Sunday, 2 August 2015

On This Day in Math - August 2

The whole form of mathematical thinking was created by Euler. It is only with the greatest of difficulty that one is able to follow the writings of any author preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first to teach.

Ferdinand Rudio

The 214th day of the year; The 11th perfect number 2106 (2107−1) has 214 divisors. Also, 214*412+1 is prime. *Prime Curios
214 is the middle number in a string of three consecutive semiprimes


1133 The last total solar eclipse at Jerusalem took place on August 2, 1133 . The next total solar eclipses will be on August 8, 2241. *NSEC

1733 Benjamin Franklin suggest writers could improve their literary style if they learned a little Geometry in The Pennsylvania Gazette, August 2, 1733. "If a Writer would persuade, he should proceed gradually from Things already allow’d, to those from which Assent is yet with-held, and make their Connection manifest. .... Perhaps a Habit of using good Method, cannot be better acquired, than by learning a little Geometry or Algebra. " *Natl. Archives

In 1870, Tower Subway, the first tube railway in the world, was opened under the River Thames in London, England. Engineer James Henry Greathead used a tunnelling shield he modified from Barlow's design to bore the 6-ft diameter tunnel near the Tower of London. It opened with steam operated lifts and a 12-seat carriage shuttled from end to end by wire rope powered by a steam engine. It was not successful due to low use and frequent breakdowns, and the railway closed within three months (Nov 1870). The tunnel was converted to a foot tunnel with stairs. It was closed in 1894 when the opening of the nearby Tower Bridge made it redundant. The tunnel now holds water mains and fibre optic cables.*TIS

1876 The dead man's hand is a two-pair poker hand, namely "aces and eights". This card combination gets its name from a legend that it was the five-card-draw hand held by Wild Bill Hickok, when he was murdered on August 2, 1876, in Saloon No. 10 at Deadwood, South Dakota. "Wild Bill" Hickok was shot and killed by a drunken stranger at a poker table in Nuttall & Mann's Saloon No. 10 in Deadwood on August 2, 1876. Hickok had come to the Black Hills to explore the gold fields there, leaving his wife in Cincinnati. High School students should be able to find the probability of getting “the Dead Man’s hand” in a five card hand delt from a standard 52 card deck. *PB

In 1880, Greenwich Mean Time (GMT) was adopted officially by Parliament. Greenwich had been the national centre for time since 1675. GMT was originally set-up to aid naval navigation, but was not was used on land until transportation improved. In the 1840 's with the introduction of the railways there was a need in Britain for a national time system to replace the local time adopted by major towns and cities. (Thony Christie wrote to tell me that Edmund Halley had used Greenwich as 0 degree on a map in 1738)
GMT was adopted by the U.S. at noon on 18 Nov 1883 when the telegraph lines transmitted time signals to all major cities. Prior to that there were over 300 local times in the USA. GMT was adopted worldwide on 1 Nov 1884 when the met International Meridian Conference in Washington, DC, USA and 24 time zones created.*TIS  "The first printed chart or map known to have used Greenwich as its Prime Meridian was published in 1738. The Bradley Meridian not only defined the Zero of longitude for the first Ordnance Survey map published in 1801, but also remains the Zero Meridian used by the Ordnance Survey today." (This is about six meters west of the line agreed to in 1884 which is defined by the Airy Meridian now visited regularly by thousands (pb))  *The Greenwich Meridian

1932 Carl D. Anderson discovered the positron in 1932, for which he won the Nobel Prize for Physics in 1936. Anderson also coined the term positron. The positron was the first evidence of antimatter and was discovered when Anderson allowed cosmic rays to pass through a cloud chamber and a lead plate. A magnet surrounded this apparatus, causing particles to bend in different directions based on their electric charge. The ion trail left by each positron appeared on the photographic plate with a curvature matching the mass-to-charge ratio of an electron, but in a direction that proved its charge was positive.
Anderson wrote in retrospect that the positron could have been discovered earlier based on Chung-Yao Chao 's work, if only it had been followed up. *Wik

1939 Albert Einstein “wrote” President F. D. Roosevelt that “Some recent work by E. Fermi and L. Szilard ... leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. ... This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may be constructed.”
The letter, drafted by Fermi, Szilard, and Wigner and seems not to have actually been signed by Einstein until August 10, and was then given to Alexander Sachs, a confident of Roosevelt, who did not deliver it to him until October 30. Roosevelt quickly started the Manhattan Project. Einstein later regretted signing this letter. *(VFR & Brody & Brody); (the letter can be read at Letters of Note) They recognized the process could generate a lot of energy leading to power and possibly weapons. There was also concern the Nazi government of Germany was already searching for an atomic weapon. This letter would accomplish little more than the creation of a "Uranium Committee" with a budget of $6,000 to buy uranium and graphite for experiments.
Sir Fred Soddy's book, The Interpretation of Radium, inspired H G Wells to write The World Set Free in 1914, and he dedicated the novel to Soddy's book. Twenty years later, Wells' book set Leo Szilard to thinking about the possibility of Chain reactions, and how they might be used to create a bomb, leading to his getting a British patent on the idea in 1936. A few years later Szilard encouraged his friend, Albert Einstein , to write a letter to President Roosevelt about the potential for an atomic bomb. The prize-winning science-fiction writer, Frederik Pohl , talks about Szilard's epiphany in Chasing Science (pg 25),
".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."

2012 First of two full moons in a single month, August 2, August 31. August will have a "blue moon" on August 31 The last month with two full moons was March of 2010 on March 1 and March 30. The next month with a blue moon will be in the following month, September of 2012. After that, you have to wait until July of 2015.
(The Farmer's Almanac uses a different notation for "blue moon", the third full moon in a season of four full moons.)*Wik

1754 Pierre-Charles L'Enfant (August 9, 1754 - June 14, 1825 (aged 70))French-born and educated as an architect, L'Enfant came to the U.S. as a French engineer who assisted the American Continental Army in its fight against the British during the American Revolution. Appointed by President Washington in 1791 to design the new federal city, L'Enfant designed the basic plan for Washington, D.C., based on many European cityscapes. L'Enfant was dismissed from his job in 1792 following professional disagreements and personality clashes with the three commissioners appointed by President Washington to oversee the project.*TIS

1820 John Tyndall FRS (2 August 1820 – 4 December 1893) was a prominent 19th century physicist. His initial scientific fame arose in the 1850s from his study of diamagnetism. Later he studied thermal radiation, and produced a number of discoveries about processes in the atmosphere. He was the first to prove the "Greenhouse Theory" of the Earth's atmosphere. Tyndall published seventeen books, which brought state-of-the-art 19th century experimental physics to a wider audience. From 1853 to 1887 he was professor of physics at the Royal Institution of Great Britain in London. *Wik

1835 Elisha Gray (August 2, 1835 – January 21, 1901) was a U.S. scientist and innovator who would have been known to us as the inventor of the telephone if Alexander Graham bell hadn't got to the patent office before him earlier that day, resulting in a famous legal battle. He subsequently joined Western Electric where he designed the telegraph printer, the answer-back call-box of the A.D.T. System, and the needle annunciator, among other inventions. He also goes down in history as the accidental creator of the first electronic musical instrument using his discovery of the basic single note oscillator and design of a simple loudspeaker device.*TIS
It is interesting that Bell died on the date of Gray's birth.

1856 Ferdinand Rudio (2 Aug 1856 in Wiesbaden, Germany - 21 June 1929 in Zürich, Switzerland)worked on group theory, algebra and geometry. He is best remembered for his work in the history of mathematics, in particular he wrote a major article on squaring the circle and he also wrote biographies of mathematicians.
One of his most important contributions to mathematics was editing the collected works of Euler. Rudio proposed the project in 1883 since this was the centenary of Euler's death. He continued to advocate the importance of this project and at the International Congress of Mathematicians at Zurich in 1897 he suggested it would be a suitable memorial for the year 1907 which was the bicentennial of Euler's birth. The project was not approved until 1909, twenty six years after Rudio first proposed it.
Rudio was appointed general editor for the project. He edited two volumes himself and collaborated in the editing of three more. In fact he supervised the production of over 30 volumes in his role as general editor. *SAU

1887 Oskar Johann Viktor Anderson (2 August 1887, Minsk, Belarus – 12 February 1960, Munich, Germany) was a German-Russian mathematician. He was most famously known for his work on mathematical statistics.Anderson was born from a German family in Minsk (now in Belarus), but soon moved to Kazan (Russia), on the edge of Siberia. His father, Nikolai Anderson, was professor in Finno-Ugric languages at the University of Kazan. His older brothers were the folklorist Walter Anderson and the astrophysicist Wilhelm Anderson. Oskar Anderson graduated from Kazan Gymnasium with a gold medal in 1906. After studying mathematics for one year at University of Kazan, he moved to St. Petersburg to study economics at the Polytechnic Institute. From 1907 to 1915, he was Aleksandr Chuprov's assistant. In 1912 he started lecturing at a commercial school in St. Petersburg. In 1918 he took on a professorship in Kiev but he was forced to flee Russia in 1920 due to the Russian Revolution, first taking a post in Budapest (Hungary) before becoming a professor at the University of Economics at Varna (Bulgaria) in 1924. In 1935 he was appointed director of the Statistical Institute for Economic Research at the University of Sofia and in 1942 he took up a full professorship of statistics at the University of Kiel, where he was joined by his brother Walter Anderson after the end of the second world war. In 1947 he took a position at the University of Munich, teaching there until 1956, when he retired.*Wik

1902 Mina Spiegel Rees (2 August 1902 - 25 October 1997) was an American mathematician. She was the first female President of the American Association for the Advancement of Science (1971) and head of the mathematics department of the Office of Naval Research of the United States. She was valedictorian at Hunter College High School in New York City.[1] She graduated Summa cum Laude with a math major at Hunter College in 1923. She received a masters in mathematics from Columbia University in 1925. At that time she was told unofficially that "the Columbia mathematics department was not really interested in having women candidates for Ph.D's". She started teaching at Hunter College then took a sabbatical to study for the doctorate at the University of Chicago in 1929. She earned her doctorate in 1931 with a thesis on "Division algebras associated with an equation whose group has four generators," published in the American Journal of Mathematics, Vol 54 (Jan. 1932), 51-65. Her advisor was Leonard Dickson. *Wik
She became one of the earliest female computer pioneers. Before her death in 1997, Rees would leave her mark in the worlds of computers, mathematics, and education. Rees graduated with degrees in mathematics from Hunter College and Columbia University and ran the Office of Naval Research (ONR) after World War II, where she organized work on early computers such as the Harvard Mark I. Throughout her career, she made many important contributions to the use of computers in solving applied mathematical problems and was known for her strong administrative skills and influence. *CHM

1971 Ruth Elke Lawrence-Naimark (2 August 1971, Bristol, UK; ) is an Associate Professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. Lawrence's 1990 paper, Homological representations of the Hecke algebra, in Communications in Mathematical Physics, introduced, among other things, certain novel linear representations of the braid group — known as Lawrence–Krammer representation. In papers published in 2000 and 2001, Daan Krammer and Stephen Bigelow established the faithfulness of Lawrence's representation. This result goes by the phrase "braid groups are linear." Outside academia, she is best known for being a child prodigy in mathematics. She passed the GCSE in Math at age five, and in 1981 she passed the Oxford University interview entrance examination in mathematics, coming first out of all 530 candidates sitting the examination, and joining St Hugh's College in 1983 at the age of just twelve.*Wik


1823 Lazare Nicolas Marguerite, Comte Carnot (13 May 1753 – 2 August 1823) died. Carnot is best known as a geometer. In 1803 he published Géométrie de position in which sensed magnitudes were first systematically used in geometry.*Wik

1922 Alexander Graham Bell (March 3, 1847 – August 2, 1922) Scottish inventor of the telephone died in Beinn Bhreagh, Nova Scotia. Born in 1847, Bell's career was influenced by his grandfather (who published The Practical Elocutionist and Stammering and Other Impediments of Speech), his father (whose interest was the mechanics and methods of vocal communication) and his mother (who was deaf). As a teenager, Alexander was intrigued by the writings of German physicist Hermann Von Helmholtz, On The Sensations of Tone. At age 23 he moved to Canada. In 1871, Bell began giving instruction in Visible Speech at the Boston School for Deaf Mutes. This background set his course in developing the transmission of voice over wires. *TIS

1962 John Smith graduated from Glasgow University and then stayed on as a lecturer. He taught at Campbeltown Grammar School and Dollar Academy and then became an HM Schools Inspector. *SAU

1976 László Kalmár (March 27, 1905 – August 2, 1976) worked on mathematical logic and theoretical computer science. He was ackowledged as the leader of Hungarian mathematical logic. *SAU

*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

Saturday, 1 August 2015

On This Day in Math - August 1

Regarding all these basic topics in infinitesimal calculus which we teach today as canonical requisites ... the question is never raised, "Why so?" or "How does one arrive at them?" Yet all these matters must at one time have been goals of an urgent quest, answers to burning questions, at the time, namely, when they were created. If we were to go back to the origins of these ideas, they would lose that dead appearance of cut-and-dried facts and instead take on fresh and vibrant life again.
Otto Toeplitz - The calculus : A genetic approach (Chicago, 1963)

This is the 213th day of the year; 213 is a square free number as it has no repeated prime factors. How many days of the year are square free?

For 213, the sum of the digits and the product of the digits are equal, and forms a prime when one is added or subtracted.
The square of 213 is a sum of distinct factorials: 2132 = 45369 = 1! + 2! + 3! + 7! + 8!, it is the smallest 3 digit number with this property. (what's next?)

1767 “Mason and Dixon finished drawing the world’s longest straight line.” [366 Dumb Days in History, by Tom Koch]

In 1774, Joseph Priestley, British Presbyterian minister and chemist, identified a gas which he called "dephlogisticated air" -- later known as oxygen. Priestley found that mercury heated in air became coated with "red rust of mercury," which, when heated separately, was converted back to mercury with "air" given off. Studying this "air" given off, he observed that candles burned very brightly in it. Also, a mouse in a sealed vessel with it could breathe it much longer than ordinary air. A strong believer in the phlogiston theory, Priestley considered it to be "air from which the phlogiston had been removed." Further experiments convinced him that ordinary air is one fifth dephlogisticated air, the rest considered by him to be phlogiston. *TIS

1786 Caroline Herschel discovered her first comet, Comet Herschel C/1786 P1 and became history's first woman with this distinction. Her comet came to be known as the "first lady's comet" and brought with it the fame that secured her own place in history books.*The Woman Astronomer

1814 Almost a month after eloping with Georgiana Whitmore; a marriage of which his father did not approve, Charles Babbage writes to his friend John Herschel, who knew nothing of his secret romance, "I am married and have quarreled with my father." Then after a few lines of self-justification, he explains some theorems he has been working on. Herschel was shocked, and responded on the seventh of the same month.*Anthony Hyman, Charles Babbage: Pioneer of the Computer

In 1831, New London Bridge opened to traffic. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendour by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for $2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971.*TIS

1861 First use of "weather forcast". From the BBC I read, "Telling people what had happened was useful, but not as useful as telling them what was going to happen. The man who made the first attempt to bridge that gap, and who coined the phrase "weather forecast", was Admiral Robert Fitzroy. Thirty years before, he had been captain of the Beagle voyage that carried Charles Darwin, so he was no stranger to the perils of weather when at sea. In 1854, Fitzroy was given the job of collecting data on weather at sea, leading what later became the Met Office. After a few years, he saw that weather systems could be tracked. He became convinced that predictions were possible and that storm warnings would save many lives. His bosses did not agree that predictions were realistic, but in spite of them Fitzroy started to issue storm warnings in 1861. Then, on the 1st of August 1861 (exactly 151 years ago), Fitzroy issued the first ever weather forecast for the general public, published in The Times. This earned him a slap on the wrist and a huge amount of criticism, because it was considered that the forecasts could not possibly be accurate. After a lot of debate, the public forecasts ended in 1866."   A tweet from @ Rebekah Higgitt corrected this to : weather predictions existed long before (including, but not only, astrological), bt Aug 1861 *is* 1st use of term "weather forecast"..

1944 The MARK I computer began operation at Harvard. *VFR

1946 President Harry Truman signs the McMahon Act creating the Atomic Energy Commission.
* HT to Ben Gross ‏@bhgross144

1947 The Netherlands issued a postage stamp honoring Jans(Johan) de Witt (1625–1672), who did important early work dealing with analytic geometry. *VFR Besides being a statesman Johan de Witt, also was an accomplished mathematician. In 1659 he wrote "Elementa Curvarum Linearum" as an appendix to his translation of René Descartes' "La Géométrie". In this, De Witt derived the basic properties of quadratic forms, an important step in the field of linear algebra. *Wik

In 1957, the Solar Building (Bridgers and Paxton Office Building), Albuquerque NM, was the first commercial building to be heated by the sun's energy. It was subsequently listed in the National Register of Historic Places for its "exceptional importance," in the area of engineering because it was an early solar-heated commercial building, the equipment for which survived largely intact. It was constructed when active solar-energy systems were still considered experimental. The site is privately owned, at 213 Truman St., NE., Albuquerque, NM. The architectural design was provided by Wright and Stanley.*TIS

1963 Greece issued a postage stamp picturing the “Acropolis at Dawn” by Lord Baden-Powell.*VFR

1967US Navy recalls Hopper to head COBOL effort.  The US Navy recalls Captain Grace Murray Hopper to active duty to help develop the programming language COBOL. With a team drawn from several computer manufacturers and the Pentagon, Hopper -- who had worked on the Mark I and II computers at Harvard in the 1940s -- created the specifications for COBOL (COmmon Business Oriented Language) with business uses in mind. These early COBOL efforts aimed at creating easily-readable computer programs with as much machine independence as possible. Designers hoped a COBOL program would run on any computer for which a compiler existed with only minimal modifications.
Hopper made many major contributions to computer science throughout her very long career, including what is likely the first compiler ever written, "A-0." She appears to have also been the first to coin the word "bug" in the context of computer science, taping into her logbook a moth which had fallen into a relay of the Harvard Mark II computer. She died on January 1, 1992.
The U.S. Navy commissioned their most advanced ship, the U.S.S. Hopper (DDG 70), on September 6, 1997 named in honor of Grace Hopper. *CMH

1980 Michael Aschbaher wrote Daniel Gorenstein that he had completed the classification of the finite simple groups. This culminated a 20-year effort by some 300 group theorists. The complete proof is about 5000 pages long. [Mathematics Magazine 54 (1981), p. 41

2011   Carolin Crawford selected as the Gresham Professor of Astronomy. *Wik

1817 Sir (Joseph) Henry Gilbert (1 August 1817 - 23 December 1901) English chemist who as co-director with John Bennet Lawes of the Rothamsted Experimental Station, Hertfordshire, for over 50 years established a premier reputation for research at the first organized agricultural experimental station in the world. Their work applied skills in chemistry, meteorology, botany, animal and vegetable physiology, and geology to determine practical improvements for agricultural methods. They studied the nitrogen requirements of plants, how the element was taken up by plants, and the effects of nitrogen fertilizers on grain production and quality. In the 1840s, they initiated the manufacture of superphosphate fertilizer, one of their inventions.*TIS

First Astronomy Class at Vassar College 1866
1818 Maria Mitchell (August 1, 1818 – June 28, 1889) First professional woman astronomer in the United States, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Scienes.
She became professor of astronomy at Vassar College in 1865, the first person (male or female) appointed to the faculty.  She was also named as Director of the Vassar College Observatory. After teaching there for some time, she learned that despite her reputation and experience, her salary was less than that of many younger male professors. She insisted on a salary increase, and got it. She taught at the college until her retirement in 1888, one year before her death.She died at age 70 in Lynn, Mass. *TIS

1861 Ivar Otto Bendixson (August 1, 1861 – 1935) taught at Stockholm, then from 1913 to 1927 he was rector of Stockholm University. He worked on set theory and differential equations. He is best remembered for the Poincaré - Bendixson theorem. *SAU

1881 Otto Toeplitz (1 August 1881, Breslau – 15 February 1940, Jerusalem) born in Breslau, Germany. In 1905 he received his Ph.D. in algebraic geometry at the university there and then moved to G¨ottingen, where he was deeply influenced by the work of Hilbert. He was also interested in the history of mathematics and held that only a mathematician of stature is qualified to be a historian of mathematics. In 1949 he published an introduction to the calculus on a historical basis. This delightful book is available in English as The Calculus. A Genetic Approach. *VFR

1905 Helen Battles (Sawyer) Hogg (1 Aug 1905, 28 Jan 1993) was a Canadian astronomer who located, cataloged and measured the distances to variable stars in globular clusters (stars with cyclical changes of brightness found within huge, dense conglomerations of stars located in the outer halo of the Milky Way galaxy). Her interest in astronomy was spurred when she witnessed a total eclipse of the sun in 1925. Alongside her career work, she was also foremost in Canada in popularizing astronomy, about which she wrote a column in the Toronto Star for thirty years. She was the first woman to become president of the Royal Canadian Institute. In 1989, the observatory at the National Museum of Science and Technology in Ottawa was dedicated in her name.*TIS

1924 Georges Charpak (1 August 1924 – 29 September 2010) was a French physicist who was awarded the Nobel Prize in Physics in 1992 "for his invention and development of particle detectors, in particular the multiwire proportional chamber". This was the last time a single person was awarded the physics prize. *Wik

1937 Barry Edward Johnson (1 Aug 1937 Woolwich, London, England – 5 May 2002 Newcastle upon Tyne, England) is well known for his work on Banach algebras and operator algebras, in particular, studying cohomology in these algebras. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. In these he examined the theory of centralizers and the continuity of transformations. In 1964 he wrote a joint paper with Ringrose Derivations of operator algebras and discrete group algebras and his next papers continued to examine the continuity of homomorphisms, derivations and linear operators. He developed cancer on February 2000 and fought the disease bravely. Despite his deteriorating physical condition, he continued to undertake cutting edge mathematical research. He died of cancer in St Oswald's Hospital in Newcastle upon Tyne aged 64. *SAU

1955 Bernadette Perrin-Riou (August 1, 1955 - ) was awarded the 1999 Ruth Lyttle Satter Prize in recognition of her number theoretical research on p-adic L-functions and Iwasawa theory.

1970 Elon Lindenstrauss (August 1, 1970 - ) was the first Israeli to be awarded the Fields Medal, for his results on measure rigidity in ergodic theory, and their applications to number theory.
Since 2004, he has been a professor at Princeton University. In 2009, he was appointed to Professor at the Mathematics Institute at the Hebrew University.
Lindenstrauss is the son of the mathematician Joram Lindenstrauss, the namesake of the Johnson–Lindenstrauss lemma, and computer scientist Naomi Lindenstrauss, both professors at the Hebrew University.
Lindenstrauss was awarded the Erdős Prize and the Fermat Prize in 2009. *Wik

1630 Federico Cesi (13 Mar 1585; 1 Aug 1630 at age 45) Italian scientist who founded the Accademia dei Lincei (1603, Academy of Linceans or Lynxes), often cited as the first modern scientific society, and of which Galileo was the sixth member (1611). Cesi first announced the word telescope for Galileo's instrument. At an early age, while being privately educated, Cesi became interested in natural history and that believed it should be studied directly, not philosophically. The name of the Academy, which he founded at age 18, was taken from Lynceus of Greek mythology, the animal Lynx with sharp sight. He devoted the rest of his life to recording, illustrating and an early classification of nature, especially botany. The Academy was dissolved when its funding by Cesi ceased upon his sudden death(at age 45). *TIS It was revived in its currently well known form of the Pontifical Academy of Sciences, by the Vatican, Pope Pius IX in 1847.

1920 Bal Gangadhar Tilak (23 July 1856 – 1 August 1920, age 64), scholar, mathematician, philosopher, and militant nationalist who helped lay the foundation for India's independence. He founded (1914) and served as president of the Indian Home Rule League and, in 1916, concluded the Lucknow Pact with Mohammed Ali Jinnah, which provided for Hindu-Muslim unity in the struggle for independence. *TIS

1987 Evelyn Merle Nelson (November 25, 1943 – August 1, 1987), born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science. Nelson's teaching record was, according to one colleague, "invariably of the highest order". However, before earning a faculty position at McMaster, prejudice against her lead to doubts about her teaching ability. Nelson published over 40 papers during her 20-year career before she died from cancer in 1987.
She, along with Cecilia Krieger, is the namesake of the Krieger–Nelson Prize, awarded by the Canadian Mathematical Society for outstanding research by a female mathematician. *Wik

1992 Leslie Fox (September 1918 Dewsbury, Yorkshire-1 August 1992 Oxford) was a British Mathematician noted for his contribution to numerical analysis.
Fox studied mathematics as a Scholar of Christ Church, Oxford graduating with a First in 1939 and continued to undertake research in the engineering department. While working on his D.Phil. in computational and engineering mathematics under the supervision of Sir Richard Southwell he was also engaged in highly secret war work. He worked on the numerical solution of partial differential equations at a time when numerical linear algebra was performed on a desk calculator. Computational efficiency and accuracy was thus even more important than in the days of electronic computers. Some of this work was published after the end of the Second World War jointly with his supervisor Richard Southwell.
On gaining his doctorate in 1942 Fox joined the Admiralty Computing service. Following the war, in 1945 he went to work in the mathematics division of the National Physical Laboratory. He left the National Physical Laboratory in 1956 and spent a year at the University of California. In 1957 Fox took up an appointment at Oxford University where he set up the Computing Laboratory. In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford and Fellow of Balliol College, Oxford.
Fox's laboratory at Oxford was one of the founding organisations of the Numerical Algorithms Group, and Fox was also a dedicated supporter of the Institute of Mathematics and its Applications (IMA). The Leslie Fox Prize for Numerical Analysis of the IMA is named in his honour.*Wik

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

Friday, 31 July 2015

On This Day in Math - July 31

I advise my students to listen carefully the moment
they decide to take no more mathematics courses.
They might be able to hear the sound of closing doors.
~Caballero, James

The 212th day of the year; Besides being the Fahrenheit boiling point of water at sea level, 212 produces a prime of the form k10+k9+...+k2+k+1, when k=212. (Edward Shore@edward_shore sent me a note:" That number would be 184,251,916,841,751,188,170,917.")
(students might explore different values of k, and different maximum exponents to produce when k is 2, then 26 +25+...+22+2+1 is prime


1669 Lucasian professor Isaac Barrow sent John Collins a manuscript of Newton’s De analysi and thereby Newton’s anonymity began to dissolve. It was a summary of Newton’s work on the calculus and was written after Newton saw Nicholas Mercator’s Logarithmotechnia (1668). Newton wrote his paper in order that he would not lose credit for his work on infinite series. Collins immediately recognized Newton’s genius. Although not published until 1711, this paper led to Newton’s appointment as Lucasian professor on 29 October 1669.*VFR

1790 The U.S. Patent Office issued its first patent to Samuel Hopkins of Vermont for his “process for making pot and pearl ashes,” whatever they are. Since George Washington and Thomas Jefferson signed Hopkins’ patent, more than 4 million have been issued. *VFR In 1790, the first U.S. patent was granted to Samuel Hopkins of Vermont for a process for making potash and pearl ashes. Potash was important as an ingredient in soap and fertilizer. The patent was granted for a term of 14 years and signed by President George Washington, who had the previous month signed the first U.S. patent statute into law on 10 April 1790. Hopkins did not get Patent with a serial No.1 as thousands of patents were issued before the Patent Office began to number them. Congress had passed the Patent Act on 10 Apr 1790. Two other patents were granted that year - one for a new candle-making process and the other the flour-milling machinery of Oliver Evans. The next year, 1791, Samuel Hopkins also was granted the first Canadian patent.*TIS

1851 Gauss witnessed the opening ceremonies when the newly constructed railway from Cassel reached Gottingen. *VFR

1943 Ireland issued—as its first stamp with a mathematical theme—two stamps to celebrate the centenary of the discovery of Quaternions by Sir William Rowan Hamilton. [Scott #126-7]. *VFR

2015 The second full moon this month (the other was on the 2nd). This only happens “Once in a blue moon”—and this is the origin of the phrase. Consequently, there were be thirteen full moons this year.  The last "blue moon" was in 1985, and the next is predicted in 2018.


1704 Gabriel Cramer (31 July 1704 – 4 January 1752). He is best known for “Cramer’s Rule,” a method for solving systems of simultaneous linear equations using determinants. *VFR Gabriel Cramer (31 July 1704 – 4 January 1752) was a Swiss mathematician, born in Geneva. He showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics. In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. He published his best known work in his forties. This was his treatise on algebraic curves, "Introduction à l'analyse des lignes courbes algébriques", published in 1750. It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position. He edited the works of the two elder Bernoullis; and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746). He was professor at Geneva, and died at Bagnols-sur-Cèze.*Wik

1712 Samuel König (July 31, 1712, Büdingen – August 21, 1757, Zuilenstein near Amerongen) was a German mathematician who is best remembered for his part in a dispute with Maupertuis over the Principle of Least Action.*SAU

1718 John Canton (31 July 1718 – 22 March 1772) British physicist and teacher, born Stroud, Gloucestershire. He made a number of minor discoveries in physics and chemistry. As a result of preparing artificial magnets in 1749 he was elected to the Royal Society. In 1762, he demonstrated that water was slightly compressible. He invented a number of devices in connection with electricity. His notable work, between 1756 and 1759, was to record that on days when the aurora borealis was particularly bright, a compass needle behaved with more irregularity than usual. Thus he was the first to record this as an electromagnetic phenomenon for what is now known to be a magnetic storm.*TIS

1826 Daniel Friedrich Ernst Meisse mathematical work covers number theory, work on Möbius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem. *SAU

1843 Friedrich Robert Helmert (July 31, 1843 – June 15, 1917) German geodesist and an important writer on the theory of errors.
From 1887 Helmert was professor of advanced geodesy at the University of Berlin and director of the Geodetic Institute.
Helmert received many honours. He was president of the global geodetic association of "Internationale Erdmessung", member of the Prussian Academy of Sciences in Berlin, was elected a member of the Royal Swedish Academy of Sciences in 1905, and recipient of some 25 German and foreign decorations. *TIA

1858 Richard Dixon Oldham (31 July 1858 – 15 July 1936) Irish geologist and seismologist who discovered evidence for the existence of the Earth's liquid core (1906). In studying seismograms of great 1897 Indian Earthquake he identified P (primary) and S (secondary) waves. It is interesting that he did not get a clue to the presence of the core from the S waves, which are actually incapable of being transmitted through the liquid of the outer core. (The liquid core does not transmit the shear wave energy released during an earthquake.) Rather he noted the existence of a shadow zone in which P waves from an earthquake in the opposite hemisphere of the earth failed to appear*TIS

1863 George Abram Miller (31 July 1863 – 10 February 1951) was an early group theorist whose many papers and texts were considered important by his contemporaries, but are now mostly considered only of historical importance.
Miller was born in Lynnville, Lehigh County, Pennsylvania, and died in Urbana, Illinois.*Wik

1923 Joseph B. Keller (born July 31, 1923, Paterson, New Jersey) is an American mathematician who specializes in applied mathematics. He is best known for his work on the "Geometrical Theory of Diffraction" (GTD).
He worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein-Brillouin-Keller method for computing eigenvalues in quantum mechanical systems.
In 1988 he was awarded the U.S. National Medal of Science, and in 1997 he was awarded the Wolf Prize by the Israel-based Wolf Foundation. In 1996, he was awarded the Nemmers Prize in Mathematics.*Wik

1945 John O'Connor (31st July 1945 in Luton, Bedfordshire, England.- )
Lists his Research interests A lapsed topologist, I am interested in Computational Algebra.
I am interested in the History of Mathematics and at present am supervising two research students in this area. * His Personal web page

1927 F. E. Browder born. Worked in Nonlinear monotone operators and convex sets in Banach spaces. and more.


1726 Nikolaus II Bernoulli died (February 6, 1695, Basel, Switzerland – July 31, 1726, St. Petersburg, Russia). *VFR Nicolaus(II) Bernoulli was the favourite of three sons of Johann Bernoulli. He made important mathematical contributions to the problem of trajectories while working on the mathematical arguments behind the dispute between Newton and Leibniz.*SAU

1784 Denis Diderot died. (October 5, 1713 – July 31, 1784) was a French philosopher, art critic, and writer. He was a prominent persona during the Enlightenment and is best-known for serving as co-founder and chief editor of and contributor to the Encyclopédie. *Wik

1896 Ludwig Christian Wiener (7 December 1826 Darmstadt – 31 July 1896 Karlsruhe) was a German mathematician, physicist and philosopher, known for his explanation of Brownian motion , which identified him as a skillful experimenter. He mainly dealt with geometry.*Wik

1913 John Milne (30 December 1850 – 31 July 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease*TIS

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

Thursday, 30 July 2015

On This Day in Math - July 30

I have created a new universe from nothing.
~Janos Bolyai

The 211th day of the year; 211 is a primorial prime,(a prime that is one more, or one less than a primorial  can you find the next larger (or smaller) primorial prime? 211 is also the sum of three consecutive primes (67 + 71 + 73)...

There are also 211 primes on a 24-hour digital clock. (00:00 - 23:59) *Derek Orr@ Derektionary


1738 Euler sends a letter to John Bernoulli with the solution to a question from Danial Bernoulli regarding isoperimetric curves, particularly the  one for which the integral of rm gave a maximum or minimum.

1859 Bernhard Reimann is appointed full professor at Gottingen, succeeding his two former teachers, Gauss and Dirichlet. He also is allowed to occupy Gauss' apartments at the observatory. *John Derbyshire, Prime Obsession, pg 135

In 1898, Corn Flakes were invented by William Kellogg. At Battle Creek Sanitarium, Sanitarium superintendent, Dr. John Harvey Kellogg and Will Keith Kellogg, his younger brother and business manager, invented many grain-based foods, including a coffee substitute, a type of granola, and peanut butter to provide patients a strict nutritious diet. In 1894 they unintentionally invented a flaked cereal process based on wheat. By 1898, W.K. Kellogg had developed the first flaked corn cereal. Patients enjoyed the cereals and wanted more to take home. In 1906, the Battle Creek Toaster Corn Flake Company was founded by W.K. Kellogg.*TIS

1918 Richard Courant sat down with Ferdinand Springer and signed a contract for the series of books now famous as the “Yellow Series.” *Constance Reid, Courant in Gottingen and New York, p. 72

1971 Apollo 15 mission became the fourth mission to land on the moon when the Falcon lunar lander touched down. This mission allowed the astronauts to spend more time on the surface of the moon. The lander stayed three days on the surface and the crew conducted over 18 hours of outside work. They also were aided for the first time by a lunar rover vehicle.*Science Today


1857 Thorstein Bunde Veblen, (July 30, 1857 – August 3, 1929) was an American economist and sociologist, and a leader of the so-called institutional economics movement. Besides his technical work he was a popular and witty critic of capitalism, as shown by his best known book The Theory of the Leisure Class (1899).

1863 Henry Ford (July 30, 1863 – April 7, 1947) American inventor and car manufacturer, born in Dearborn, Mich. Ford first experimented with internal combustion engines while he was an engineer with the Edison Illuminating Company. He completed his first useful gas motor on 24 Dec 1893. The Quadricycle, he designed made its first road test on 4 Jun 1896. In 1903 the Ford Motor Company was incorporated. By 1908, Ford was manufacturing the low cost, reliable Model T, while continuing to revolutionize his industry. Ford introduced precision manufactured parts designed to be standardized and interchangeable parts. In 1913, production was increased using a continuous moving assembly line. By 1918, half of all cars in America were Model T's.*TIS

1878 Joel Stebbins (July 30, 1878 – March 16, 1966) was an American astronomer who pioneered photoelectric photometry in astronomy.
He earned his Ph.D at the University of California. He was director of University of Illinois observatory from 1903 to 1922 and the Washburn Observatory at the University of Wisconsin-Madison from 1922 to 1948. After 1948, Stebbins continued his research at Lick Observatory until his final retirement in 1958.
Stebbins brought photoelectric photometry from its infancy in the early 1900s to a mature technique by the 1950s, when it succeeded photography as the primary method of photometry. Stebbins used the new technique to investigate eclipsing binaries, the reddening of starlight by interstellar dust, colors of galaxies, and variable stars.
Stebbins received the following awards:
Rumford Prize of the American Academy of Arts and Sciences (1913)
Henry Draper Medal of the National Academy of Sciences (1915)
Bruce Medal of the Astronomical Society of the Pacific (1941)
Gold Medal of the Royal Astronomical Society (1950)
Henry Norris Russell Lectureship of the American Astronomical Society (1956)
The Lunar crater Stebbins and the asteroid 2300 Stebbins are named in his honor. *TIA

1887 Felix Andries Vening Meinesz (The Hague July 30, 1887 - Amersfoort August 10, 1966) was a Dutch geophysicist and geodesist who was known for his measurements of gravity at sea for which he devised the Vening Meinesz pendulum apparatus with comparable accuracy as on land. Starting in 1923 he conducted several global gravity surveys on voyages on submarines, particularly to and in the Indonesian Archipelago. He detected strong gravity anomaly belts running parallel to the Indonesian deep sea trenches. He explained these Meinesz belts as sites of downbuckling of the Earth's crust. He introduced the concept of regional isostasy taking flexure of an elastic crust into account. He also contributed to physical geodesy: The Vening Meinesz formula connects the deviation of the vertical from the plumbline to gravity anomalies. *TIS

1888 Vladimir Zworykin (July 29 [O.S. July 17] 1888 – July 29, 1982) was born in Russia. After emigrating to Pittsburgh, Zworykin took a job at Westinghouse Electric Corp., where in 1923 he filed a patent for the iconoscope, the first television transmission tube and a technology that was to become of interest to early computer designers. With a later invention, the kinescope, Zworykin was able to create the first all-electric television system. Zworykin took the technology to RCA in 1929, where he continued his work and earned the title "father of television.*CMH


1762 William Braikenridge (1700; 30 July 1762 in London, England) was an English clergyman who worked on geometry and discovered independently many of the same results as Maclaurin.*SAU

1978 Rufus Bowen (23 February 1947 - 30 July 1978) worked on dynamical systems. Rufus died of a cerebral hemorrhage at the age of 31. *SAU
In 1970, Bowen completed his doctorate in Mathematics at Berkeley under Stephen Smale, and joined the faculty as assistant professor in that year. At this time he began calling himself Rufus, the nickname he had been given because of his red hair and beard.  He was an invited speaker at the 1974 International Mathematical Conference in Vancouver, British Columbia.He was promoted to full professorship in 1977.
Bowen's mature work dealt with dynamical systems theory, a field which Smale, Bowen's dissertation advisor, explored and broadened in the 1960s.

1985 Julia Robinson (December 8, 1919 – July 30, 1985) died of leukemia. After receiving her Ph.D. in 1948 under the direction of Alfred Tarski, she began work on Hilbert’s tenth problem, the problem which occupied most of her professional life.*VFR She also worked on computability, decision problems and non-standard models of arithmetic. *SAU Her sister was Constance Reid who wrote biographies of several mathematicians and several popular math books.

2002 Dr. Lyle B. Borst, (Nov 24, 1912 - July 30, 2002) was a nuclear physicist who helped build Brookhaven National Laboratory's nuclear reactor and was an early member of the Manhattan Project.
In 1950, Dr. Borst led the construction of the Brookhaven Graphite Research Reactor, which was the largest and most powerful reactor in the country and the first to be built solely for research and other peacetime uses of atomic energy.
Within the first nine months of operating the reactor, Dr. Borst announced that it had produced a new type of radioactive iodine, which is used in treating thyroid cancer.
In 1952, based on studies of new types of atomic nuclei created in the reactor, Dr. Borst helped explain the mystery behind giant stars, known as supernovae, that burst with the energy of billions of atomic bombs and flare for several years with the brilliance of several million suns.
Dr. Borst found that beryllium 7, an isotope of beryllium that does not occur naturally on earth, is formed in supernovae by the fusion of two helium nuclei. The fusion takes place after the star has used up its hydrogen supply. This reaction absorbs huge quantities of energy, causing the star to collapse in the greatest cosmic explosion known. *NY Times obit.

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