Monday, 23 July 2018

On This Day in Math - July 23

Men love to wonder, and that is the seed of science.

-Ralph Waldo Emerson

The 204th day of the year; 204 is the sum of consecutive primes in two different ways: as the sum of a twin prime (101 + 103) and as the sum of six consecutive primes (23 + 29 + 31 + 37 + 41 + 43). (one might wonder what is the smallest number that is the sum of consecutive primes in more than one way... And what is the smallest prime number that is expressible as the sum of consecutive Primes in more than one way?)

And a trio from *Derek Orr @MathYearRound :
204 = 1²+2²+3²+4²+5²+6²+7²+8².
Sum of first 204 primes is prime.
100...00099...999 (204 0's and 204 9's) is prime.


594 The Sun was well up (17°) at 6:11 am when totality occurred. On a warm summer's morning it must have got surprisingly cold as totality approached, giving a clue that something unusual was about to happen. At 258 km wide this was an Eclipse with a very wide track and a good duration of over 3 minutes. The Eclipse track traveled into Denmark, Norway, Sweden, Finland, Estonia and Russia. *NSEC

1754 Joseph Louis Lagrange, 18, published his first work in the form of a letter in Italian (He was Italian born. Only his great-great-grandfather Lagrange was French, all other ancestors were Italian). A month later he realized that he had rediscovered Leibniz’s formula for the n-th derivative of a product. *VFR

1788 Jefferson's interest in surveying, and measurement in general led him to inquire of Benjamin Vaughan, then of England, about a British odometer, "I have heard that they make in London an Odometer, which may be made fast between two spokes of any wheel, and will indicate the revolutions of the wheel by means of a pendulum which always keeps it’s vertical position while the wheel is turning round and round. Thus [see Fig. 1.] I will thank you to inform me whether it’s indications can be depended on, and how much the instrument costs. " *Jefferson Letters

1829, William Austin Burt, a surveyor, of Mount Vernon, Michigan, received a patent for his typographer, a forerunner of the typewriter (U.S. No. 5581X). The Patent Office fire of 1836 destroyed the original patent model. Burt's typographer was a heavy, box-like contraption, made almost entirely of wood. Like today's familiar toy typewriter, the typographer had type mounted on a metal wheel, with a rotating, semicircular frame. By turning a crank, Burt was able to move the wheel until it came to the letter he wanted. Then he would pull a lever, driving the type against the paper and making an inked impression. *TIS

1904 The ice cream cone was introduced at the St. Louis world’s fair.*VFR by some accounts, the ice cream cone was invented by Charles E. Menches during the Louisiana Purchase Exposition in St. Louis. *TIS

1927 The term Eigenvalue first appears in a letter to Nature from A. S. Eddington beginning “Among those ... trying to acquire a general acquaintance with Schrödinger's wave mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem—to determine the eigenvalues and eigenfunctions for the hydrogen atom" *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

1962 Tens of millions of people watched a historic broadcast as Telstar beamed live transatlantic video into viewers’ living rooms for the first time. The age of satellite television had dawned.
In homes across Rome, people barely touched their dinners. London’s pubs were packed, but bartenders served nary a drink. Throughout Europe, more than 100 million people huddled around television sets on the evening of July 23, 1962, to tune in to history. With Europeans watching eagerly, a black-and-white image of the Statue of Liberty flickered onto their screens. The picture itself was not particularly noteworthy except for one thing: it was live, via satellite. *History.Com
The first broadcast was to have been remarks by President John F. Kennedy, but the signal was acquired before the president was ready, so the lead-in time was filled with a short segment of a televised game between the Philadelphia Phillies and the Chicago Cubs at Wrigley Field before the President's address.

1985 the legendary Commodore Amiga was released In 1985 Commodore revolutionized the home computer market by introducing the high end Commodore Amiga with a graphic power that was unheard of by that time in this market segment. Based on the Motorola 68000 microprocessor series the Amiga was most successful as a home computer, with a wide range of games and creative software, although early Commodore advertisements attempted to cast the computer as an all-purpose business machine. In addition, it was also a less expensive alternative to the Apple Macintosh and IBM-PC as a general-purpose business or home computer. The platform became particularly popular as a gaming platform. *

1995 The comet Hale–Bopp was discovered on July 23, 1995, independently by two observers, Alan Hale and Thomas Bopp, both in the United States. Hale–Bopp's orbital position was calculated as 7.2 astronomical units (AU) from the Sun, placing it between Jupiter and Saturn and by far the greatest distance from Earth at which a comet had been discovered by amateurs. It was discovered at such a great distance from the Sun that it raised expectations that the comet would brighten considerably by the time it passed close to Earth. Although predicting the brightness of comets with any degree of accuracy is very difficult, Hale–Bopp met or exceeded most predictions when it passed perihelion on April 1, 1997. The comet was dubbed the Great Comet of 1997.


1773 Sir Thomas Makdougall Brisbane, (23 July 1773 – 27 January 1860) Baronet British soldier and astronomical observer for whom the city of Brisbane, Australia, is named. He was Governor of NSW (1821-25). Mainly remembered as a patron of science, he built an astronomical observatory at Parramatta, Australia, made the first extensive observations of the southern stars since Lacaille in (1751-52) and built a combined observatory and magnetic station at Makerstoun, Roxburghshire, Scotland. He also conducted (largely unsuccessful) experiments in growing Virginian tobacco, Georgian cotton, Brazilian coffee and New Zealand flax.*TIS

1775 Etienne Louis Malus (23 July 1775 – 24 February 1812) born in Paris. He was the son on the Treasurer of France. His primary interest was mathematical optics. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, p. 473] *VFR He studied geometric systems called ray systems, closely connected to Julius Plücker's line geometry. He conducted experiments to verify Christiaan Huygens' theories of light and rewrote the theory in analytical form. His discovery of the polarization of light by reflection was published in 1809 and his theory of double refraction of light in crystals, in 1810.
Malus attempted to identify the relationship between the polarising angle of reflection that he had discovered, and the refractive index of the reflecting material. While he deduced the correct relation for water, he was unable to do so for glasses due to the low quality of materials available to him (most glasses at that time showing a variation in refractive index between the surface and the interior of the glass). It was not until 1815 that Sir David Brewster was able to experiment with higher quality glasses and correctly formulate what is known as Brewster's law.
Malus is probably best remembered for Malus' law, giving the resultant intensity, when a polariser is placed in the path of an incident beam. His name is one of the 72 names inscribed on the Eiffel tower.*Wik

1854 Ivan Vladislavovich Sleszynski (23 July 1854 in Lysianka, Cherkasy, Kiev gubernia, Ukraine - 9 March 1931 in Kraków, Poland)Sleszynski's main work was on continued fractions, least squares and axiomatic proof theory based on mathematical logic. In a paper of 1892, based on his doctoral dissertation, he examined Cauchy's version of the Central Limit Theorem using characteristic function methods, and made several significant improvements and corrections. Because of the work, he is recognised as giving the first rigorous proof of a restricted form of the Central Limit Theorem. *SAU

1856 Bal Gangadhar Tila (23 July 1856 – 1 August 1920, age 64) Scholar, mathematician, philosopher, and militant nationalist who helped lay the foundation for India's independence. Tilak was a great Sanskrit scholar and astronomer. He fixed the origin and date of Rigvedic Aryans, which was highly acclaimed and universally accepted by orientalists of his time. 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

1886 Walter Schottky (23 July 1886, Zürich, Switzerland – 4 March 1976, Pretzfeld, West Germany) Swiss-born German physicist whose research in solid-state physics led to development of a number of electronic devices. He discovered the Schottky effect, an irregularity in the emission of thermions in a vacuum tube and invented the screen-grid tetrode tube (1915). The Schottky diode is a high speed diode with very little junction capacitance (also known as a "hot-carrier diode" or a "surface-barrier diode.") It uses a metal-semiconductor junction as a Schottky barrier, rather than the semiconductor-semiconductor junction of a conventional diode. *TIS

1906 Vladimir Prelog (23 July 1906 – 7 January 1998) Yugoslavian-born Swiss chemist who shared the 1975 Nobel Prize for Chemistry with John W. Cornforth for his work on the stereochemistry of organic molecules and reactions. Stereochemistry is the study of the three-dimensional arrangements of atoms within molecules. He authored systematic naming rules for molecules and their mirror-image version, that is, which configuration will be referred to as "dextra" and which will be the "levo" (right or left). Also, by X-ray diffraction, he elucidated the structure of several antibiotics.*TIS

1920 Chushiro Hayashi (July 23, 1920 – February 28, 2010) Japanese astrophysicist who with his coworkers created evolutionary models for stars of mass between 0.01 to 100 times that of the Sun. In 1950, he contributed to the abg (Alpher, Bethe, Gamow) (also see April 1, Events) model of nucleosynthesis in the hot big bang. Hayashi pioneered in modeling stellar formation and pre-main sequence evolution along “Hayashi tracks” (1961) downward on the Hertzprung-Russell diagram until stars reach the main sequence. He and Takenori Nakano studied the formation of low-mass, brown dwarf stars. Hayashi also investigated the formation of the solar system and of the earth and its atmosphere. He retired in 1984. He was presented the Bruce Medal in 2004 for lifetime contributions to astronomy.*TIS

1928 Vera Rubin (July 23, 1928 - ) is an American astronomer who pioneered work on galaxy rotation rates. Her opus magnus was the uncovering of the discrepancy between the predicted angular motion of galaxies and the observed motion, by studying galactic rotation curves. This phenomena became known as the galaxy rotation problem. Currently, the theory of dark matter is the most popular candidate for explaining this. The alternative theory of MOND (Modified Newtonian Dynamics) has little support in the community.
Rubin received the Gold Medal of the Royal Astronomical Society in 1996. She was only the second female recipient of this medal, the first being Caroline Herschel in 1828. The asteroid 5726 Rubin is named in her honor. *TIA

1930 Daniel McCracken, (July 23, 1930 – July 30, 2011) who wrote the first textbook on FORTRAN, was born. A student of mathematics and chemistry, McCracken started working in computers at General Electric in 1951, training workers in using the new technology. Based on this teaching experience, McCracken wrote several important computer programming textbooks, most notably ""A Guide to FORTRAN Programming"" in 1961.*CHM

1932 Derek Thomas "Tom" Whiteside FBA (July 23, 1932–April 22, 2008[4]) was a British historian of mathematics. He was the foremost authority on the work of Isaac Newton and editor of The Mathematical Papers of Isaac Newton. From 1987 to his retirement in 1999, he was the Professor of the History of Mathematics and Exact Sciences at Cambridge University. *Wik

1952 Mark David Weiser (July 23, 1952 – April 27, 1999) American computer scientist and visionary who developed the pioneering idea for what he referred to as "ubiquitous computing," He coined that term in 1988 to describe a future in which PC's will be replaced with tiny computers embedded in everyday "smart" devices (everyday items such as coffeepots and copy machines) and their connection via a network. He said, "First were mainframes, each shared by lots of people. Now we are in the personal computing era, person and machine staring uneasily at each other across the desktop. Next comes ubiquitous computing, or the age of calm technology, when technology recedes into the background of our lives." *TIS


1903 Eduard Weyr (22 June 1852 Praha – 23 July 1903 Záboří) wrote geometrical papers and books mainly in projective geometry and differential geometry. He also worked on algebra, in particular studying linear algebra, matrices and hypercomplex systems.
Weyr published Differential calculus in 1902. This led to controversy with a young mathematician J V Pexider who sharply criticised Weyr's textbook. Jindrich Beèváo and Ludek Zajièek give an interesting account of this episode in a paper in the book .* website

1916 William Ramsay (2 October 1852, Glasgow, Scotland - 23 July 1916 (aged 63)
High Wycombe, Bucks., England) died. Ramsay was a British chemist who discovered the four gases neon, argon, krypton and xenon. He also determined they belonged with helium and radon to form a family of gases called the noble gases. This discovery would earn him the 1904 Nobel Prize in Chemistry.*Science History

1932 Alberto Santos-Dumont (July 20, 1873 – July 23, 1932) was a Brazilian aviation pioneer, deemed the Father of Aviation by his countrymen. At the age of 18, Santos-Dumont was sent by his father to Paris where he devoted his time to the study of chemistry, physics, astronomy and mechanics. His first spherical balloon made its first ascension in Paris on 4 July 1898. He developed steering capabilities, and in his sixth dirigible on 19 Oct 1901 won the "Deutsch Prize," awarded to the balloonist who circumnavigated the Eiffel Tower. He turned to heavier-than-air flight, and on 12 Nov 1906 his 14-BIS airplane flew a distance of 220 meters, height of 6 m. and speed of 37 km/h. to win the "Archdecon Prize." In 1909, he produced his famous "Demoiselle" or "Grasshopper" monoplanes, the forerunners of the modern light plane. *TIS

1964 Samarendra Nath Roy or S. N. Roy (11 December 1906 – 23 July 1964). He was well known for his pioneering contribution to multivariate statistical analysis, mainly that of the Jacobians of complicated transformations for various exact distributions, rectangular coordinates and the Bartlett decomposition. His dissertation included the Post master's work at the Indian Statistical Institute where he worked under Mahalanobis. To commemorate his Birth Centenary an International Conference on "Multivariate Statistical Methods in the 21st Century: The Legacy of Prof. S.N. Roy" was held at Kolkata, India during December 28–29, 2006. The Journal of Statistical Planning and Inference published a special Issue for celebrating of the Centennial of Birth of S. N. Roy*Wik

1964 W. W. Rogosinski died. *VFR He wrote on Fourier Series with G.H. Hardy

1993 Florence Nightingale David, (August 23, 1909 – July 23, 1993) also known as F. N. David was an English statistician, born in Ivington, Herefordshire, England. She was named after Florence Nightingale, who was a friend of her parents.
David read mathematics at Bedford College for Women in London. After graduation, she worked for the eminent statistician Karl Pearson at University College, London as his research student. She calculated the distribution of correlation coefficients, producing in 1938 her first book, Tables of the correlation coefficient.
After Karl Pearson died in 1934, she returned to the Biometrics laboratory to work with Jerzy Neyman where she submitted her last four published papers as her PhD thesis. During World War II, David worked for the Ministry of Home Security. In late 1939 when war had started but England had not yet been attacked, she created statistical models to predict the possible consequences of bombs exploding in high density populations such as the big cities of England and especially London. From these models, she determined estimates of harm to humans and damage to non-humans This included the possible numbers living and dead, the reactions to fires and damaged buildings as well as damages to communications,utilities such as phones, water, gas, electricity and sewers. As a result when the Germans bombed London in 1940 and 1941, vital services were kept going and her models were updated and modified with the evidence from the real harms and real damage.
David became head of the Statistics Department at the University of California at Riverside in 1970.*Wik

2012  Sally Kristen Ride (May 26, 1951 – July 23, 2012) was an American physicist and a former NASA astronaut. Ride joined NASA in 1978, and in 1983 became the first American woman—and then-youngest American, at 32—to enter space. In addition to being interested in science, she was a nationally ranked tennis player. Ride attended Swarthmore College and then transferred to Stanford University, graduating with a bachelor's degree in English and physics. Also at Stanford, she earned a master's degree and a Ph.D. in physics, while doing research in astrophysics and free electron laser physics.In 1987 she left NASA to work at Stanford University's Center for International Security and Arms Control.
Sally Ride died on July 23, 2012 after a 17-month battle with pancreatic cancer.   US President Barack Obama called her a "national hero and a powerful role model" who "inspired generations of young girls to reach for the stars."*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

Sunday, 22 July 2018

Why the Divisible by Eleven Rule works, and an extension

Another repost of an old blog that needed dusting off:

Over some tweets about division mental tricks lately I got a question about why the somewhat well known test for eleven works.

If you are not one who grew up BC(before calculators) working with mental arithmetic, some of these may not be known to you, so here is the one about which they were asking.

If you take a number, say 31492435 and want to know if it is divisible by eleven, the old-school common trick was to take every other digit and find the sum, then do the same with t he remaining digits. If these two totals differ by a multiple of eleven, then it is divisible by 11. ( I like a more effective one that tests divisibility by 7, 11, and 13 all at once, and I think is a simpler approach that I will explain after answering the primary question.)

So to begin, I'd like to explain why the more common test of "Casting Out Nines" works.

The secret behind casting out nines is hidden in the following set of equalities:

10 = 1*9+1

100 = 11*9 +1

1000= 111*9+1

10000= 1111*9+1

So if we have a number like 1234, which is 1000+200 + 30 + 4, we can rewrite it as 1(111*9 + 1) + 2(11*9+1) + 3(1*9+1) + 4. Distributing the numbers powers of ten gives me 111*9 + 1+ 22*9+2 + 3*9+3 + 4 collecting all the terms that are multiples of nine gives us 136*9 + 10. Since nine will divide evenly into the 136*9, the remainder is the remainder when ten is divided by nine, and of course we know that 10 = 1*9+1, so the remainder is one.

For elevens the pattern is slightly different. Notice that :

10 = 1*11 –1

100 = 9*11 +1

1000= 91*11-1

10000= 909*11+1

100,000= 9091*11-1

….. and each multiple of ten alternates being one more than or one less than a multiple of 11. So if we expand 1234 as before into 1000+200 + 30 + 4, we can rewrite it as 1(91*11 –1) + 2(9*11+1)+ 3(1*11-1) + 4 . Expanding as before we get some powers of eleven, and the remaining numbers are –1 + 2 – 3 + 4 = 2; so the 1234 divided by 11 leaves a remainder of 2.

It is very similar to the method of casting out nines, except that we alternate adding and subtracting instead of adding all the terms. Most people find it easier to start at the right since the constant term is always added, but you must be able to deal with small negative numbers. For instance if we use 4152, we will do 2 – 5 + 1 – 4 which yields –6. We know there can not be a negative remainder, so what to do. Simply remove this amount from the base, 11, and the answer is revealed. The remainder is 5.
Just be aware that if you get a negative number, it means the remainder is the elevens compliment (11-r) of that number. If you just use the sums of the alternate terms, you don't know the remainder for certain, but it still tests divisibility.

My favorite method that I mentinoed above, uses the idea that 7*11*13 = 1001, so for big numbers, it can be quicker to subtract out multiples of 1001, or 10010, or 100100, etc.

For 4153 you can quickly see by inspection that it is not divisible by 2, 3, or 5. If you reduce it by subtracting 4*1001 = 4004 to get 149. Since 7 goes into that with remainder of two, the original number has a remainder of two on division by 7 also. And since 1+9 - 4 is not zero, or a multiple of eleven then it is not divisible by 11, and a quick mental inspection says that 149 is not divisble by 13 either, so we've eliminated a lot of numbers quickly in testing for primes.

On This Day in Math - July 22

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.

~David van Dantzig

This is the 203rd day of the year; 203 is the 6th Bell number, i.e. it is the number of partitions of a set of size 6.

203^2 + 203^3 + 1 is prime.

203 is the number of nondegenerate triangles that can be made from rods of lengths 1,2,3,4,...,11

203 is the number of triangles pointing in opposite direction to largest triangle in triangular matchstick arrangement of side length 13

Saw a tweet about July 22 as "Casual Pi Day" at Rimwe@RimweLLC which he told me he found at page of GeorgeTakei.

The NCTM uses "Pi Approximation Day" for it's poster


1694 Johann Bernoulli sent “L’Hospital’s rule” to L’Hospital under the terms of their agreement of 17 March 1694. *VFR The agreement between them led to the first real calculus text in 1696.

1925 After Norbert Wiener suggested to his friend Phillip Franklin in a letter that they hang a sign outside their office at MIT reading “Wiener and Franklin. Wholesale and Retail Mathematicians and Exporters,” he wrote: “As to the state of the market: differential geometry seems rather quiet, and some of the principal operators have deserted it for other securities. Real and complex variables continue firm, without much change. Analysis situs has a bull market. Bull operators have been very active in differential equations, also. Quantum theory continues speculative, with chances of a very sharp rise, but the market contains a lot of wildcat stock. Hilbert, Brouwer, and Co. are doing well with mathematical logic.” From Science in America, ed. Nathan Reingold, p. 384.*VFR

1933 Wiley Post startled the world by completing the first solo airplane flight around the world. The 15,400 mile flight lasted seven days, 18 hours, 49 and 1/2 minutes. Two years later he was killed in an airplane crash with humorist, Will Rogers. [Scientific American, November 1933]*VFR   He had made an accompanied flight around the world in 1931. Born 22 Nov 1898, Wiley Post made his first solo flight in 1926, the year he got his flying license, signed by Orville Wright, despite wearing a patch over his left eye, lost in an oilfield accident. Post invented the first pressurized suit to wear when he flew around the world. Another credit was his research into the jet streams. He died with his passenger, humorist Will Rogers, 15 Aug 1935 in a plane crash in Alaska.*TIS

1976 “researchers from Univ of Illinois announced they had found an unavoidable set containing 1936 reducible configurations effectively proving the four color theorem.*VFR

1978 Roger Apéry gave a talk entitled "Sur l'irrationalité de ζ(3)." to outline proofs that ζ(3) and ζ(2) were irrational. Alfred J. Van der Poorten's reprint of the talk describes the less than hopeful anticipation of the audience.,
"The board of programme changes informed us that R. Apery (Caen) would speak Thursday, 14:00 ‘Sur l’irrationalit'e de ζ(3)’. Though there had been earlier rumours of his claiming a proof, scepticism was general. The lecture tended to strengthen this view to rank disbelief. Those who listened casually, or who were afflicted with being non-Francophone, appeared to hear only a sequence of unlikely assertions"
"I heard with some incredulity that, for one, Henri Cohen (then Bordeaux, now Grenoble) believed that these claims might well be valid. Very much intrigued, I joined Hendrik Lenstra (Amsterdam) and Cohen in an evening’s discussion in which Cohen explained and demonstrated most of the details of the proof. We came away convinced that Professeur Apery had indeed found a quite miraculous and magnificent demonstration of the irrationality of ζ(3)." *, Poorten, A PROOF THAT EULER MISSED , with special thanks to Tim Pentilla who helped me establish the date of the original address.

1983 Science reported that Gerd Faltings of Wuppertal University in Germany proved the sixty-year ­old Mordell conjecture: most equations of degree higher than three have only a finite number of rational solutions. In particular, this applies to Fermat’s Last Theorem. [Mathematics Magazine 57 (1984), p. 52].*VFR  In number theory, the Mordell conjecture is the conjecture made by Mordell (1922) that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points. The conjecture was later generalized by replacing Q by a finite extension. It was proved by Gerd Faltings (1983), and is now known as Faltings' theorem.

1997Apple Announces OS 8-Apple Computer Inc. announces a new operating system for its Macintosh computers, OS 8. An important move at a time when Apple's upper-level management and profits were experiencing significant problems, the new operating system offered new features such as easier integration of the Internet and a three-dimensional look. Immediately after the announcement, the software earned positive reviews from users, although it was not expected to end Apple's financial troubles as it faced growing competition from improvements in the Microsoft Windows operating system used on IBM-compatible PCs. *CHM

2009 A total solar eclipse the longest-lasting total eclipse of the 21st century – takes place. It lasted a maximum of 6 minutes and 39 seconds off the coast of Southeast Asia, causing tourist interest in eastern China, Japan, India, Nepal and Bangladesh. It will not be surpassed until 13 June 2132. *Wik

2381 The maximum theoretical length for a British total eclipse is 5.5 minutes. The eclipse of June 16, 885 lasted for almost 5 minutes and the same will be true for the Scottish total eclipse of 22 Jul, 2381. This TSE will be the first total solar eclipse
in Amsterdam since 17 June 1433. *NSEC


1784 Friedrich Wilhelm Bessel born (22 July 1784 – 17 March 1846). He is noted for the special class of functions that have become an indispensable tool in applied mathematics. This, like all of his mathematical work, was motivated by his work in astronomy. *VFR    In 1809, at the age of 26, Bessel was appointed director of Frederick William III of Prussia's new Königsberg Observatory and professor of astronomy, where he spent the rest of his career. His monumental task was determining the positions and proper motions for about 50,000 stars, which allowed the first accurate determination of interstellar distances. Bessel's work in determining the constants of precession, nutation and aberration won him further honors. Other than the sun, he was the first to measure the distance of a star, by parallax, of 61 Cygni (1838). In mathematical analysis, he is known for his Bessel function. *TIS

1795 Gabriel Lam´e (22 July 1795 – 1 May 1870) born in Tours, in today's département of Indre-et-Loire.
He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:
 \left|\,{x\over a}\,\right|^n + \left|\,{y\over b}\,\right|^n =1
where n is any positive real number.
He is also known for his running time analysis of the Euclidean algorithm. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digits of b. He also proved a special case of Fermat's last theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics. *Wik
Piet Hein's Super Ellipse is a Lame Curve

1822 Gregor Mendel (July 20, 1822 – January 6, 1884) (Original name (until 1843) Johann Mendel). Austrian pioneer in the study of heredity. He spent his adult life with the Augustinian monastery in Brunn, where as a geneticist, botanist and plant experimenter, he was the first to lay the mathematical foundation of the science of genetics, in what came to be called Mendelism. Over the period 1856-63, Mendel grew and analyzed over 28,000 pea plants. He carefully studied for each their plant height, pod shape, pod color, flower position, seed color, seed shape and flower color. He made two very important generalizations from his pea experiments, known today as the Laws of Heredity. Mendel coined the present day terms in genetics: recessiveness and dominance.

1882 Konrad Knopp (22 July 1882 – 20 April 1957) born. He is best known for comprehensive book on infinite series.*VFR

1887 - Gustav Hertz born (22 July 1887 – 30 October 1975) .Hertz was a German physicist who shares the 1925 Nobel Prize in Physics with James Franck for their Frank-Hertz experiment. The Frank-Hertz experiment shows that an atom absorbs energy in discrete amounts, confirming the quantum theory of atoms. This experiment was an important step confirming the Bohr model of the atom. *TIS

1902 Reinhold Baer (July 22, 1902 – October 22, 1979) Baer's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups.*SAU

1914 Edward (Rolke) Farber was an American who invented a portable, battery-operated stroboscopic flash unit for still cameras (1937) that effectively "stopped action." He began his career as a photojournalist on the staff of the Milwaukee Journal. After studying electrical engineering at Northwestern University, Farber went on to design flash equipment for the U.S. Army during World War II, and then established his own electronic-flash manufacturing firm. He was a good friend and collaborator of Harold Edgerton and developed the first practical portable strobe flash for news photographers. In 1942, the Milwaukee Journal became the first newspaper to furnish all of its photographers with the portable flash. Weighing only 13.5 pounds, it was a considerable improvement over the 90-pound units photographers used prior to Farber's invention. He sold his Strobe Research firm in 1954. He was a photographic adviser to the U.S. Government during its intercontinental ballistic missile testing program in the late 1950's.*TIS

1935 John Robert Stallings (July 22, 1935 – November 24, 2008) In 1968 Stallings published his most famous paper On torsion-free groups with infinitely many ends in the Annals of Mathematics. L Neuwirth explains what is contained in the paper:-
In this remarkable paper, the author, using very little besides his bare hands, proves the following theorem:
1. If G is a torsion-free, finitely presented group, with infinitely many ends, then G is a non-trivial free product.
This simple sounding theorem proves to be very powerful, implying
(with a little work) the following two theorems:
2. A torsion-free, finitely generated group, containing a free subgroup of finite index, is itself free.
3. A finitely generated group of cohomological dimension 1 is free.
This last theorem answers a question which had been unanswered for over ten years and which had received considerable attention over that period of time. Theorem
2 answers a question of J-P Serre, who proved an analogue of Theorem 2 for pro-p groups. The proof of Theorem 1 is both combinatorial and geometric in nature and, as suggested, is self-contained.
For this truly outstanding paper the American Mathematical Society awarded Stallings their Frank Nelson Cole Prize in Algebra in 1970. Also in 1970 he was invited to address the International Congress of Mathematicians in Nice, France. He gave a talk on Group theory and 3-manifolds. He had been honoured in the previous year when invited to give the James K Whittemore Lecture in Mathematics at Yale University in 1969. His topic was Group theory and three-dimensional manifolds. This lecture and his Nice address were both published in 1971.
Among the 50 or so papers Stalling published, we should highlight another two which have proved particularly important: Topology on finite graphs (1983) and Non-positively curved triangles of groups (1991). The first of these introduced the 'Stallings subgroup graph' as a method to describe subgroups of free groups. It also introduced a foldings technique now known as 'Stallings' foldings method' which has been the basis for much later work. The second of these two papers introduced the notion of a triangle of groups which became the basis for later work on the theory of complexes of groups.*SAU


1575  Francisco Maurolico (Messina, Sicily, 16 Sept 1494 - near Messina, Sicily, 21/22 July 1575) was an Italian Benedictine who wrote important books on Greek mathematics. He also worked on geometry, the theory of numbers, optics, conics and mechanics.*SAU

1826 Giuseppe Piazzi (July 16, 1746 – July 22, 1826) Italian astronomer and author, born in Valtellina, discovered the first asteroid - Ceres. He established an observatory at Palermo and mapped the positions of 7,646 stars. He also discovered that the star 61 Cygni had a large Proper Motion , which led Bessel to chose it as the object of his parallax studies. He discovered Ceres in 1801, but was able to make only three observations. Fortuitously, Gauss had recently developed mathematical techniques that allowed the orbit to be calculated. This was the first asteroid discovered. The thousandth Asteroid discovered was named Piazzia in his honor.*TIS  (His dates of birth and death are six days apart)

1869 John A. Roebling (June 12, 1806 – July 22, 1869) German-American engineer who pioneered the design and construction of suspension bridges. In 1831 he immigrated to Saxonburg, near Pittsburgh, Pa., and shortly thereafter was employed by the Pennsylvania Railroad Corp. to survey its route across the Allegheny Mountains. He then demonstrated the practicability of steel cables in bridge construction and in 1841 established at Saxonburg the first U.S. factory to manufacture steel-wire rope. Roebling utilized steel cables in the construction of numerous suspension bridges including a railroad suspension bridge over the Niagara River at Niagara Falls (1851-55). He designed the Brooklyn Bridge. He died from injuries while supervising preliminary construction operations.*TIS

1915 Sir Sandford Fleming (January 7, 1827 – July 22, 1915) Scottish surveyor and leading railway engineer who divided world into time zones. He emigrated at age 17 years to Quebec, Canada, on April 24, 1845, as a surveyor. Later became one of the foremost railway engineers of his time. While in charge of the initial survey for the Canadian Pacific Railway, the first Canadian railway to span the continent, he realized the problems of coordinating such a long railway. This lead him to the idea of time zones, which contribution to the adoption of the present system of time zones earned him the title of "Father of Standard Time." Fleming also designed the first Canadian postage stamp. Issued in 1851, it cost three pennies and depicted the beaver, now the national animal of Canada.*TIS

1932 Reginald Aubrey Fessenden (October 6, 1866 – July 22, 1932), was a Canadian inventor and engineer with 300 patents. He broadcast the first program of voice and music. In 1893, Fessenden moved to Pittsburgh as the head of electrical engineering at the university, Fessenden read of Marconi's work and began experimenting himself. Marconi could only transmit Morse code. But Fessenden's goal was to transmit the human voice and music. He invented the "continuous wave": sound superimposed onto a radio wave for transmission. A radio receiver extracts the signal so the listener with the original sound. Fessenden made the first long-range transmissions of voice on Christmas Eve 1906 from a station at Brant Rock, Massachusetts, heard hundreds of miles out in the Atlantic.*TIS

1938 Ernest (William) Brown (29 November 1866 – 22 July 1938) was a British astronomer who devoted his career to the theory of the Moon's motion and constructing accurate lunar tables. His theory took account of "the gravitational action of every particle of matter which can have a sensible effect on the Moon's motion," some 1500 terms. He then determined the numerical values of the constants by analyzing 150 years of Greenwich observations, and computed tables accurate to 0.01 arcsec. After 30 years of work, Brown published his lunar tables Tables of the Motion of the Moon in 1919. In 1926 Brown published a paper in which he ascribed fluctuations in the Moon's motion to irregular changes in the Earth's period of rotation, which has subsequently proved correct. *TIS

1943 William Fogg Osgood died (March 10, 1864, Boston - July 22, 1943, Belmont, Massachusetts). Although his nickname was “Foggy,” this was not an apt description of him as a teacher. He instilled the habit of careful thought in Harvard students for 43 years. His A First Course in Differential and Integral Calculus (1907) was revised once and reprinted 17 times.*VFR From 1899 to 1902, he served as editor of the Annals of Mathematics and in 1904–1905 was president of the American Mathematical Society, whose Transactions he edited in 1909–1910. In 1904, he was elected to the National Academy of Sciences.
The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations. He was invited by Felix Klein to write an article on complex analysis in the Enzyklopädie der mathematischen Wissenschaften which was later expanded in the book Lehrbuch der Funktionentheorie. Besides his research on analysis, Osgood was also interested in mathematical physics and wrote on the theory of the gyroscope. *Wik

1959 David van Dantzig (September 23, 1900, Amsterdam – July 22, 1959) was at secondary school when he wrote his first mathematics paper. He was only thirteen years old at the time. However, his main interest in secondary school was not mathematics, rather it was chemistry. After leaving school he continued with his studies of chemistry, but this he did not enjoy and when he was forced to give up his academic studies to help support his family van Dantzig took on a number of jobs purely to make money.
By now van Dantzig knew that mathematics was the subject which he really wanted to study but he was not in a position to do so, both because he had to earn money and also because he did not have the necessary school qualifications. He put in hours of work on mathematics in the evenings after finishing his money earning tasks for the day. He took the state mathematics examinations in 1921, at a higher level the following year and again in 1923 he passed at a higher level still. Entering the University of Amsterdam to study mathematics he soon passed examinations which took him essentially to Master's Degree level.
Van Dantzig became an assistant to Schouten in 1927 at Delft Technical University. Then, for a short time, he taught at a teacher training institution, but he returned to Delft as a lecturer in 1932. This was the year in which he received his doctorate from Gröningen for a thesis which he submitted in 1931 Studiën over topologische Algebra. In this work he coined the now familiar term topological algebra but the thesis is memorable in other ways too. It -
... is a fine example of mathematical style: it consists of a concise string of definitions and theorems organised in such a way that in this context each theorem is obvious and none needs a proof.
He was promoted to extraordinary professor at Delft in 1938 and then an ordinary professor in 1940. The Dutch had tried to remain neutral when World War II broke out in 1939 but in the spring of 1940 German troops, in a strategic move on their way to attack France, entered Holland and the Dutch were defeated in a week. Van Dantzig was dismissed from his chair when the Germans occupied Holland and he was forced to move with his family from the Hague to Amsterdam.
After the war ended, he was appointed professor at the University of Amsterdam in 1946. In Amsterdam he was the cofounder of the research and service institution, the Mathematisch Centrum. He played a major role in both this Centre and in the University of Amsterdam where he continued to hold his chair until his death.
Van Dantzig studied differential geometry, electromagnetism and thermodynamics. His most important work was in topological algebra and in addition to his doctoral thesis which we mentioned above, he wrote a whole series of papers on topological algebra. He studied metrisation of groups rings and fields. One paper classified fields with a locally compact topology.*SAU

1966 Philipp Frank (20 Mar 1884; 22 Jul 1966 at age 82) Austrian-American physicist and mathematician whose theoretical work covered a broad range of mathematics, including variational calculus, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Frank had a deep and lasting interest in the philosophy of science. In a number of writings, he strove to reconcile science and philosophy and “bring about the closest rapprochement between” them. The 1907 paper he wrote analyzing the law of causality caught Einstein's attention, who in 1912 recommended Frank as his successor as professor of theoretical physics at the German University of Prague. He held that position until 1938, when he moved to Harvard University in the U.S., first as visiting lecturer, but remaining there until retirement in 1954. He wrote on misinterpretations of the Theory of Relativity.*TIS

1995  Otakar Boruvka (10 May 1899 in Uherský Ostroh – 22 July 1995 in Brno)   To many people Boruvka is best known for his solution of the Minimal Spanning Tree problem which he published in 1926 in two papers On a certain minimal problem (Czech) and Contribution to the solution of a problem of economical construction of electrical networks (Czech). Let us quote the problem as it appears in the second of these 1926 papers:-
There are n points in the plane whose mutual distances are different. The problem is to join them with a net in such a way that:
1. any two points are joined to each other either directly or by means of some other points;
2. the total length of the net will be minimal.
In modern graph theoretical terms this can be stated as: Given an undirected graph with weights assigned to its edges, find a spanning tree of minimal weight.
In fact the problem had been suggested to Boruvka before he became a university student. He had a friend, Jindrich Saxel, who worked for the firm West-Moravian Powerplants and he suggested the problem which he stated in terms of cities and the distances between them. At the time that Saxel suggested the problem to Boruvka, World War I was still happening and Czech universities were closed. Boruvka was offered a job with West-Moravian Powerplants at this time but declined. The authors write:-
The Minimal Spanning Tree problem is a cornerstone of Combinatorial Optimisation and in a sense its cradle. The problem is important both in its practical and theoretical applications. Moreover, recent development places Boruvka's pioneering work in a new and very contemporary context. One can even say that out of many available Minimal Spanning Tree algorithms, Boruvka's algorithm is presently the basis of the fastest known algorithms.  *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Saturday, 21 July 2018

On This Day in Math - July 21

The saddest aspect of life right now is that
science gathers knowledge faster than society gathers wisdom.

-Isaac Asimov

Today is the 202nd day of the year; in an alphabetical listing of the first one-thousand numbers, 202 is last.

202293 begins with the digits 293 and 293202 begins with the digits 202. *jim wilder ‏@wilderlab

There are 46 palindromes in the 365 (or 366) days of the year, 202 is the 30th of these.


1807 Gauss, in a letter to his friend Olbers, praised the mathematical ability of Sophie Germain. *VFR Although Gauss thought well of Germain, his replies to her letters were often delayed, and he generally did not review her work. Eventually his interests turned away from number theory, and in 1809 the letters ceased. Despite the friendship of Germain and Gauss, they never met.*Wik

1820 Oersted announced his discovery of electromagnetism. *VFR The actual discovery of electromagnetism was made during a lecture demonstration that Oersted was conducting for advanced students during the spring of 1820. It is perhaps the only case known in the history of science when a major scientific discovery was mate in front of a classroom of students.

1814 Joseph von Fraunhofer was the eleventh child of an indigent glazier he was orphaned and apprenticed to Philipp Weichselberger. It may seem strange to say that he was lucky to have the dilapidated building which was the house and shop of Weichselberger collapse on top of him. But being the only survivor made him newsworthy, and when he was visited by Maximilian Joseph, the Bavarian Elector, he was given a sum of eighteen ducats with which he bought a glass making machine, books, and his freedom from his apprenticeship. Ahead in his brief life, he would discover the spectral lines which still carry his name. *Timothy Ferris, Coming of Age in the Milky Way

These dark fixed lines were later shown to be atomic absorption lines, as explained by Kirchhoff and Bunsen in 1859. These lines are still called Fraunhofer lines in his honor - although they had previously been noted by Wollaston in 1802.

1925 John Scopes is found guilty of teaching evolution in violation of Tennessee's Butler Act.
"After eight days of trial, it took the jury only nine minutes to deliberate. Scopes was found guilty on July 21 and ordered to pay a US$100 fine (approximately $1,345 in present day terms when adjusted from 1925 for inflation). Raulston imposed the fine before Scopes was given an opportunity to say anything about why the court should not impose punishment upon him and after Neal brought the error to the judge's attention the defendant spoke for the first and only time in court:

Your honor, I feel that I have been convicted of violating an unjust statute. I will continue in the future, as I have in the past, to oppose this law in any way I can. Any other action would be in violation of my ideal of academic freedom—that is, to teach the truth as guaranteed in our constitution, of personal and religious freedom. I think the fine is unjust. (World's Most Famous Court Trial, p. 313.)

1959 The first “International Mathematical Olympiad” began in Brasov, Romania. It lasted until 31 July and involved 52 competitors on teams from seven Eastern European countries. The Romanian Team won the team event, and the individual Gold Medal went to Bohuslav Diviš from Czechoslovakia. *IMO Website

1961 popularization of the term "Big Science" is usually attributed to an article by Alvin M. Weinberg, then director of Oak Ridge National Laboratory, published in Science #OTD

1967 Brazil (Scott #1053) issued a stamp to commemorate the 6th Brazilian Mathematical Congress. It depicted, in bright blue and black, a M¨obius strip—the first time that this famous shape has been shown on either stamp or coin. [Journal of Recreational Mathematics, 1(1968), 44] *VFR

In 1970, the Aswan High Dam in Egypt was completed after 18 years of work. It is a huge rockfill dam that lies just north of the border between Egypt and Sudan. It captures the world's longest river, the Nile, in the world's third largest reservoir, Lake Nasser. Built with Soviet aid at a cost of $1 billion, it now produces hydroelectricity meeting 50% of Egypt's power needs. It holds several years of irrigation reserves, assists multi-cropping, has increased productivity 20-50%, enormously increased Egypt's arable land, and overall, increased Egypt's agricultural income by 200%. The embankment is 111 metres high, with a width of near 1,000 metres. Lake Nasser is 480 long and up to 16 km wide. *TIS

In 1982, the first look at the Three Mile Island Unit 2 partial core meltdown was recorded by a mini-TV camera. This was the first inspection of the core made since the nuclear power plant in Harrisburg, Pennsylvania, first experienced a serious accident on 28 Mar 1979, due to a loss of water coolant. With the camera nothing was seen until five feet down - signifying that five feet of the core was gone. Many fuel rods had melted causing the tubes to break, spilling uranium to the bottom of the pressure vessel. Thus out of reach of the control rods, the uranium fission continued. Fifty percent of the core was destroyed or molten and an estimated twenty tons of uranium pellets had travelled to the bottom of the pressure vessel. *TIS

1990 Meteorologist Joe Rao was able to coerce American Trans-Air Airlines to alter the course of one of their regularly scheduled flights in order to be in the right position to experience the total phase of the July 22-21, 1990 total solar eclipse. The
eclipse began on Sunday, July 22, with the path of totality passing over Helsinki, Finland. The shadow path then moved across northernmost sections of Russia, then crossed the International Date Line, causing the eclipse date to change to Saturday, July 21.
The totality track swept southeast over Alaska's Aleutian Island chain, before reaching its end at a point midway between Honolulu, Hawaii and San Francisco, California. American Trans-Air Flight 403 normally flies from Hawaii to San Francisco on Saturday afternoons. A few weeks in advance of the eclipse, Rao informed the airline that by delaying the flight by 41 minutes out of Honolulu, that Flight 403 would likely be in position to catch the total phase. The airline agreed to make the attempt, allowing most of the 360 persons on board their Lockheed L-1011 jet the opportunity to witness totality. Rao, his wife Renate, and two friends, flew out of New York's JFK airport late on Friday night, July 20 . . . arrived in San Francisco early on Saturday morning for a few hours of sleep, before boarding ATA Flight 402 to Hawaii. They were in Honolulu for 45 minutes before turning around and heading back for San Francisco (encountering the eclipse along the way). After spending the night in San Francisco, they returned to New York the next day, having traveled over 11,000 miles in 46 hours just to see 73 seconds of a total eclipse!*NSEC

1620 Jean Picard (July 21, 1620 – July 12, 1682) Astronomer, born La Flêche, France. Picard is regarded as the founder of modern astronomy in France. He introduced new methods, improved the old instruments, and added new devices, such as Huygens' pendulum clock to record times and time intervals. Jean Picard was the first to put the telescope to use for the accurate measurement of small angles, making use of Gascoigne's micrometer. His most important work was the first measurement of the circumference of the earth. He used the method of Eratosthenes, but with greater accuracy. The concept behind neon signs began in 1675, when astronomer Jean Picard observed a glow in a barometer.*TIS (Dates of Birth and death are only 9 days apart)

1810 Henri-Victor Regnault (21 July 1810 – 19 January 1878) French chemist and physicist noted for his work on the properties of gases. His invaluable work was done as a skilful, thorough, patient experimenter in determining the specific heat of solids, liquids, gases, and the vapour-tensions of water and other volatile liquids, as well as their latent heat at different temperatures. He corrected Mariotte's law of gases concerning the variation of the density with the pressure, determined the coefficients of expansion of air and other gases, devised new methods of investigation and invented accurate instruments. Two laws governing the specific heat of gases are named after him.*TIS

1849 Robert Simpson Woodward (July 21, 1849–June 29, 1924) was an American physicist and mathematician, born at Rochester, Michigan. He graduated C.E. at the University of Michigan in 1872 and was appointed assistant engineer on the United States Lake Survey. In 1882 he became assistant astronomer for the United States Transit of Venus Commission. In 1884 he became astronomer to the United States Geological Survey, serving until 1890, when he became assistant in the United States Coast and Geodetic Survey. In 1893 he was called to Columbia as professor of mechanics and subsequently became professor of mathematical physics as well. He was dean of the faculty of pure science at Columbia from 1895 to 1905, when he became president of the Carnegie Institution of Washington, whose reputation and usefulness as a means of furthering scientific research was widely extended under his direction. He was elected to the National Academy of Sciences in 1896. In 1898-1900 he was president of the American Mathematical Society, and in 1900 president of the American Association for the Advancement of Science. In 1915 he was appointed to the Naval Consulting Board. He died in 1924 in Washington, D.C.
Professor Woodward carried on researches and published papers in many departments of astronomy, geodesy, and mechanics. In the course of his work with the United States Coast and Geodetic Survey he devised and constructed the "iced bar and long tape base apparatus," which enables a base line to be measured with greater accuracy and with less expense than by methods previously employed. His work on the composition and structure of the earth and the variation of latitude found expression in a number of valuable papers. *Wik (Calendar Dates of birth and death less than one month apart)

1861 Herbert Ellsworth Slaught born.(21 July 1861 in Seneca Lake, Watkins, New York, USA - 21 May 1937 in Chicago, Illinois, USA)*VFR During 1902-3 Slaught travelled in Europe attending lectures by the leading mathematicians. Perhaps he felt that he could never achieve the depth of research he was exposed to at this time for, after a worrying time of indecision, he decided that he was not cut out for a research career but could give most to the world of mathematics by concentrating on teaching.
After seeking Dickson's advice on the best way to serve the mathematical community, he accepted Dickson's suggesting of becoming co-editor of the American Mathematical Monthly. He also became active in the organisation of the Mathematical Association of America, the National Council of Teachers of Mathematics, and the Chicago section of the American Mathematical Society. He served as secretary of the last named Society from 1906 to 1916.
Bliss describes Slaught as:-... one of the men most widely known by teachers and students of mathematics... His lifelong devotion to... the promotion of the study of mathematics, his skill as a teacher, his effective leadership in the mathematical organizations which he sponsored, and his influence with teachers of mathematics the country over, were remarkable. *Wik

1880 Milan (Rastislav) Stefánik (July 21, 1880 – May 4, 1919) Slovakian astronomer and general who, with Tomás Masaryk and Edvard Benes, from abroad, helped found the new nation of Czechoslovakia by winning much-needed support from the Allied powers for its creation as a post-WWI republic, (1918-19). Before the war, the famous observatory in Meudon near Paris sent a scientific expedition to the 4810m high Mont Blanc. He joined the expedition, which was paid for by the French government to go to the roof of Europe.*TIS

1926 John Leech (July 21, 1926 in Weybridge, Surrey – 28 September 1992 in Scotland) is best known for the Leech lattice which is important in the theory of finite simple groups.*SAU  He also discovered Ta(3) in 1957. (In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways. The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, and was made famous in the early 20th century by a story involving Srinivasa Ramanujan.
\begin{matrix}\operatorname{Ta}(3)&=&87539319&=&167^3 &+& 436^3 \\&&&=&228^3 &+& 423^3 \\&&&=&255^3 &+& 414^3\end{matrix}

1725  Johann Philipp von Wurzelbau (28 September 1651 in Nürnberg; 21 July 1725 Nürnberg )was a German astronomer.
A native of Nuremberg, Wurzelbauer was a merchant who became an astronomer. As a youth, he was keenly interested in mathematics and astronomy but had been forced to earn his living as a merchant. He married twice: his first marriage was to Maria Magdalena Petz (1656–1713), his second to Sabina Dorothea Kress (1658–1733). Petz bore him six children.
He first published a work concerning his observations on the great comet of 1680, and initially began his work at a private castle-observatory on Spitzenberg 4 owned by Georg Christoph Eimmart (completely destroyed during World War II), the director of Nuremberg's painters' academy. Wurzelbauer was 64 when he began this second career, but proved himself to be an able assistant to Eimmart. A large quadrant from his days at Eimmart's observatory still survives.
After 1682, Wurzelbauer owned his own astronomical observatory and instruments, and observed the transit of Mercury, solar eclipses, and worked out the geographical latitude of his native city. After 1683, he had withdrawn himself completely from business life to dedicate himself to astronomy.
By 1700, Wurzelbauer had become the most well-known astronomer in Nuremberg. For his services to the field of astronomy, he was ennobled in 1692 by Leopold I, Holy Roman Emperor and added the von to his name. He was a member of the French and the Prussian academies of the sciences.
The crater Wurzelbauer on the Moon is named after him. *Wik

1873 Delfino Codazzi (March 7, 1824 – July 21, 1873) was an Italian mathematician who worked in differential geometry.*SAU He made some important contributions to the differential geometry of surfaces, such as the Gauss–Codazzi–Mainardi equations. *Wik

1925 Giovanni Frattini (January 8, 1852 Rome – July 21, 1925, Rome) was an Italian mathematician, noted for his contributions to group theory.  In 1885 he published a paper where he defined a certain subgroup of a finite group. This subgroup, now known as the Frattini subgroup, is the subgroup Φ(G) generated by all the non-generators of the group G. He showed that Φ(G) is nilpotent and, in so doing, developed a method of proof known today as Frattini's argument.*TIS
He entered the University of Rome in 1869, where he studied mathematics with Giuseppe Battaglini, Eugenio Beltrami, and Luigi Cremona, obtaining his PhD. in 1875.*Wik

1926 Washington Roebling U.S. civil engineer under whose direction the Brooklyn Bridge, New York City, was completed in 1883. The bridge was designed by Roebling with his father, John Augustus Roebling, from whom he had gained experience building wire-rope suspension bridges. Upon his father's death, he superintended the building of the Brooklyn Bridge (1869-83). He was disabled by decompression sickness after entering a caisson in 1872. He was brought out nearly insensible and his life was saved with difficulty. Because of resulting poor health, he directed operations from his home in Brooklyn overlooking the site. Though he continued to head the family's wire-rope manufacturing business for several years, medical problems forced retirement (1888).

1937 Edwin Bailey Elliott (1 June 1851, Oxford, England - 21 July 1937 in Oxford, England)After outstanding achievements at university, Elliott became a Fellow and Mathematical Tutor of Queen's College, Oxford, in 1874.
In addition to his Fellowship at Queen's College, Elliott was appointed a lecturer in mathematics at Corpus Christi College in Oxford in 1884. These appointments came to an end in 1892 when Elliott became the first Waynflete professor of Pure Mathematics. This chair was named after William of Waynflete, the English lord chancellor and bishop of Winchester who founded Magdalen College in the 15th century. The Waynflete chair came with a Fellowship at Magdalen College so Elliott was again attached to his old College. One year after being appointed to the Waynflete Chair of Pure Mathematics, Elliot married Charlotte Amelia Mawer.
Elliott held the Waynflete chair for 29 years until his retirement in 1921. During this time he was much involved with the London Mathematical Society, being President of the Society from 1896 to 1898. A few years before this, in 1891, he had been honoured by being elected a Fellow of the Royal Society. As Chaundy writes-
Elliott's mathematical life circulated round the twin foci of Oxford and London. Besides his work in formal teaching and lecturing at Oxford, he was one of the founders (1888) of the Oxford Mathematical Society, its first secretary, and later its president.
His mathematical work included algebra, algebraic geometry, synthetic geometry, elliptic functions and the theory of convergence. However his most important contribution was the book An introduction to the algebra of quantics which was first published in 1895. This work was a major contribution to invariant theory. *SAU

1966 Francesco Cantelli (20 December 1875, Palermo – 21 July 1966, Rome) was an Italian mathematician who made contributions to the theory of probability.*SAU  He was the founder of the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics.
His early papers were on problems in astronomy and celestial mechanics.
The later work was all on probability and it is in this field where his name graces the Borel–Cantelli lemma and the Glivenko–Cantelli theorem.  *Wik

1966 Philipp Frank (March 20, 1884, Vienna, Austria - July 21, 1966, Cambridge, Massachusetts, USA) was a physicist, mathematician and also an influential philosopher during the first half of the 20th century. He was a logical-positivist, and a member of the Vienna Circle.He was born on 20 March 1884 in Vienna, Austria, and died on 21 July 1966 in Cambridge, Massachusetts, USA. He studied physics at the University of Vienna and graduated in 1907 with a thesis in theoretical physics under the supervision of Ludwig Boltzmann. Albert Einstein recommended him as his successor for a professorship at the German Charles-Ferdinand University of Prague, a position which he held from 1912 until 1938. He then emigrated to the United States, where he became a lecturer of physics and mathematics at Harvard University.
Astronomer Halton Arp described Frank's Philosophy of Science class at Harvard as being his favorite elective.
He was a colleague and admirer of both Mach and Einstein. In lectures given during World War II at Harvard, Frank attributed to Mach himself the following graphic expression of "Mach's Principle":"When the subway jerks, it's the fixed stars that throw you down."
In commenting on this formulation of the principle, Frank pointed out that Mach chose the subway for his example because it shows that inertial effects are not shielded (by the mass of the earth): The action of distant masses on the subway-rider's mass is direct and instantaneous. It is apparent why Mach's Principle, stated in this fashion, does not fit with Einstein's conception of the retardation of all distant action.*Wik

1971 Yrjo Vaisala (6 September 1891 – 21 July 1971) Finnish meteorologist and astronomer regarded as the "father of space research in Finland," As early as 1946, he had suggested that geodetic triangulation at that time being done with rockets or balloons with onboard flashes could better be accomplished by artificial satellites. By the next year he was talking about artificial satellites being used for solar system exploration. In the 1950's he founded Tuorla Observatory and went on to build a tunnel under the hill at Tuorla Observatory to enable making interference measurements to accurately define the length standard for geodesy. He was outstanding in his ability to produce excellent optics for telescopes. Vaisala, together with Liisa Oterman at Tuorla, outpaced the rest of the world in their discovery of minor planets*TIS

1993 Edwin James George Pitman was born in Melbourne on 29 October 1897 and died at Kingston near Hobart on 21 July 1993.
In 1920 he completed the degree course and graduated B.A. (1921), B.Sc. (1922) and M.A. (1923). In the meantime he was appointed Acting Professor of Mathematics at Canterbury College, University of New Zealand (1922-23). He returned to Australia when appointed Tutor in Mathematics and Physics at Trinity and Ormond Colleges and Part-time Lecturer in Physics at the University of Melbourne (1924-25). In 1926 Pitman was appointed Professor of Mathematics at the University of Tasmania, a position he held until his retirement in 1962.
Pitman described himself as 'a mathematician who strayed into Statistics'; nevertheless, his contributions to statistical and probability theory were substantial.
Pitman was active in the formation of the Australian Mathematical Society in 1956. He also took an active part in the Summer Research Institutes organized by the Mathematical Society, and used them as a sounding board for his research on statistical inference.
He was a renowned member of the Statistical Society of Australia, attending its biennial conferences. In 1978 the Statistical society established the Pitman Medal.
Pitman presented the first systematic account of non-parametric inference and lectured extensively on the subject, both in Australia and in the United States. The kernel of the subject, as described by him, is 'Suppose that the sum of two samples A, B is the sample C. Then A, B are discordant if A is an unlikely sample from C.' Again, he writes, 'The approach to the subject, starting from the sample and working towards the population instead of the reverse, may be a bit of a novelty'; and later, 'the essential point of the method is that we do not have to worry about the populations which we do not know, but only about the sample values which we do know'.
The notes of the 'Lectures on Non-parametric Inference' given in the United States, though never published, have been widely circulated and have had a major impact on the development of the subject. Among the new concepts introduced in these Lectures are asymptotic power, efficacy, and asymptotic relative efficiency.
A major contribution to probability theory is his elegant treatment of the behavior of the characteristic function in the neighborhood of the origin, in three papers. This governs such properties as the existence of moments. There are also interesting properties of the Cauchy distribution, and of subexponential distributions.
On his death, on 21 July 1993, Edwin was buried at the Hobart Regional Cemetery in Kingston. He lives on in the memory of many of us who are grateful for his life and legacy.
*Evan J. Williams, Australian Academy of Science

1998 Alan (Bartlett) Shepard, Jr. (November 18, 1923 – July 21, 1998) was America's first man in space and one of only 12 humans who walked on the Moon. Named as one of the nation's original seven Mercury astronauts in 1959, Shepard became the first American into space on 5 May 1961, riding a Redstone rocket on a 15-minute suborbital flight that took him and his Freedom 7 Mercury capsule 115 miles in altitude and 302 miles downrange from Cape Canaveral, FL. (His flight came three weeks after the launch of Soviet cosmonaut Yuri Gagarin, who on 12 Apr 1961, became the first human space traveler on a one-orbit flight lasting 108 minutes.) Although the flight of Freedom 7 was brief, it was a major step for the U.S. in a race with the USSR.*TIS

2011 Franz Leopold Alt (November 30, 1910 – July 21, 2011) was an Austrian-born American mathematician who made major contributions to computer science in its early days. He was best known as one of the founders of the Association for Computing Machinery, and served as its president from 1950 to 1952. *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