Friday, 25 May 2018

On This Day in Math - May 25

Some people are always critical of vague statements. 
I tend rather to be critical of precise statements; 
they are the only ones which can correctly be labeled wrong.

~ Raymond Smullyan on criticism

The 145th day of the year; 145= 1! + 4! + 5!. There are only four such numbers in base ten. 1, 2 and 145 are three of them, what's the fourth? Such numbers are called factorions, a term created by Cliff Pickover in 1995  (**answer at bottom of post)

145 is the result of 34 + 43, making it a Leyland number. a number of the form xy + yx where x and y are integers greater than 1. They are named after the British number theorist, Paul Leyland. (There are ten days of the year that are Leyland numbers)

Prime Curios points out several curiosities related to 145, The 145th prime number is 829 and their concatenation, 145829 is prime. And the largest prime factor of 145, is 1+4+5+8+2+9. and 149 is congruent to 1 in mod 8, mod 2, and mod 9.


1581 John Dee, mathematician and mystic, first saw spirits in his crystal globe. [Daniel Cohen, Masters of the Occult , Dodd and Mead, 1971, p. 28] *VFR

1694 Isaac Newton to Nathaniel Hawes: “A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about figure, force and motion, is never at rest till he gets over every rub.” Westfall takes this as the title of his fabulous biography of Newton, Never at Rest. Reportedly he received one of the early Golden Fleece Awards of Senator Proxmire for a grant to write this book. [But we have been unable to find a reference for this last statement.] *VFR

1721 John Copson of High Street in Philadelphia posted an offering in the American Weekly Mercury on this date announcing that he would open an office to provide fire insurance for "vessels, goods, and merchandise."  With that, he became the first Insurance agent in continental America.  *Kane, First Famous Facts

1747 Benjamin Franklin describes his electrical experiments in a letter to Peter Collinson. " Hence have arisen some new Terms among us. .... Or rather B is electrised plus and A minus. And we daily in our Experiments electrise Bodies plus or minus as we think proper. These Terms we may use till your Philosophers give us better. To electrise plus or minus, no more needs to be known than this; that the Parts of the Tube or Sphere, that are rub'd, do, in the Instant of the Friction, attract the Electrical Fire, and therefore take it from the Thing rubbing: the same Parts immediately, as the Friction upon them ceases, are disposed to give the Fire they have received, to any Body that has less."  *Collinson, "Experiments and Observations on Electricity Made at Philadelphia in America."

1832 Galois writes to his friend, Auguste Chevalier, about his broken romance for Stephanie. The fatal duel looms only five days away. Mario Livio tells the story wonderfully in "The Equation That Couldn't be Solved".

1842 Johann Christian Doppler (1803–1853) presented a lecture on
the Doppler effect. It was first experimentally verified in 1845 using a locomotive drawing an open car with several trumpeters. *VFR

1844 the first news communicated by telegraph in the U.S. was sent 80 miles to the Baltimore Patriot, Maryland, from Washington, D.C. giving the information that "One o'clock. There has just been made a motion in the House to go into committee of the whole on the Oregon question. Rejected. Ayes 79 - Nays 86." This was just one day after Samuel Morse transmitted his famous "What hath God wrought!" message from the U.S. Supreme Court room and opened America's first telegraph line linking Washington and Baltimore.*TIS

1862 Caricature published to celebrate first aerial photographer, Nadar, was Published in Le Boulevard. Nadar "elevating photography to the condition of art", caricature by Honoré Daunier. The first known aerial photograph was taken in 1858 by French photographer and balloonist, Gaspar Felix Tournachon, known as "Nadar". In 1855 he had patented the idea of using aerial photographs in mapmaking and surveying, but it took him 3 years of experimenting before he successfully produced the very first aerial photograph. It was a view of the French village of Petit-Becetre taken from a tethered hot-air balloon, 80 meters above the ground. This was no mean feat, given the complexity of the early collodion photographic process, which required a complete darkroom to be carried in the basket of the balloon! Unfortunately, Nadar's earliest photographs no longer survive, and the oldest aerial photograph known to be still in existence is James Wallace Black's image of Boston from a hot-air balloon, taken in 1860. Following the development of the dry-plate process, it was no longer necessary carry so much equipment, and the first free flight balloon photo mission was carried out by Triboulet over Paris in 1879. *History of Aerial Photography

1946 The Soviet Union issued two stamps to celebrate the 125th anniversary of Pafnuti Lvovich Chebyshev (1821–1894). [Scott #1050-1].*VFR (see May 16th Births)

1961 the formal announcement of an American lunar landing was made by President John F. Kennedy speaking to the Congress: "I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth. No single space program in this period will be more impressive to mankind, or more important in the long-range exploration of space; and none will be so difficult or expensive to accomplish." *TIS

The Gateway Arch in St Louis, Missouri was inaugurated on this date by U S Vice President, Hubert Humphrey. Although it is often mistaken for a parabola, the arch is built in the form of an inverted, weighted catenary arch. It is the world's tallest arch, the tallest man-made monument in the Western Hemisphere, and Missouri's tallest accessible building. Built as a monument to the westward expansion of the United States,the centerpiece of the Jefferson National Expansion Memorial and has become an internationally famous symbol of St. Louis. Appropriately, Thomas Jefferson is credited for the first use of the term catenary in English in correspondence with Thomas Paine on bridge construction.. *Wik *@HistoryTime_

2142 The next total solar eclipse in Ostend, Belgium. The last total solar eclipse took place more than 11 centuries ago, 29 September 878. But only 9 years later, on 14 June 2151, there will be another one. *NASA Solar Eclipse Catalog (I know I can hardly wait!)


1828 Karl Peterson (25 May 1828 in Riga, Russia (now Latvia) - 19 April 1881 in Moscow, Russia)
was a Latvian mathematician worked in differential geometry and partial differential equations.  .. by means of a uniform general method, he deduced nearly all the devices known at that time for finding general solutions of different classes of equations.
Largely because he was not at a university his results were not well known but they did influence Egorov in Moscow, but Peterson gained an international reputation only when Darboux and Bianchi used his results.

1873 Michele Angelo Besso (25 May 1873 Riesbach – 15 March 1955 Genoa) was a Swiss/Italian engineer of Jewish Italian (Sephardi) descent. He was a close friend of Albert Einstein during his years at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, and then at the patent office in Bern. Besso is credited with introducing Einstein to the works of Ernst Mach, the sceptical critic of physics who influenced Einstein's approach to the discipline. Einstein called Besso "the best sounding board in Europe" for scientific ideas.
In a letter of condolence to the Besso family Albert Einstein wrote his now famous quote "Now Besso has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion" *Wik

1919 Raymond Merrill Smullyan ( May 25, 1919 -  ) is an American mathematician, concert pianist, logician, Taoist philosopher, and magician. His first career (like Persi Diaconis a generation later) was stage magic. He then earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied under Alonzo Church. Smullyan is the author of many books on recreational mathematics, recreational logic, etc. Most notably, one is titled "What Is the Name of This Book?". *Wik For example the book is described on the cover as follows:"Beginning with fun-filled monkey tricks and classic brain-teasers with devilish new twists, Professor Smullyan spins a logical labyrinth of even more complex and challenging problems as he delves into some of the deepest paradoxes of logic and set theory, including Gödel's revolutionary theorem of undecidability."
Martin Gardner described this book in Scientific American as:"The most original, most profound and most humorous collection of recreational logic and mathematics problems ever written."

1954 Clyde P. Kruskal (born May 25, 1954) is an American computer scientist,[1][2] working on parallel computing architectures, models, and algorithms. He got his A.B. degree in mathematics and computer science from Brandeis University, M.Sc. (1978) and Ph.D. (1981) from New York University under Jack Schwartz. Since then he has worked as assistant professor at University of Illinois (1981–85) and University of Maryland, College Park (1985–88), as associate professor (1988–). He has published extensively, becoming an ISI highly cited researcher. His father was the world-renowned mathematician Martin Kruskal. *Wik


1555 Gemma Frisius ; (December 9, 1508–May 25, 1555) was a Dutch mathematician who applied his mathematical expertise to geography, astronomy and map making. He became the leading theoretical mathematician in the Low Countries.*SAU Frisius created or improved many instruments, including the cross-staff, the astrolabe and the astronomical rings. His students included Gerardus Mercator (who became his collaborator), Johannes Stadius, John Dee, Andreas Vesalius and Rembert Dodoens.*Wik
It was Frisius who created the modern symbol for degrees, o , in the 1569 edition of Arithmeticae practicae moethodus facilis. *Cajori 
 Math Historian Thony Christie informed me that "Regnier Gemma Frisius", a name sometimes used for him (and I had) was not his name. "His birth name was Jemme Reinerzoon, i.e. Jemma son of Reiner, his humanist name simply Gemma Frisius."

1676 Johann Rahn (10 March 1622 in Zürich, Switzerland - 25 May 1676 in Zürich, Switzerland)
was a Swiss mathematician who was the first to use the symbol "÷",called an obelus, for a division symbol in Teutsche Algebra (1659). The invention is also sometimes credited to British Mathematician John Pell who was Rahn's tutor for a while. The book, written in German, contains an example of Pell's equation also. Here is more on the various symbols used for division

1956 Johann Radon (16 December 1887 – 25 May 1956) worked on the calculus of variations, differential geometry and measure theory. 
Radon is known for a number of lasting contributions, including:
  • his part in the Radon–Nikodym theorem;
  • the Radon measure concept of measure as linear functional;
  • the Radon transform, in integral geometry, based on integration over hyperplanes — with application to tomography for scanners (see tomographic reconstruction);
  • Radon's theorem, that d + 2 points in d dimensions may always be partitioned into two subsets with intersecting convex hulls
  • the Radon-Hurwitz numbers.
  • He is possibly the first to make use of the so called Radon-Riesz property. *Wik

1989 Ruby Violet Payne-Scott, (28 May 1912 – 25 May 1981) was an Australian pioneer in radiophysics and radio astronomy, and was the first female radio astronomer.
One of the more outstanding physicists that Australia has ever produced and one of the first people in the world to consider the possibility of radio astronomy, and thereby responsible for what is now a fundamental part of the modern lexicon of science, she was often the only woman in her classes at the University of Sydney.
Her career arguably reached its zenith while working for the Australian government's Commonwealth Scientific and Industrial Research Organisation (then called CSIR, now known as CSIRO) at Dover Heights, Hornsby and especially Potts Hill in Sydney. Some of her fundamental contributions to solar radio astronomy came at the end of this period. She is the discoverer of Type I and Type III bursts and participated in the recognition of Type II and IV bursts.
She played a major role in the first-ever radio astronomical interferometer observation from 26 January 1946, when the sea-cliff interferometer was used to determine the position and angular size of a solar burst. This observation occurred at either Dover Heights (ex Army shore defence radar) or at Beacon Hill, near Collaroy on Sydney's north shore (ex Royal Australian Air Force surveillance radar establishment - however this radar did not become active until early 1950).[4]
During World War II, she was engaged in top secret work investigating radar. She was the expert on the detection of aircraft using PPI (Plan Position Indicator) displays. She was also at the time a member of the Communist Party and an early advocate for women's rights. The Australian Security Intelligence Organisation (ASIO) was interested in Payne-Scott and had a substantial file on her activities, with some distortions.

**The fourth factorion is 40585 = 4! + 0! + 5! + 8! + 5!

*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, 24 May 2018

On This Day in Math - May 24

 Hence no force, however great, 
can stretch a cord, however fine,
into a horizontal line 
which is accurately straight:
there will always be a bending downwards.
~William Whewell

The 144th day of the year; 144 is the only non-trivial square in the Fibonacci Sequence.In fact, there are only four  Fibonacci numbers that are  perfect powers, 0, 1, 8, and 144. And we haven't known that for so very long. Here is the story from , Professor Stewart's Incredible Numbers.

\(144^5 = 27^5 + 84^5 + 110^5 + 133^5 \) This counter-example disproved Euler's Conjecture that n nth powers are needed to sum to an nth power. It is also part of one of the shortest papers ever published in a math journal(two sentences)

(Squares are important in knowing if a number, n is Fibonacci or not. N is Fibonacci IFF one or both of \(5n^2 \pm 4\) is a perfect square. )

144 is also the smallest square number which is also a square when its digits are reversed 144 = 12 2 while 441= 212

The sum of the first 144 decimal digits of pi (don't use the 3.) is 666, "The Number of the Beast."  One person wrote that they thought that was gross!  (  sorryf   :-{  , bad pun)

144 is the only year day that is a square number that is the perimeter of a primitive Pythagorean Triangle.  (16, 63, 65) *Benjamin Vitale@BenVitale


997 Al-Bırunı in Kath and Abul-Wafa in Baghdad simultaneously watch a lunar eclipse. The time obtained by this prearranged cooperation allowed them to determine the difference in longitude between the cities. *VFR

1032 The renowned Arab scientist Ibn Sina noted, “I saw Venus as a spot on the surface of the sun,” This is the first known record of witnessing the transit of Venus. The first recorded observation of a transit of Venus was made by Jeremiah Horrocks from his home at Carr House in Much Hoole, near Preston in England, on 4 December 1639. Kepler predicted the 1761 transit of Venus, the first such prediction in Western recorded history, and one that inspired several astronomical expeditions. *Sky and Telescope (A.M.S ‏@amoshaye pointed out that he was NOT Arabic, {Persian I believe}. It was once common to lump mid-eastern scholars who wrote in Arabic as Arabian. I write in English, but am not English, a fact that I, and all of England are equally grateful for.)

1543 An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR

1547 Ferrari replied to Tartaglia’s letter of 21 April 1547 by sending 31 challenge problems of his own. Tartaglia solved all but the five dealing with cubic equations. *VFR  For more on this "math wars" story, see this Renaissance Mathematicus blog.

1626 Manhattan bought from the Indians for \( $24 \) *VFR {In 1626 Peter Minuit bought Manhattan island from the local Indians for a load of cloth, beads, hatchets, and other odds and ends then worth 60 Dutch guilders. Estimated to have been worth  \($24 \) Dollars at a much later time. If we convert that to silver prices at the time, you could purchase about 18 Troy ounces of Silver.. Today the price of silver is about  \($35 \) per ounce, so .. not such a good investment in that sense... }

1683 The Ashmolean, Britain's first Museum, first opened to the public on 24 May 1683. *Ashmolean (in full the Ashmolean Museum of Art and Archaeology) on Beaumont Street, Oxford, England, is the world's first university museum. Its first building was built in 1678–1683 to house the cabinet of curiosities Elias Ashmole gave Oxford University in 1677. *Wik

1727 Euler arrived at St. Petersburg for the first time on 24 May 1727, only seven days after the Russian empress Katherine I, the wife of Peter I (an adopted daughter of Ernst Glilck, the provost of Marienburg, now Aliiksne) died, and he worked at the St. Petersburg Academy of Sciences until 1741 when he moved to
Berlin, there to stay until 1766. *Historia Mathematica

1844 Samuel F. B. Morse dispatched the first telegraphic message over an experimental line from Washington, D.C., to Baltimore. The message, taken from the Bible, Numbers 23:23 and recorded on a paper tape had been suggested to Morse by Annie Ellsworth, the young daughter of a friend. {Nice to have influential friends, she was the teenage daughter of the Commissioner of Patents. Congress appropriated $30,000  for a telegraph wire to be strung the 80 miles between Washington and Baltimore}..Morse sent the message from the chamber of the Supreme Court, then in the United States Capitol, to his assistant Albert Vail at the Mount Clair depot in Baltimore in 1844.*Library of Congress

A photo of the actual paper tape with raised dots and dashes in the Library of Congress is here. Across the top of this artifact of his historic achievement Morse has given credit to Annie Ellsworth for suggesting the message.

Wolfram alpha will let you convert any message to Morse code, or from Morse code by typing [Morse code "input"] to encode, or Morse Code message to decode.

1883 Brooklyn Bridge was opened over the East River, New York City, USA, of a breadth of 1,600 feet, navigable water with a single span. What was then regarded as the greatest engineering feat still stands in service today, and remains the world's only stone-towered, steel cabled bridge. Twice the size of the Niagara Suspension Bridge and four times the longest non-extension spans ever attempted, the total length of this colossal structure is 6,927 ft. The road bed is 80 feet wide, and at an elevation of 186 feet above high water. John Roebling, and after his death his son Washington Roebling, worked on its construction for 13 years. *TIS
Contrary to the New York Times Magazine of 27 March 1983, the cables hang in the shape of parabolas, not catenaries. *VFR

1937 A temporary science exhibition called Le Palais de la Decouverte opened its doors in the west wing of the Grand Palais in time for the 1937 International Exposition of Art and Technology in Modern Life, which was to be held in Paris. It was primarily the inspiration of French physicist Jean Perrin, who won the Nobel prize in 1926 for his work on the atom. An interesting mathematical anecdote relates to the museum.
The museum contains a circular room known as the "pi room". On its wall is inscribed 707 digits of the number π. The digits are large wooden characters attached to the dome-like ceiling. The digits were based on an 1853 calculation by English mathematician William Shanks, which included an error in the 528th digit. The error was detected in 1946 and corrected in 1949
Shank's 707 digits was the record at that time, taken from his teacher William Rutherford, whose record was 404 digits.His record, now adjusted to the 528 digits he had right, was the last record of hand computation.  D. F. Ferguson's 1946 calculation of 606 digits was done with a desk top calculating machine.

1961 MIT's Clark Begins Work on LINC Computer :
Wes Clark began his work on LINC, or the Laboratory Instrument Computer, at MIT's Lincoln Laboratory. His plan was to create a computer for biomedical research, that was easy to program and maintain, that could be communicated with while it operated, and that could process biotechnical signals directly. Building on his previous experience in developing the Whirlwind, TX-0, and other early computers, Clark set to work on one of the earliest examples of a "user friendly" machine -- setting the standard for personal computer design in the following decades. *CHM

1965, Hansard, the official record of all English parliamentary debates, recorded in an Appendix the statement by Mr Jay (President of the Board of Trade) saying he was impressed by the case for adoption of the metric system - by a long-term, gradual, voluntary process - and was arranging for the British Standards Institution to investigate. Eventually, as a member of the European Common Market, the transition to the metric system for trade and commerce became obligatory.*TIS

1973 French mathematicians Jean Guilloud and Mlle. Martine Bouyer computed π on a CDC 7600 computer to one million decimal places, the greatest accuracy to (that) date. The value was not verified until September 3, 1973. It is published in a 400 page book. *VFR

1983 Marshall Stone received the National Medal of Science, the nation’s highest scientific honor, “for his original synthesis of analysis, algebra and topology into the new, vital area of functional analysis, in modern mathematics.” Notices AMS, v. 30, p. 485, contains more information. *VFR

2014 NASA predicts a never before seen meteor shower. The shower is the May Camelopardalids (a faint constellation near the North Star), caused by dust from periodic comet 209P/LINEAR. No one has ever seen it before, but this year the Camelopardalids could put on a display that rivals the well-known Perseids of August.
"Some forecasters have predicted more than 200 meteors per hour," *


1544 William Gilbert (24 May 1544 – 30 November 1603)  English scientist, the "father of electrical studies" and a pioneer researcher into magnetism, who spent years investigating magnetic and electrical attractions. Gilbert coined the names of electric attraction, electric force, and magnetic pole. He became the most distinguished man of science in England during the reign of Queen Elizabeth I. Noting that a compass needle not only points north and south, but also dips downward, he thought the Earth acts like a bar magnet. Like Copernicus, he believed the Earth rotates on its axis, and that the fixed stars were not all at the same distance from the earth. Gilbert thought it was a form of magnetism that held planets in their orbits. *TIS  "Gilbert shall live, till Load-stones cease to draw,   Or British Fleets the boundless Ocean awe. ~ John Dryden

1640 John Mayow (24 May 1640 - October 1679 ) English chemist and physiologist who, about a hundred years before Joseph Priestley and Antoine-Laurent Lavoisier, identified spiritus nitroaereus (oxygen) as a distinct atmospheric entity. He further recognized the role of oxygen in the combustion of metals. His medical writings include a remarkably correct anatomical description of respiration. *TIS  {It is said that he observed a mouse in a sealed jar with a candle, and as the candle flame was going out, the mouse fainted...}

1686 Daniel Gabriel Fahrenheit (24 May 1686 – 16 September 1736) German physicist and maker of scientific instruments. He is best known for inventing the alcohol thermometer (1709) and mercury thermometer (1714) and for developing the Fahrenheit temperature scale. He devoted himself to the study of physics and the manufacture of precision meteorological instruments. He discovered, among  other things, that water can remain liquid below its freezing point and that the boiling point of  liquids varies with atmospheric pressure.*TIS

1794 William Whewell,  (24 May 1794 – 6 March 1866)  British scientist, best known for his survey of the scientific method and for creating scientific words. He founded mathematical crystallography and developed Mohr's classification of minerals. He created the words scientist and physicist by analogy with the word artist. They soon replaced the older term natural philosopher. (actually the use of scientist was a very slow process often not well received.)  Other useful words were coined to help his friends: biometry for Lubbock; Eocine, Miocene and Pliocene for Lyell; and for Faraday, anode, cathode, diamagnetic, paramagnetic, and ion (whence the sundry other particle names ending -ion). In metereology, Whewell devised a self-recording anemometer. He was second only to Newton for work on tidal theory. He died as a result of being thrown from his horse*TIS  
 In a single letter to Faraday on 25 April, 1834;  he invented the terms cathode, anode and ion.  The letter is on display at the Wren Library at Trinity College, Cambridge, UK.

1820  William Chauvenet (24 May 1820, Milford, Pennsylvania - 13 December 1870, St. Paul, Minnesota) was born on a farm near Milford, Pennsylvania, in 1820 and was raised in Philadelphia. Early in life he exhibited a knack for mathematics and all things mechanical, and he attended Yale University. Entering Yale at age 16, he graduated in 1840 with high honors and soon after began his scholarly career by assisting a professor at Girard College in Philadelphia, Pennsylvania in a series of magnetic observations. In 1841 he was appointed professor of mathematics in the U.S. Navy and for a few months served on the U.S. steamer Mississippi, where he taught midshipmen. He later taught at and was instrumental in the establishment of the U.S. Naval Academy at Annapolis, Maryland.*Wik

1903  Władysław Roman Orlicz (May 24, 1903 in Okocim, Austria-Hungary (now Poland) – August 9, 1990 in Poznań, Poland) was a Polish mathematician of Lwów School of Mathematics.  His main interest was topology. *Wik

1909 Karl Heinrich Weise (24 May 1909 in Gera, Thüringen, Germany, 15 April 1990 in Kiel, Germany) Weise's mathematical work was mainly on questions from differential geometry and topology. In 1951, jointly with Robert König, he published the book Mathematische Grundlagen der Höheren Geodäsie und Kartographie.
Weise acted as supervisor of PhD students from a wide range of mathematical fields, a dozen of them went on to become professors, among them Wolfgang Gaschütz (finite groups), Wolfgang Haken (knot theory and the solution of the four-colour-problem), Wilhelm Klingenberg (differential geometry) and Jens Mennicke (topology). Let us look in a little more detail at Weise's influence on one of these students, Wolfgang Haken, who studied mathematics, physics and philosophy at the University of Kiel. Haken attended Heinrich Heesch's talk on his contributions to the Four Colour Problem, but he was most enthused by Weise's lectures on topology. In these lectures, Weise described three long-standing unsolved problems - the Poincaré Conjecture, the Four Colour Problem, and a problem on knot theory. Haken decided to attempt to solve all three problems and began this challenge while studying for a doctorate at Kiel with Weise as his thesis advisor. His thesis, submitted in 1953, was Ein topologischer Satz über die Einbettung (d-1)-dimensionaler Mannigfaltigkeiten in d-dimensionale Mannigfaltigkeiten. He had solved the knot theory problem and this led to his appointment at the University of Illinois in the United States. Eventually, assisted by Kenneth Appel, he solved the Four Colour Problem in 1976 with the aid of computer techniques.
Weise was retired on 30 September1977, and in the following year the Christian Albrechts Universität conferred on him the title of 'Ehrensenator' (honorary senator). *SAU

1914 Federico Cafiero (24 May 1914 in Riposto, Catania, Sicily, 7 May 1980 in Naples, Italy) Cafiero played an important role in building a vigorous mathematical school at Naples which included (in alphabetical order) Luigi Albano, Ugo Barbuti, Antonio Chffi, Paolo De Lucia, Nicola Fedele, Renato Fiorenza, Francesco Guglielmino, Giuseppe Pulvirenti, Giuseppe Santagati and Antonio Zitarosa. We have already seen that Cafiero made contributions to the theory of ordinary differential equations and to the theory of measure and integration.
Two notable awards the Cafiero received for his mathematical contributions were the Tenore prize of the Accademia Pontaniana (awarded in 1953 for his monograph Funzioni additive d'insieme e integrazione negli spazi astratti) and the Golden medal 'Benemeriti della Scuola, della Cultura, dell'Arte' which he received from the President of the Italian Republic in 1976. *SAU


1543 Nicolaus Copernicus (19 February 1473 – 24 May 1543) Polish astronomer who proposed that the planets have the Sun as the fixed point to which their motions are to be referred; that the Earth is a planet which, besides orbiting the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes    *TIS     An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR  Over 450 years after his death, Copernicus was reburied in the cathedral at Frombork on Poland’s Baltic coast. The astronomer whose ideas were once declared heresy by the Vatican—was reburied with full religious honors. 

1659 Georg Ernst Stahl (22 October 1659 – 24 May 1734 [NS}) was a German chemist, physician and philosopher. He was a supporter of vitalism, and until the late 18th century his works on phlogiston were accepted as an explanation for chemical processes
Stahl used the works of Johann Joachim Becher to help him come up with explanations of chemical phenomena. The main theory that Stahl got from J. J. Becher was the theory of phlogiston. This theory did not have any experimental basis before Stahl. He was able to make the theory applicable to chemistry.[4] Becher's theories attempted in explaining chemistry as comprehensively as seemingly possible through classifying different earths according to specific reactions. Terra pinguis was a substance that escaped during combustion reactions, according to Becher.[10] Stahl, influenced by Becher's work, developed his theory of phlogiston.People who dismiss Phlogiston theory as early ignorance should read The Renaissance Mathematicus blog, The Phlogiston Theory – Wonderfully wrong but fantastically fruitful.

1843  Sylvestre François Lacroix (April 28, 1765, Paris – May 24, 1843) was the writer of important textbooks in mathematics and through these he made a major contribution to the teaching of mathematics throughout France and also in other countries. He published a two volume text Traité de calcul differéntiel et du calcul intégral (1797-1798) which is perhaps his most famous work. In the first of these volumes Lacroix introduces for the first time the expression "analyic geometry" writing:-
There exists a manner of viewing geometry that could be called géométrie analytique, and which would consist in deducing the properties of extension from the least possible number of principles, and by truly analytic methods.
He expanded his masterpiece to three volumes for the second edition published between 1810 and 1819.
 Lacroix's texts had an influence beyond France,... and it was through English translations of Traité élémentaire de calcul differéntiel et du calcul intégral by Babbage, Peacock and Herschel that the 'new continental mathematics' entered universities in Britain. It is interesting that Lacroix held the view that algebra and geometry:-
... should be treated separately, as far apart as they can be, and that the results in each should serve for mutual clarification, corresponding, so to speak, to the text of a book and its translation.
His texts appeared in many editions for over 50 years .  *SAU

1896 Luigi Menabrea (4 Sept 1809 in Chambéry, Savoy, France - 24 May 1896 in St Cassin (near Chambéry), France) was a French-born soldier and engineer who made contributions to elasticity theory and became prime-minister of Italy. *SAU

1904 Cecil John Alvin Evelyn (25 August 1904 in London, England, 24 May 1976 in Deptford, Kent, England) He graduated with a B.A. in 1927. At Oxford he had become friendly with Hubert Linfoot who was one year older than Evelyn. Linfoot graduated in 1926 but had remained at Oxford undertaking research advised by G H Hardy. Both Evelyn and Linfoot were interested in number theory at this time and they worked together.
Between 1929 and 1933, Evelyn and Linfoot produced six joint papers, all with the title On a problem in the additive theory of numbers.
A book was to be Evelyn's final mathematical publication. He published the book (with G B Money-Coutts and J A Tyrrell) The seven circles theorem and other new theorems (1974) which was translated into French and published as (with G B Money-Coutts and J A Tyrrell) Le théorème des sept cercles (1975). R D Nelson, Ampleforth College, York, writes :-
This elegant book will please all geometers, amateur and professional, and deserves a place in every library. Using a variety of essentially elementary methods, the authors present and prove a number of new or little known theorems in plane geometry. To emphasise the aesthetic appeal of these results and to assist the argument in places, over forty of its pages carry diagrams of high quality. The book has three independent sections but the style of writing is uniform. The authors invite and sometimes require the co-operation of the reader as he works through the book and, in this way, they prepare him for the intricacies of the final and most difficult section. The first part re-introduces an algebra of vectors, due to Silberstein, in which the laws of addition and equivalence are such that few of the usual properties are obvious. For example, associativity of addition requires two applications of Desargues' theorem for its proof. No use is made of this algebra. The second section opens with a delightful new theorem concerning seven Pascal lines derived from a heptagon inscribed in a conic. This is followed by a number of extensions and generalisations of the theorems of Pascal and Brianchon. ... Finally there are four new theorems about closed chains of six circles ... In the first theorem each circle touches a seventh, in the second the circles alternately touch a pair of parallel lines, in the third each circle touches two of the sides of a triangle and in the fourth each circle touches two out of three fixed circles making a configuration of nine circles in all. The first theorem, beautifully proved by inversion, gives the book its title.

The remarkable thing about this book is that the theorem of the title is an elementary geometry theorem which appears to have been first discovered by the authors of this book. The theorem concerns six circles, all inside and touching a seventh circle. These six circles all touch each other. Join each of the six points on the outer circle where the six inner circles touch it, to the point of contact directly opposite it. The theorem states that these three lines are concurrent. *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
*WM = Women of Mathematics, Grinstein & Campbell

Wednesday, 23 May 2018

On This Day in Math - May 23

 (a symbol) We can repudiate completely and 
which we can abandon without regret 
because one does not know 
what this pretended sign signifies
nor what sense one ought to attribute to it. 

Cauchy in 1847 in regard to the square root of negative one..

The 143rd day of the year; there are 143 three-digit primes.

Also, 1432 is a divisor of 143143.HT to Matt McIrvin who found the pattern for numbers such that n^2 divides n.n (where the dot represents concatenation) and then found it is at OEIS

143 is also the number of moves that it takes 11 frogs to swap places with 11 toads on a strip of 2(11) + 1 squares (or positions, or lily pads) where a move is a single slide or jump. This activity dates back to the 19th century, and the incredible recreational mathematician, Edouard Lucas *OEIS. I should point out that every number greater than one for which this is true involves the digits 143, in order, and includes a mystery offering from one-seventh.
Prof. Singmasters Chronology of Recreational Mathematics suggests that this was first introduced in the American Agriculturalist in 1867, and I have an image of the puzzle below. The fact that they call it, "Spanish Game" suggests it has an older antecedent. (anyone know more?)


1221 "On the first day of the fifth month (May 23), at noon, the Sun was eclipsed and it was total. All the stars were therefore seen. A short while later the brightness returned. At that time we were on the southern bank of the river. The eclipse (began) at the south-west and (the Sun) reappeared from the north-east. At that place it is cool in the morning and warm in the evening; there are many yellow flowers among the grass. The river flows to the north-east. On both banks there are many tall willows. The Mongols use them to make their tents. [Later] (Ch'ang-ch'un) asked (an astronomer) about the solar eclipse on the first day of the month
(May 23). The man replied: 'Here the Sun was eclipsed up to 7 fen (6/10) at the hour of ch'en (7-9 h)'. The Master continued, 'When we were by the Lu-chu Ho (Kerulen River), during the hour wu (11-13 h) the Sun was seen totally eclipsed and also south-west of Chin-shan the people there said that the eclipse occurred at the hour szu (9-11 h) and reached 7 fen. At each of these three places it was seen differently. According to the commentary on the ch'un-ch'iu by K'ung Ying-ta, when the body (of the Moon) covers the Sun, then there will be a solar eclipse. Now I presume that we must have been directly beneath it; hence we observed the eclipse to be total. On the other hand, those people on the sides (of the shadow) were further away and hence (their view) gradually became different. This is similar to screening a lamp with a fan. In the shadow of the fan there is no light or brightness. Further away from the sides (of the fan) then the light of the lamp gradually becomes greater." Refers to a total solar eclipse of 23 May 1221. From: Ch'ang-ch'un Chen-jen Tao-ts'ang('The Journey of the Adept Ch'ang-ch'un to the West'). *NASA Eclipse Calendar

1576 Brahe is given use of the island of Hveen for an observatory. [Wadsworth] *VFR

1771 Benjamin Franklin visits Joseph Priestley at his home in Leeds just after he begins experimenting with placing mint under a glass to see how long it took to die. Priestly had put insects, small animals, candles etc under glass to measure the time it took to use up the "life force" in the air. To his surprise, the mint flourished in his pneumatic trough. Eventually he would realize that the "spent" air could be rejuvenated by placing a living plant inside the glass. *Steven Johnson, The Invention of Air

1785, a letter from Benjamin Franklin documented his invention of his new bifocal glasses. He was writing from France to a friend describing the solution to carrying around two pairs of glasses to see objects at different distances, with the comment that "I have only to move my eyes up and down as I want to see far or near." Franklin incorporated a two part lens for each eye, each parts having a different focussing power. The invention had limited acceptance at a time when even ordinary spectacles in the colonies already cost as much as $100 per pair. *TIS

1825, the electromagnet in a practical form was first exhibited by its inventor, William Sturgeon, on the occasion of reading a paper, recorded in the Transactions of the Society of Arts for 1825 (Vol xliii, p.38). The publication showed pictures of his set of improved apparatus for electromagnetic experiments, including two electromagnets, one of horse-shoe shape and one  a straight bar. The formed was bent from a rod about 1 foot (30 cm) long and one-half inch (1.3 cm) in diameter, varnished for insulation, then coiled with a single spiral of 18 turns of stout copper wire. In return for the Society's medal and premium, Sturgeon deposited the apparatus in the museum of the Society. Sadly, this was lost after the society's museum was dispersed. *TIS  This would have been the day after his forty-second birthday.  (see May 22)

1933  Max Wasserberg received a patent for a "beach and lawn chair" (U.S. No. 1,911,127). *TIS  Why is this American hero not better known?  

1958 Explorer I, the 1st US satellite in orbit, ceases transmission. *David Dickinson ‏@Astroguyz

1994 Java development begins in earnest:
Sun Microsystems Inc. formally announced its new programs, Java and HotJava at the SunWorld '95 convention. Java was described as a programming language that, combined with the HotJava World Wide Web browser, offered the best universal operating system to the online community. The concept behind the programs was to design a programming language whose applications would be available to a user with any kind of operating system, eliminating the problems of translation between Macintoshes, IBM-compatible computers, and Unix machines. *CHM

2014 "Tonight, Tonight, won't be just any night." NASA predicts a never before seen meteor shower. The shower is the May Camelopardalids (a faint constellation near the North Star), caused by dust from periodic comet 209P/LINEAR. No one has ever seen it before, but this year the Camelopardalids could put on a display that rivals the well-known Perseids of August.

"Some forecasters have predicted more than 200 meteors per hour," *


1606 Juan Caramuel Y Lobkowitz (May 23, 1606 in Madrid — September 8, 1682 in Vigevano)  His Mathesis biceps of 1670 expounds the general principle of number systems with an arbitrary base b. Caramuel points out that some of these might be of more use than the decimal system. [DSB 3, 61] *VFR 
Donald Knuth writes in The Art of Computer Programming Volume 2:- The first published discussion of the binary system was given in a comparatively little-known work by a Spanish bishop, Juan Caramuel Lobkowitz, 'Mathesis biceps' (Campaniae, 1670) pp. 45-48: Caramuel discusses the representation of numbers in radices 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 60 at some length, but gave no examples of arithmetic operations in nondecimal systems (except for the trivial operation of adding unity). He loved puzzles and published a collection containing some that he had composed when he was only ten years old. Mathematical puzzles and games of chance form part of Mathesis biceps (1670). He proposed a new method of trisecting an angle and developed a system of logarithms to base 109 where log 1010 = 0 and log 1 = 10. He was the first to publish log tables in Spanish. Among Caramuel's other scientific work ...a system he developed to determine longitude using the position of the moon. He wrote widely on grammar, linguistics and rhetoric but perhaps his most interesting proposal in this area was to argue for the creation of a universal language. *SAU

1820 James Buchanan Eads (May 23, 1820 – March 8, 1887) was an American engineer who built the two-tier triple-arch steel bridge over the Mississippi River at St. Louis, Missouri. At the age of 22, he invented a boat and diving bell which enabled walking on the river bottom. In 12 years' time he made a fortune with his salvage boat operation. During the Civil War, he built ironclad warships. After the war, he built the Mississippi River bridge, the first major bridge to use steel and cantilevered construction, which was opened 4 Jul 1874. Each roughly 500-ft span rested on piers built on bedrock about 100 feet beneath the river bottom. He created a year-round navigation channel for New Orleans scoured out with a system of jetties harnessing the river's water flow (1879)*TIS

1849 Arthur Edwin Haynes,(May 23, 1849;Baldwinsville, Onondaga County, New York, USA - Mar. 12, 1915; Minneapolis, Minnesota) Professor of Mathematics and Physics at Hillsdale College from 1875 until 1890. He came to Michigan in June 1858. They located near the village of Reading in southwestern Hillsdale Co. where the father had a farm.
Arthur received a common school education and remained on the family farm until he reached twenty years of age.
In the fall of 1870, Arthur entered Hillsdale College where he remained, a diligent student, until he was graduated from that institution in June 1875. He taught several terms of district school before graduation and was also employed during his college course as a tutor in mathematics in the college. During the summer between his junior and senior years, he assisted in the erection of the Central College building, in order to earn money to continue his studies. He carried a hod from the first story until the completion of the fourth, shouldering 80 pounds of brick and walking from the bottom to the top of the ladder (20 feet) without touching the hod handle, a feat that he was justly proud of. His classroom at Hillsdale was in that same building.
Immediately following graduation,he married and was appointed instructor in mathematics in Hillsdale College in the fall of 1875, and two years later was elected to the full Professorship. In 1885 he was elected a member of the London Mathematical Society. In 1890 he switched to the University of Minnesota. He wrote a paper on "The Mounting and Use of a Spherical Blackboard." He died in Minneapolis in 1915 and his body was removed back to Hillsdale where he was buried in Oak Grove Cemetary *PB notes

1887 Thoralf Skolem (23 May 1887 – 23 March 1963)  number theorist and logician. At the International Congress of Mathematicians in Cambridge in 1950 he said “We ought not to regard all that is written in the traditional textbooks as something sacred.” It was this attitude that earlier allowed him to discover that the real numbers could have countable models, a fact known as Skolem’s paradox.

1907 Boris A. Kordemsky ( 23 May 1907 – 29 March, 1999) was a Russian mathematician and educator. He is best known for his popular science books and mathematical puzzles. He is the author of over 70 books and popular mathematics articles.
Kordemsky received Ph.D. in education in 1956 and taught mathematics at several Moscow colleges.
He is probably the best-selling author of math puzzle books in the history of the world. Just one of his books, Matematicheskaya Smekalka (or, Mathematical Quick-Wits), sold more than a million copies in the Soviet Union/Russia alone, and it has been translated into many languages. By exciting millions of people in mathematical problems over five decades, he influenced generations of solvers both at home and abroad. *Age of Puzzles, by Will Shortz and Serhiy Grabarchuk (mostly)

1908 John Bardeen (23 May 1908; 30 Jan 1991 at age 82) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

1917  Edward Norton Lorenz   (May 23, 1917 - April 16, 2008) American mathematician and meteorologist known for pointing out the "butterfly effect" whereby chaos theory predicts that "slightly differing initial states can evolve into considerably different states." In his 1963 paper in the Journal of Atmospheric Sciences, he cited the flapping of a seagull's wings as changing the state of the atmosphere in even such a trivial way can result in huge changes in outcome in weather patterns. Thus very long range weather forecasting becomes almost impossible. He determined this unexpected result in 1961 while running a computer weather simulation that gave wildly different results from even tiny changes in the input data. *TIS

1946 Dr. H. Paul Shuch (May 23, 1946- ) is an American scientist and engineer who has coordinated radio amateurs to help in the search for extraterrestrial intelligence. Shuch, an aerospace engineer and microwave technologist is believed by colleague Jack Unger to be the creator of the world's first commercial home satellite TV receiver. A visiting professor at Lycoming College and the Heidelberg University of Applied Sciences, Shuch continues to volunteer as the Executive Director Emeritus of The SETI League, Inc. He has taught physics, astronomy, and engineering on various campuses for over three decades.
Shuch is a Vietnam-era Air Force veteran and active instrument flight instructor. He founded Microcomm Consulting in 1975, where in 1978 he designed and produced a commercial home satellite TV receiver.*Wik

1950 Malcolm John Williamson (May 23, 1950 - ) discovered in 1974 what is now known as Diffie-Hellman key exchangeHe was then working at GCHQ.
Williamson studied at Manchester Grammar School, winning first prize in the 1968 British Mathematical Olympiad. He also won a Silver prize at the 1967 International Mathematical Olympiad in Cetinje, Yugoslavia and a Gold prize at the 1968 International Mathematical Olympiad in Moscow. He read mathematics at Trinity College, Cambridge, graduating in 1971. After a year at Liverpool University, he joined GCHQ, and worked there until 1982.
From 1985 to 1989 Williamson worked at Nicolet Instruments in Madison, Wisconsin where he was the primary author on two digital hearing aid patents. *Wik


1691 Adrien Auzout (28 January 1622 – 23 May 1691) was a French astronomer.
In 1664–1665 he made observations of comets, and argued in favor of their following elliptical or parabolic orbits. (In this he was opposed by his rival Johannes Hevelius.) Adrien was briefly a member of the Académie Royale des Sciences from 1666 to 1668, and a founding member of the French Royal Obseratory. (He may have left the academy due to a dispute.) He was elected a Fellow of the Royal Society of London in 1666. He then left for Italy and spent the next 20 years in that region, finally dying in Rome in 1691. Little is known about his activities during this last period.
Auzout made contributions in telescope observations, including perfecting the use of the micrometer. He made many observations with large aerial telescopes and he is noted for briefly considering the construction of a huge aerial telescope 1,000 feet in length that he would use to observe animals on the Moon. In 1647 he performed an experiment that demonstrated the role of air pressure in function of the mercury barometer. In 1667–68, Adrien and Jean Picard attached a telescopic sight to a 38-inch quadrant, and used it to accurately determine positions on the Earth. The crater Auzout on the Moon is named after him. *Wik

1857 Augustin-Louis Cauchy (21 August 1789 – 23 May 1857)Augustin-Louis Cauchy pioneered the study of analysis, both real and complex, and the theory of permutation groups. He also researched in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.*SAU
A few hours before his death, age 68,  was talking animatedly with the Archbishop of Paris of the charitable works he had in view—for charity was a life long interest of Cauchy. His last words were “Men pass away but their deeds abide.” [Bell, Men of Mathematics, p 293]. *VFR   Cauchy was active in the Saint Vincent de Paul society, Irish relief, and homes for unwed mothers, but he will always be remembered more as the man who refused Abel's paper to the French Academy.

 1889   George Henri Halphen (30 October 1844, Rouen – 23 May 1889, Versailles) was a French mathematician. He did his studies at École Polytechnique (X 1862). He was known for his work in geometry, particularly in enumerative geometry and the singularity theory of algebraic curves, in algebraic geometry. He also worked on invariant theory and projective differential geometry. *Wik

2015 1928 John Forbes Nash, Jr (born June 13, 1928- May 23, 2015) was an American mathematicia whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Serving as a Senior Research Mathematician at Princeton University during the later part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.
Nash is the subject of the Hollywood movie "A Beautiful Mind". The film, loosely based on the biography of the same name, focuses on Nash's mathematical genius and struggle with paranoid schizophrenia *Wik Nash, 86, and his wife Alicia, 82, died in a car crash in a taxi on the New Jersey turnpike on May 23, 2015.

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

Tuesday, 22 May 2018

On This Day in Math - May 22

The Le Petit Journal cover, on 1912 April 21, shows eclipse watchers in 1912 along with the solar eclipse of May 22, 1724, the previous total solar eclipse visible from Paris, France

“Biographical history, as taught in our public schools, is still largely a history of boneheads:
ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals 
- the flotsam and jetsam of historical currents. 
The men who radically altered history, 
the great scientists and mathematicians, 
are seldom mentioned, if at all.” 
Martin Gardner

The 142nd day of the year; there are 142 possible planar graphs with six vertices.

142 is the smallest Semi-prime (having exactly 2 prime factors), whose sum of divisors is a cube. 142+71+2+1 = 63

The binary representation of 142 has the same number of zeros and ones.

142 is the number of ways of partitioning 25 into distinct parts... which must be the number of ways of partitioning them into odd parts according to Euler.

1453 A lunar eclipse fulfilled an omen for many prior to one of the red-letter dates in medieval history. On May 22, 1453 a partially eclipsed Moon rose over the city of Constantinople. One can only imagine the fear that it inspired in the embattled city that had already been under siege for a month. It certainly didn’t raise morale that legends had foretold that an eclipse would mark the fall of the Byzantine Empire. In a case of self-fulfilling prophecy, 7 days later Constantinople fell to Ottoman forces led by 21yr old Sultan Mehmed II.
*Fall of Constantinople, by Theophilos Hatzimihail, *Wik

1649 Pascal obtained a monopoly by royal decree for his computing machine. [DSB 10, 332] *VFR

1724 A total solar eclipse occurred on May 22, 1724. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun, blocking all direct sunlight, turning day into darkness.
This solar eclipse crossed the United Kingdom near sunset, north-west to south-east track, from southern Wales and Devon in the west, eastwards to Hampshire and Sussex, but passing to the south of London.
It crossed the city Los Angeles, CA in the morning, unfortunately it wasn't settled until after 1771, 47 years later. The next total eclipse over Los Angeles won't occur until April 1, 3290. *Wik

1788 William Herschel reads a paper to the Royal Society describing the observation of two satellites around the "Georgian Planet." *Phil. Trans. R. Soc. Lond. 1788 78, 364-378
On 13 March 1781, when he discovered the new celestial object  he named  it "Georgium Sidus (the Georgian planet)".  It would later become the planet Uranus.
Herschel even claimed in 1797 that he saw rings around the seventh planet and drew a small diagram of the ring and noted that it was "a little inclined to the red". For nearly two centuries the claim was dismissed as a mistake but in 1977 rings around Uranus were detected during an experiment.*

1849, Abraham Lincoln was issued a patent for "buoying boats over shoals" (No. 6,469). He was the first American president to receive a patent. (Note: he was NOT President in 1849) His idea utilized inflated cylinders to float grounded vessels through shallow water. Lincoln had worked as a deck-hand on a Mississippi flat-boat. *TIS

1866 Herman von Helmholtz published his paper “On the facts that underlie the foundations of geometry,” containing an account of elliptic geometry. *VFR

1906, the brothers Orville and Wilbur Wright received a patent for  "new and useful improvements in Flying Machines" (U.S. No. 821,393). This was the first airplane patent in the USA. *TIS

1936  M. C. ESCHER visited the Alhambra on 18‑24 Oct 1922 and was impressed by the patterns, but he didn't really use them in his art until after his second visit on 22-26 May 1936

1973 Robert Metcalfe wrote a memo describing a way to transmit data from the early generation of personal computers to a new device, the laser printer. He called his multipoint data communications system Ethernet, and today it continues to dominate as the standard computer network. A U.S. patent for "a Multipoint data communication system with collision detection" was issued 13 Dec 1977 ( 4,063,220) to Metcalfe, and others who developed the Ethernet. The patent was assigned to the Xerox Corporation. *TIS

1995 astronomers Amanda S. Bosh and Andrew S. Rivkin found two new moons of Saturn in photos taken by the Hubble Space Telescope. *TIS

1999 These beautiful magic squares, consisting of 11-digit palindromic primes, are by Carlos Rivera and Jaime Ayala. They were e-mailed to *Harvey Heinz,

2010 A Pac-Man Mini version, originally created by Google as an animated logo for the game's 30th anniversary on May 22, 2010. Play it here.


1783 William Sturgeon  (22 May 1783 - 4 December 1850) English electrical engineer who devised the first electromagnet capable of supporting more than its own weight (1825). The 7-oz (200-g) magnet supported 9-lb (4-kg) of iron with a single cell's current. He built an electric motor (1832) and invented the commutator, now part of most modern electric motors. In 1836, he invented the first suspended coil galvanometer, a device for measuring current. Sturgeon also worked on improving the voltaic battery, developing a theory of thermoelectricity, and even atmospheric charge conditions. From 500 kite flights made in calm weather, he found the atmosphere is consistently charged positively with respect to the Earth, and increasingly so at increased height. *TIS

1848 Hermann Schubert (22 May 1848 in Potsdam, Germany – 20 July 1911 in Hamburg, Germany) worked on parts of algebraic geometry that involve a finite number of solutions. This is called Enumerative Geometry. *SAU

1865 Alfred Cardew Dixon (22 May 1865 in Northallerton, Yorkshire, England - 4 May 1936 in Northwood, Middlesex, England) Alfred Dixon graduated from London and Cambridge and then had professorial appointments in Galway

1903 Yves-André Rocard  (Vannes, 22 May 1903 – 16 March 1992 in Paris)  French mathematician and physicist who contributed to the development of the French atomic bomb and to the understanding of such diverse fields of research as semiconductors, seismology, and radio astronomy. During WW II, as Head of the Research Department of the Free French Naval Forces in England, he learnt about radars in England and interference from strong radio emission from the Sun. After the war, Rocard returned to France and proposed that France started a project to conduct radio astronomy. In the last part of his life he studied biomagnetism and dowsing which reduced his standing in the eyes of many of his colleagues. *TIS

1916 Albrecht Fröhlich FRS (22 May 1916 – 8 November 2001) was a mathematician famous for his major results and conjectures on Galois module theory in the Galois structure of rings of integers.
He was born in Munich to a Jewish family. He fled from the Nazis to France, and then to Palestine. He went to Bristol University in 1945, gaining a Ph.D in 1951 with a dissertation entitled On Some Topics in the Theory of Representation of Groups and Individual Class Field Theory under the supervision of Hans Heilbronn. He was a lecturer at the University of Leicester and then at the Keele University, then in 1962 moved as reader to King's College London where he worked until his retirement in 1981 when he moved to Robinson College, Cambridge.
He was elected a Fellow of the Royal Society in 1976. He was awarded the Berwick Prize of the London Mathematical Society in 1976 and its De Morgan Medal in 1992. The Society's Fröhlich Prize is named in his honour.
He is the brother of Herbert Fröhlich. *Wik

1920 Thomas Gold (22 May 1920; 22 Jun 2004 at age 84) Austrian-British-American astronomer known for a steady-state theory of the universe, explaining pulsars, and naming the magnetosphere. In 1948, as a graduate student at Cambridge, he (together with Hermann Bondi and Fred Hoyle) proposed that, a continuous creation of matter in space is gradually forming new galaxies, maintaining the average number of galaxies in any part of the universe, despite its expansion. This is not accepted, as there is more evidence for the Big Bang theory. In 1967, Gold presented his theory on the nature of pulsars (objects in deep space that produce regularly pulsing radio waves). He suggested that they were rotating neutron stars - tiny, extraordinarily massive stars - which emit waves as they spin. *TIS


1626 Caspar Schott SJ, and Gaspar Schott or Kaspar Schott (February 5 1608 in Königshofen, May 22 1666 in Würzburg) was a scientific author and educator.
Schott attended the Würzburg Jesuit High School and entered the Order in 1627. During his studies in Würzburg one of his teachers was Athanasius Kircher. When the Jesuits fled before the approaching Swedish army in 1631,Schott went to Palermo to complete his studies. He stayed in Sicily 20 years as a teacher of mathematics, philosophy, moral theology at the Jesuit school in Palermo. In 1652 was sent to Rome as support in the scientific work of Kircher. He decided to publish Kircher's work. In 1655, he returned as Professor in the Würzburg school, where he taught mathematics and physics. He was Hofmathematker and confessor of the Elector Johann Philipp von Schönborn who had just purchased the vacuum pump invented by Otto von Guericke and used at Magdburg.
He corresponded with leading scientists including Otto von Guericke, Christiaan Huygens, and Robert Boyle . The term "technology" was probably invented by Schott in his "Technica curiosa" which inspired Boyle and Hooke's vacuum experiments.
In the posthumously published work Organum mathematicum he describes his Cistula invented by him, a computing device with which you can multiply and divide. *Wik

1868 Julius Plücker (16 June 1801 – 22 May 1868)  German mathematician and physicist whose work suggested the far-reaching principle of duality, which states the equivalence of certain related types of theorems. He also discovered that cathode rays (electron rays produced in a vacuum) are diverted from their path by a magnetic field, a principle vital to the development of modern electronic devices, such as television. At first alone and later with the German physicist Johann W. Hittorf, Plücker made many important discoveries in spectroscopy. Before Bunsen and Kirchhoff, he announced that spectral lines were characteristic for each chemical substance and this had value to chemical analysis. In 1862 he pointed out that the same element may exhibit different spectra at different temperatures. *TIS

1967 Josip Plemelj (December 11, 1873 – May 22, 1967) was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the application of integral equations to potential theory. He was the first chancellor of the University of Ljubljana.*Wik

1974 Irmgard Flugge-Lotz (6 July 1903 - 22 May 1974)born in Hameln, Germany. Her father encouraged her in mathematics, but she chose engineering because “I wanted a life which would never be boring—a life in which new things would always occur.” She studied applied mathematics at the Technical University of Hanover and in 1929 she became a Doktor-Ingenieur, the equivalent of an American Ph.D. in Engineering. She made contributions to aerodynamics, control theory, and fluid mechanics. In 1960 she became full professor at Stanford. *WM

1991 Derrick Lehmer  (February 23, 1905 – May 22, 1991) , one of the world's best known prime number theorists, born in Berkeley, California. Before World War II, Lehmer invented a number of electromechanical sieves for finding prime numbers and made many important contributions in prime number theory throughout his life. Prime numbers are of interest in themselves as mathematical curiosities but are also of great importance to cryptography. The Computer Museum History Center has three Lehmer sieves in its permanent collection. Lehmer died in 1991.*CHM Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.His father Derrick Norman Lehmer, known mainly as a pioneer in number theory computing, also made major contributions to combinatorial computing. *Wik

2009 Walter Ledermann (18 March 1911 in Berlin, Germany - 22 May 2009 in London, England) graduated from Berlin but was forced to leave Germany in 1933 to avoid Nazi persecution. He came to St Andrews and studied under Turnbull. He worked at Dundee and St Andrews until after World War II when he moved to Manchester and then to the University of Sussex. He is especially known for his work in homology, group theory and number theory. *SAU

2010  Martin Gardner (October 21, 1914 – May 22, 2010) died.  Gardner more or less single-handedly sustained and nurtured interest in recreational mathematics in the U.S. for a large part of the 20th century. He is best known for his decades-long efforts in popular mathematics and science journalism, particularly through his "Mathematical Games" column in Scientific American. *Wik
It is said that Gardner "Turned children into mathematicians and mathematicians into children.".. For some of us he did each in turn.  More than any classroom teacher I ever had, Martin Gardner shaped my mathematical interests. "For 35 years, he wrote Scientific American's Mathematical Games column, educating and entertaining minds and launching the careers of generations of mathematicians"
Only two days before I learned of his death, I stood in the front yard of my Mother's home in Fort Worth and told Alex, my sister's grandson, aged 12, that if he wanted to nurture his curiosity for math and science he should find anything in the library by Martin Gardner and read it every year for the next ten years of his life, and each year, I promised, he would find something new in the reading.
I can not do justice to the life of a man who was the mathematical Pied-Piper of mathematics for a generation of us; so here is link to the article in Scientific American.

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