showed that the pentagonal numbers are the coefficients of the expansion of the infinite polynomial (1-x)(1-x2)(1-x3)....  John H. Conway showed that the same series can be found by taking the triangular numbers that are divisible by three, and dividing them.

At one time, a new perfect number of 155 digits was announced. On March 27,1936 The Associated Press released a story that a new 155 digit perfect number had been found by Dr. S. I. Krieger of Chicago. The number was \(2^{256}(2^{257} - 1)\) by proving the \(2^{257} -1\) was prime. This was shocking since D. H. Lehmer and M. Kraitcik had announced that the number was composite in 1922. Unfortunately, their method did not include giving a factor of the number. The perfection of the number was doubted by most mathematicians, but the actual factoring to prove it was composite didn't happen until 1952 when the SWAC confirmed it was composite by finding a proper divisor. *Beiler, Recreations in the Theory of Numbers. According to current lists, the closest number of digits for a perfect number are a 77 digit number found by Edouard Lucas in 1876, and a 314 digit number found by R M Robinson in 1952.


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.

1004 al-Biruni observed two lunar eclipses from Gurgān,(Azerbaijan)  one on 19 February and the other on 14 August. On 4 June of the following year, 1004, he observed a third lunar eclipse.  *Encylopedia . com

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. *
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

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.

1730 Euler observes that 2n + 1 is composite if n has an odd prime divisor. “Lately, reading Fermat’s works, I came upon another rather elegant theorem stating that any number is the sum of four squares, or that for any number four square numbers can be found whose sum is equal to the given number”. *Lemmemeyer, EULER, GOLDBACH, AND “FERMAT’S THEOREM” (In a letter to Carcavi in August of 1659, Fermat claimed to have a proof of the four squares theorem. )

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 derivatives:"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?"

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

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

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

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

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

 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

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?

1924 Dissatisfied with the existing derivations of planck’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 Planck’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

On this day in 2022 Google released a Bose doodle (commemorating the day in 1924 that he sent his quantum formulations to Albert Einstein).


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

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."

Does this really prove the Pythagorean Theorem?

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 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     He was the youngest person to receive a U.S. patent.  As with many school projects, Dad may have helped a little.

*Sutter Swantz 

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

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].

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)



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

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

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

1966 Svetlana Yakovlevna Jitomirskaya (born June 4, 1966) is a Soviet-born (Ukranian) American mathematician working on dynamical systems and mathematical physics.She is a distinguished professor of mathematics at Georgia Tech. She is best known for solving the ten martini problem along with mathematician Artur Avila. Both her mother, Valentina Borok, and her father, Yakov Zhitomirskii, were professors of mathematics.

Her undergraduate studies were at Moscow State University, where she was a student of, among others, Vladimir Arnold and Yakov Sinai. She obtained her Ph.D. from Moscow State University in 1991 under the supervision of Yakov Sinai. She joined the mathematics department at the University of California, Irvine in 1991 as a lecturer, and she became an assistant professor there in 1994 and a full professor in 2000.

In 2005, she was awarded the Ruth Lyttle Satter Prize in Mathematics, "for her pioneering work on non-perturbative quasiperiodic localization". *Wik



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

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

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

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

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

No comments: