Thursday, 23 July 2026

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 eighth tetrahedral number, the sum of the squares from 1 to 8. Answers the question, how many squares are there on an 8x8 checkerboard.

204 = 20^2 - 14^2=52^2 - 50^2

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.

204 is a refactorable number, it is divisible by the count of its divisors, 12

It is because it is divisible by 12 that 204 is expressible as (n+3)^2 - (n-3)^2 for n= 17 (204/12=17)

204^2 = 41616, a number that is both a square and a triangular number, the 288th triangular number. They are pretty rare as it is only the fourth. And like 204, it is the sum of twin primes also, 41616 = 20807 + 20809. Only 12 and 84 also are the sum of twin primes with a square that is also the sum of twin primes.
since I've written twin primes so many times in this entry, its probably a good time to remind you that, although the idea of primes separated by only a single composite number was known back to antiquity, the term was created around the end of the 19th century by German Mathematician Paul Stackel (in the German, of course, "Primezahlzwilling")

On an infinite chess board, a Knight can reach 204 different squares in eight moves.

200 is CC in Roman numerals, and 204 is CC in hexadecimal.

For More Math Facts for Every Year Date





EVENTS


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

 It was the first typewriting machine to be patented in the United States, although Pellegrino Turri had made one in Italy in 1808.Perhaps because of its slow speed, or because there was not yet a wide market for typewriters, it was not a commercial success

The working model that Burt constructed for his 1829 patent was destroyed in the 1836 Patent Office fire

*Wik


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

To Whichever or both, Well done.  (That is an attempt at humor, the two names are both used for the same event.)

Although Menches is often named as the first to serve his ice cream in a rolled waffle cone, its true originator is far from clear. The edible cone was widely sold at the fair, and various other people there are also claimed as the innovator. *Tis



1923  On this day in 1923, Werner Werner Heisenberg went before his ptofessors to defend his PhD thesis, and dearly failed.


Heisenberg’s oral examiners included:

Arnold Sommerfeld (advisor, theoretical physics)
Wilhelm Wien (experimental physics, Nobel laureate)
Ferdinand von Lindemann (mathematics — famous for proving π is transcendental)

When Wien asked him basic experimental physics questions — for instance, about the workings of a simple lens or how a storage battery functions — Heisenberg failed to answer properly.
Heisenberg, brilliant at abstract theory but inexperienced in practical lab work, didn’t know basic lab instruments!  Reportedly, Wien was so shocked that he wanted to fail Heisenberg outright.
Arnold Sommerfeld, recognizing Heisenberg’s exceptional theoretical talent, intervened on his behalf.

Sommerfeld is said to have told the examiners:
“Gentlemen, Heisenberg is a theoretical physicist. If he understood experimental physics well, he would not be a theoretical physicist!”  Ultimately, Heisenberg passed — but barely:

His final grade was “ausreichend”, meaning “sufficient” or just a pass.

Despite his shaky defense, Heisenberg went on to revolutionize physics: In 1925, only two years later, he published his groundbreaking paper laying the foundations of quantum mechanics.

In 1932, he received the Nobel Prize in Physics for the creation of quantum mechanics. *PBnotes



1927 The English 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
The term was derived from Hilbert’s use of “Eigenwert” in 1904, although Helmholtz had earlier used “Eigentöne” for what he called proper tones in acoustics. proper was also used by many English and American scientists throughout the 1920-1950 period. Even J. Von Neumann’s translations into English used the term “proper“.
Paul Halmos followed von Neumann’s English writings and used “proper value” in his widely-used Finite Dimensional Vector Spaces (1958). However Halmos admitted defeat in his A Hilbert Space Problem Book (1967, p. x):

“For many years I have battled for proper values, and against the one and a half times translated German-English hybrid that is often used to refer to them. I have now become convinced that the war is over, and eigenvalues have won it; in this book I use them.”

 



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. A routine fly ball hit by Phillies second baseman Tony Taylor made telecommunications history.I have a different date and perspective from a BBC History page.  "On 11 July 1962 British television viewers saw pictures beamed live from the US via the Telstar satellite. Raymond Baxter and Richard Dimbleby were on hand to provide commentary, although the precise time of the broadcast was not known in advance. The first pictures, received in Britain just after 1am, were of the chairman of AT&T, Frederick Kappel, and of poor quality, while in France they were picked up clearly. However this landmark transmission marked the beginning of satellite broadcasting, and changed the face of telecommunications."

Telstar 1 was the first satellite capable of relaying television signals from Europe to North America. The 171-pound, 34.5-inch sphere loaded with transistors and covered with solar panels was placed in orbit by a Delta rocket launched from Cape Canaveral on July 10, 1962.

The maiden program included more images from around America, such as the Mormon Tabernacle Choir singing at Mount Rushmore and President John F. Kennedy conducting a press conference. 




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. *blog.yovisto.com



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.

The image is by my former student Dan Durda, of Sterling, Michigan; who may have acquired some math knowledge from me, but not his artistic sense.


2026  If the leaks are right, the Field's Medal will have it's third female winner.  

The list of 2026 Fields Medal winners has been inadvertently leaked, revealing that Peking University alumni Hong Wang and Yu Deng are among the recipients. This marks a historic moment as it is the first time two Chinese mathematicians will receive the prestigious award in the same edition. The leak occurred when four Fields Medal laureate lecture fields, marked "HIDDEN," were discovered in the front-end code of the ICM 2026 official schedule. A curl command generated by Codex revealed the names Yu Deng, John Pardon, Jacob Tsimerman, and Hong Wang. If confirmed on July 23, this will be a significant milestone for Chinese mathematics. Notably, Hong Wang will become the third female mathematician in history to receive the Fields Medal, further highlighting the groundbreaking nature of this achievement.





2026  Congratulations to Team USA! (And to all the competitors from every nation)

At the 67th International Mathematical Olympiad, held in Shanghai from July 10 to July 20, the six-student team organized by the MAA placed 2nd overall among 117 participating teams, the largest field in IMO history.

Team USA qualifies through the MAA American Mathematics Competitions, in which roughly 300,000 students from over 6,000 schools and learning centers participate each year. Top performers are invited to the MAA Mathematical Olympiad Summer Program for intensive training. *MAA






BIRTHS


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 Tilak  (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



1914 William Wager Cooper (July 23, 1914 – June 20, 2012) was an American operations researcher, known as a father of management science and as "Mr. Linear Programming". He was the founding president of The Institute of Management Sciences, founding editor-in-chief of Auditing: A Journal of Practice and Theory, a founding faculty member of the Graduate School of Industrial Administration at the Carnegie Institute of Technology (now the Tepper School of Business at Carnegie Mellon University), founding dean of the School of Urban and Public Affairs (now the Heinz College) at CMU, the former Arthur Lowes Dickinson Professor of Accounting at Harvard University, and the Foster Parker Professor Emeritus of Management, Finance and Accounting at the University of Texas at Austin.

 Cooper was born in Birmingham, Alabama and grew up in Chicago, where his father (a former bookkeeper) owned several gasoline stations that closed in the Great Depression. Cooper, in his second year of high school, dropped out to help support his family. He worked in a bowling alley, on a golf course, and as a professional boxer. As a boxer, he won 58 bouts, lost three, and drew two. While commuting to the golf course, he met Eric Kohler, a professor at Northwestern University, who pushed him to go back to school and bankrolled his entry to the University of Chicago. At Chicago, he began studying physical chemistry but was inspired by his work for Kohler on a legal case to switch to economics, graduating with a B.A. and Phi Beta Kappa honors in 1938.

After graduation, from 1938 to 1940, he worked as an accountant for the Tennessee Valley Authority, where Kohler had become Controller. There, he worked on performance auditing and the mathematical allocation of resources, and helped Kohler testify to a congressional investigative committee. In 1940, Cooper started doing graduate studies at Columbia University; however, in 1942, with his coursework completed but his thesis unwritten, he left Columbia to serve his country during World War II. He worked in the Division of Statistical Standards of the U.S. Bureau of the Budget coordinating the government programs that collected accounting statistics; his 1945 paper describing his wartime activities was the first recipient of an award from the American Institute of Accountants for the best paper of the year.

Cooper began his academic career with a brief teaching stint, from 1944 to 1946, back at the University of Chicago. In 1945, Cooper married his wife Ruth, a lawyer and human activist, and in 1946 he joined the newly formed Graduate School of Industrial Administration at the Carnegie Institute of Technology (now the Tepper School of Business at Carnegie Mellon University). There, he formed important research collaborations with Abraham Charnes, George Leland Bach, and Herbert A. Simon, and eventually became University Professor. While at CMU, from 1949 to 1950, he also worked again as an assistant to Eric Kohler, who had by this time become Comptroller of the Marshall Plan.In 1969 he left GSIA but stayed at CMU, becoming dean of the new School of Urban and Public Affairs (now the Heinz College) there. As dean, he realized that there would soon be a much greater role in American business management for African-Americans, and worked to increase African-American representation within the school.

In 1975, Harvard University hired Cooper away from CMU to become the Dickinson Professor of Accounting, and in 1980 he moved again, to the University of Texas at Austin, where he became the Foster Parker Professor of Management, Finance and Accounting. He retired in 1993, but continued to be active in research until his death on June 20, 2012.




1920 Herbert Federer (July 23, 1920 – April 21, 2010) was an American mathematician. He is one of the creators of geometric measure theory, at the meeting point of differential geometry and mathematical analysis.

Federer was born July 23, 1920, in Vienna, Austria. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley, earning the Ph.D. as a student of Anthony Morse in 1944. He then spent virtually his entire career as a member of the Brown University Mathematics Department, where he eventually retired with the title of Professor Emeritus.

Federer wrote more than thirty research papers in addition to his book Geometric measure theory. The Mathematics Genealogy Project assigns him nine Ph.D. students and well over a hundred subsequent descendants. His most productive students include the late Frederick J. Almgren, Jr. (1933–1997), a professor at Princeton for 35 years, and his last student, Robert Hardt, now at Rice University.

Federer was a member of the National Academy of Sciences. In 1987, he and his Brown colleague Wendell Fleming won the American Mathematical Society's Steele Prize "for their pioneering work in Normal and Integral currents."

In the 1940s and 1950s, Federer made many contributions at the technical interface of geometry and measure theory. Particular themes included surface area, rectifiability of sets, and the extent to which one could substitute rectifiability for smoothness in the classical analysis of surfaces. A particularly noteworthy early accomplishment (improving earlier work of Abram Besicovitch) was the characterization of purely unrectifiable sets as those which "vanish" under almost all projections. Federer also made noteworthy contributions to the study of Green's theorem in low regularity. The theory of capacity with modified exponents was developed by Federer and William Ziemer.[FZ73] In his first published paper, written with his Ph.D. advisor Anthony Morse, Federer proved the Federer–Morse theorem which states that any continuous surjection between compact metric spaces can be restricted to a Borel subset so as to become an injection, without changing the image.*Wik



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 – December 25, 2016) was an American astronomer who pioneered work on galaxy rotation rates. She uncovered the discrepancy between the predicted and observed angular motion of galaxies by studying galactic rotation curves. By identifying the galaxy rotation problem, her work provided evidence for the existence of dark matter. These results were later confirmed over subsequent decades. *Wik

Throughout her schooling, Rubin faced the banal sexism all too common at the time for women interested in science. Her high school physics teacher ignored the few girls in class; a college admissions interviewer encouraged her to consider painting astronomical objects rather than studying them. Rubin was not deterred. “She took it all with courage, and with persistence,” says Bahcall, who was a longtime friend and colleague of Rubin.

Rubin studied astronomy at Vassar College, married mathematical physicist Bob Rubin, and began graduate school at Cornell in 1948. She completed her master’s thesis on the rotation of the universe, kicking off a long career investigating hidden galactic behavior, and a professor suggested Rubin present this research at a meeting of the American Astronomical Society (AAS) in 1950. There, she encountered a chilly reception. “I gave my memorized 10-minute talk, acceptably I thought. Then one by one many angry sounding men got up to tell me why I could not do ‘that,’” she wrote.
In 2019, almost 70 years after Rubin faced that hostile crowd at the 1950 AAS meeting, (and almost three years after her Death) the Society convened in Honolulu to agree on renaming the Large Synoptic Survey Telescope as the Vera C. Rubin Observatory. After its construction is complete, the Rubin Observatory will be the site of a 10-year survey of a mammoth swath of night sky. Bahcall sees this honor as the perfect tribute to Rubin, who cherished the many long nights she spent in observatories, peering through telescopes. “She loved being in the dome.” *APS Org





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) 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




1941  Pierre Agostini (born 23 July 1941, ) is a French experimental physicist and Emeritus professor at the Ohio State University in the United States, known for his pioneering work in strong-field laser physics and attosecond science.He is especially known for the observation of above-threshold ionization and the invention of the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) technique for characterization of attosecond light pulses. He was jointly awarded the 2023 Nobel Prize in Physics with Ferenc Krausz and Anne L’Huillier. 



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







DEATHS

1876  Joseph Rogers Brown (born Jan. 26, 1810, Warren, R.I., U.S.—died July 23, 1876, Isles of Shoals, N.H.) was an American inventor and manufacturer who made numerous advances in the field of fine measurement and machine-tool production. He perfected and produced a highly accurate linear dividing engine in 1850, and in the succeeding two years he developed a vernier caliper reading to thousandths of an inch and also applied vernier methods to the protractor. Brown's micrometer caliper, widely used in industry, appeared in 1867. He also invented a precision gear cutter in 1855 to produce clock gears, a universal milling machine in 1862, and, perhaps his finest innovation, a universal grinding machine (patented in 1877), in which articles were hardened first and then ground, thereby increasing accuracy and eliminating waste. Cofounded J.R. Brown & Sharpe in 1853. *TiS

During the 19th and 20th centuries, Brown & Sharpe was one of the best-known and most influential machine tool builders and was a leading manufacturer of instruments for machinists (such as micrometers and indicators). Its reputation and influence were such that its name is often considered to be inseparably paired with certain industrial standards that it helped establish, including:


The American wire gauge (AWG) standards for wire;

The Brown & Sharpe taper in machine tool spindle tapers; and

The Brown & Sharpe worm threadform for worm gears.

Many years ago as a young Gauge Lab Tech I had a drawer full of these beauties in various sizes.  



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 .*Math.info 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

Santos-Dumont circling the Eiffel Tower with the airship No. 5, 13 July 1901



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  (24 September 1894 – 23 July 1964) died. *VFR He wrote on Fourier Series with G.H. Hardy.  Rogosinski focused his studies on pure mathematics, physics and philosophy. His interest was analytical problems, especially in series. His dissertation, "New Application of Pfeiffer's method for Dirichlet's divisor problem", caused a stir in 1922.   

He published five papers with Hardy from 1943 to 1949, under the title Notes on Fourier series. In 1944 Rogisinski and Hardy published their book Fourier Series, which might be said to be a rewrite, using Lebesgue integral methods, of Rogosinski's 1930 book. He was a teacher in Aberdeen in 1941. In 1945, he became a lecturer at Newcastle University (prior to 1963, King's College, University of Durham). In 1947 he was appointed professor and in 1948 Head of Department.*Wik




1981 Harvey Fletcher (11 Sep 1884; 23 Jul 1981) American acoustical engineer who was the first to demonstrate stereophonic sound (1934). He was a trail blazing investigator of the nature of speech and hearing, noted for his contributions in acoustics, electrical engineering, speech, medicine, music, atomic physics, sound pictures, and education. He guided the development of the Western Electric Hearing Aid, the first such device to use vacuum tubes. He developed a group survey method using recorded sound of decreasing volume which has wide acceptance in schools throughout the nation.*TIS



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



2006  Charles Frederick Mosteller (December 24, 1916 – July 23, 2006) was an American mathematician, considered one of the most eminent statisticians of the 20th century. He was the founding chairman of Harvard's statistics department from 1957 to 1971, and served as the president of several professional bodies including the Psychometric Society, the American Statistical Association, the Institute of Mathematical Statistics, the American Association for the Advancement of Science, and the International Statistical Institute.
Mosteller worked in Samuel Wilks's Statistical Research Group in New York city during World War II on statistical questions about airborne bombing. He received his PhD in mathematics from Princeton University in 1946.

He was hired by Harvard University's Department of Social Relations in 1946, where he received tenure in 1951 and served as acting chair from 1953 to 1954. He founded the Department of Statistics and served as its first chairman from 1957 to 1969, 1973, 1975 to 1977. He chaired the Department of Biostatistics at the Harvard School of Public Health from 1977 to 1981 and later the Department of Health Policy and Management in the 1980s. His four chairmanships have not been matched. He also taught courses at Harvard Law School and Harvard's Kennedy School of Government.

He worked with his mathematical assistant Cleo Youtz from the 1950s until his departure from Harvard in 2003, and had an administrative assistant. He was well known for being a good writer, insisting on doing up to fifteen drafts of a paper or book chapter before showing it to his colleagues and several additional drafts before submitting the paper to a journal.

Mosteller was an elected member of the American Academy of Arts and Sciences (1954), the American Philosophical Society (1961), and the United States National Academy of Sciences (1974)] He retired from classroom teaching in 1987, but continued working and publishing at Harvard through 2003. On January 3, 2004, he moved to Arlington, Virginia, to be closer to his children. *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





2021 Steven Weinberg (May 3, 1933 – July 23, 2021) American nuclear physicist who shared the 1979 Nobel Prize for Physics (with Sheldon Lee Glashow and Abdus Salam) for work in formulating the electroweak theory, which explains the unity of electromagnetism with the weak nuclear force. *TIS





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









Wednesday, 22 July 2026

Kurschak's Theorem, a Geometry Jewel.

 


József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry, but he may be more well known today, by the very few who seem to know of him, for a geometric gem that involves no Trig.  The basic idea is to prove , without trig, that the area of a regular dodecagon inscribed in a circle with unit radius is exactly three.  [a footnote about unusual things to share with students; if you inscribe a regular polygon in a unit circle, there are only two of them that will have a rational area.  I just gave away one of them, the other should not be too difficult to discern.]

The classical approach for any regular polygon is the one used by MathWorld.  

The area of the dodecagon (n=12) inscribed in a unit circle with R=1 is

 \(A=\frac{n}{2} R^2 sin(\frac{2\pi}{n})=3. \)

[Teachers may discuss among themselves the appropriate deduction for a correct result that insults the entire idea of the theorem...?]

So how did he do it?  Well the essence of the pretty image at the top may mask some of the deep ideas so let's part the haze a little.  This diagram shows all the elements of the solution.  


Equlateral triangles are constructed on the sides of a square inwardly. Their apexes form a square. Prove that the midpoints of the sides of the latter and the intersections of the side lines of the triangles form a dodecagon.

The inner square is the Kurschak Tile, and the source of a second name for the image.You can observe in the image that dodecagon is tiled by 24 isosceles 15°-15°-150° triangles and 12 regular triangles. Two isosceles triangles sharing the base combine into a rhombus with the side equal to that of regular triangles.



The area of the square outside the dodecagon is composed of 8 isosceles triangles identical to the ones forming the Rhombl in the interior of the dodecagon, and an additional 8 regular triangles congruent to the ones inside.  

And now we apply two easy images fromKürschak's Tile, G. L. Alexanderson, Kenneth Seydel; The Mathematical Gazette, Vol. 62, No. 421 (Oct., 1978), pp. 192-196 

We first realize that if the circle has a radius of one, thevequilateral triangles that formed the original construction, and the tile they formed, have edges of 2 units, Thus the whole tile has an area of four, made up of four unit squares.

In one of those unit squares there are nine triangles that are inside that square so we mark them to remove.  

 

Now we look at the parts of the dodecagon in the other three squares and note that there are some blank spaces outside the dodecagon.  And in an instant you recognize that all nine of the squares from the interior of the dodecagon will nicely fill each of the missing parts outside the dodecagon in these three squares, filling a space of three square units.  

And as the cool kids say, QED



Added notes and images from *Cut -the-knot.org , *  Wolfram MathWorld.  and 



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.

Partitions, which are ways to divide the set into disjoint, non-empty subsets. These partitions can range from all elements in their own individual subset (e.g., {1},{2},{3},{4},{5},{6}) to a single subset containing all elements (e.g., {1,2,3,4,5,6}). 

The partitions of six are {6}, {5,1), {4,2}, {4,1,1}, {3,3}, (3,2,1}, {3,1,1,1), {2,2,2}, {2,2,1,1}, {2,1,1,1,1}, {1,1,1,1,1,1} 

They are often shown as Ferrer diagrams.  A nice exercise with these diagrams is to pair each partition with its conjugate (obtained by reflecting the diagram across the main diagonal):

The diagram of {4,2}   

● ● ● ● 

● ●

will pivot into {2,2,1,1}

● ●

● ●



203 is a palindrome in base 3  (21112),   base 6 (535), and base 8(313),

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,...,12


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






For More Math Facts for Every Year Date




EVENTS


1588 Joost Burgi sent emperor Rudolph II his direct method using only simple arithmetic to produce a complete table of sines from zero to 90 degrees. I have to admit I could not imagine this working.  I was shocked.  I still can't explain WHY it works, but it seems to produce ever improving approximations, 



1680  Ehrenfried Walter von Tschirnhaus was elected to the Paris Académie des Sciences.  Ehrenfried Walter von Tschirnhaus (1651 - 1708) was a German mathematician who worked on the solution of equations and the study of curves. He is best known for the transformation which removes the term of degree n-1 from an equation of degree n. *SAU.



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.
Critics of L'hospital are many, but they likely never learned that:
L’Hospital’s book is the first published textbook on differential calculus. It provided a clear, organized, and systematic presentation of ideas that had, until then, been scattered across letters and private manuscripts by Leibniz, Johann Bernoulli, and others.
The book was praised for its clarity of exposition. L’Hospital had a talent for taking complex ideas—many of them from Johann Bernoulli—and presenting them in a digestible way for learners, often using geometric intuition alongside algebraic manipulation.
Although he largely followed Leibnizian notation, L’Hospital helped standardize it through his influential book. This consistency contributed to the spread of calculus across Europe.




1799  On March 28, 1794, the president of the French commission that developed the metric system, Joseph Louis Lagrange, proposed using the day (French jour) as the base unit of time, with divisions déci-jour and centi-jour. 
In 1795, the French National Convention passed a law introducing the metric system, putting Legendre in charge of the transition to the new system. The final system, as introduced in 1795, included units for length, area, dry volume, liquid capacity, weight or mass, and currency, but not time. Decimal time of day had been introduced in France two years earlier, but was set aside at the same time the metric system was inaugurated, and did not follow the metric pattern of a base unit and prefixed units. 
On 22nd July 1799 the definitive standards of the metric system, the platinum metre and the platinum kilogramme, were ceremonially deposited in the French National Archives, and on 10th December 1799 a law was passed confirming their status as the only legal standards for measuring length and mass in France.

 (The combination metric and decimal clock is at the Fitzwilliam Museum in Cambridge, U.K. The metric is on the outside scale, the duodecimal is on the small  enamel dial inset above the center



1900   It seems that the first to discuss the problem of constructing magic squares with prime numbers was Henry Ernest Dudeney. It was in The Weekly Dispatch, 22nd July and 5th August 1900. At that time, "1" was considered as a prime number. The magic sum 111 of his 3x3 square is the lowest possible, allowing '1'." (image below)*Multimagie.com   "Henri Lebesgue (1875-1941) is said to be the last professional mathematician to call 1 prime." *Prime Curios... but then "Carl Sagan included the number 1 in an example of prime numbers in his book Cosmos." 

After I posted this on LinkedIn, Windy Appleby sent a note that, "Carl Saga was a great populariser but not noted as a mathematician. I like the story that he was giving a talk and said that he had some researchers trying to find the name of the wife of Asaph Hall, discoverer of the satellites of Mars, so he could propose that the crater on Phobos could be named after her. Someone immediately stood up and gave him her name, Agnes Stickney. The gobsmacked Sagan realized that the speaker was the noted historian of science Owen Gingerich."  
In searching for the date I found that Sagen wrote about this event in The Cosmic Connection, 1973.  He describes Prof. Gingrich as "my friend", but missed her name listing it as "Angelina Syickney", when her name was Chloe Angeline Stickney, and she was called Angeline.  I haven't found the exact date, but it is almost surely between March and October 1972.  *PB notes.  



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
In 1930, the record for flying around the world was not held by a fixed-wing aircraft, but by the Graf Zeppelin, piloted by Hugo Eckener in 1929 with a time of 21 days. On June 23, 1931, Post and the Australian navigator Harold Gatty left Roosevelt Field on Long Island, New York, in the Winnie Mae with a flight plan that would take them around the world, stopping at Harbour Grace, Flintshire, Hanover twice, Berlin, Moscow, Novosibirsk, Irkutsk, Blagoveshchensk, Khabarovsk, Nome (where his propeller had to be repaired), Fairbanks (where the propeller was replaced), Edmonton, and Cleveland before returning to Roosevelt Field. They arrived back on July 1, after traveling 15,474 miles (24,903 km) in the record time of 8 days and 15 hours and 51 minutes, in the first successful aerial circumnavigation by a single-engined monoplane. *Wik
Wiley Post with Harold Gatty in Germany, 1931

*Wikipedia



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.

A paper on a shorter proof by Tom Apostol is here




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.




1997 Apple 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

*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
The moon passes between the sun and the earth during a total solar eclipse in the northern Indian city of Varanasi July 22, 2009. 



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


BIRTHS

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
*Linda Hall Org




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) . He is best known for comprehensive book on infinite series.*VFR
Konrad was primarily educated in Berlin, with a brief sojourn at the University of Lausanne in 1901 for a single semester, before settling at the University of Berlin, where he remained for his doctoral studies. His doctoral thesis, entitled Grenzwerte von Reihen bei der Annäherung an die Konvergenzgrenze, was supervised by Schottky and Frobenius; he received his PhD in 1907.
During the First World War he was an officer and was wounded at the beginning of the war, which resulted in his discharge from the army; by the autumn of 1914 he was teaching at Berlin University. In the following year he was appointed as an extraordinary professor at the University of Königsberg, becoming an ordinary professor there in 1919. In 1926 he accepted a professorship at University of Tübingen as the chair of mathematics, and remained there until his retirement in 1950.





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

Baer studied mechanical engineering for a year at Leibniz University Hannover. He then went to study philosophy at Freiburg in 1921. While he was at Göttingen in 1922 he was influenced by Emmy Noether and Hellmuth Kneser. In 1924 he won a scholarship for specially gifted students. Baer wrote up his doctoral dissertation and it was published in Crelle's Journal in 1927.

Baer accepted a post at Halle in 1928. There, he published Ernst Steinitz's "Algebraische Theorie der Körper" with Helmut Hasse, first published in Crelle's Journal in 1910.

While Baer was with his wife in Austria, Adolf Hitler and the Nazis came into power. Both of Baer's parents were Jewish, and he was for this reason informed that his services at Halle were no longer required. Louis Mordell invited him to go to Manchester and Baer accepted.

Baer stayed at Princeton University and was a visiting scholar at the nearby Institute for Advanced Study from 1935 to 1937.[2] For a short while he lived in North Carolina. From 1938 to 1956 he worked at the University of Illinois at Urbana-Champaign. He returned to Germany in 1956.*Wik




1907 Edgar Raymond Lorch (July 22, 1907 – March 5, 1990) was a Swiss American mathematician. Described by The New York Times as "a leader in the development of modern mathematics theory", he was a professor of mathematics at Columbia University. He contributed to the fields of general topology, especially metrizable and Baire spaces, group theory of permutation groups and functional analysis, especially spectral theory, convexity in Hilbert spaces and normed rings.

Born in Switzerland, Lorch emigrated with his family to the United States in 1917 and became a citizen in 1932. He joined the faculty of Columbia University in 1935 and retired in 1976, although he continued to write and lecture as professor emeritus. For his reminiscences of Szeged, Lorch posthumously received in 1994 the Lester R. Ford Award, with Reuben Hersh as editor.*Wik 



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



1926 John Aitchison (22 July 1926 – 23 December 2016) was a Scottish statistician.

John Aitchison studied at the University of Edinburgh after being uncomfortable explaining to his headmaster that he didn’t plan to attend university. He graduated in 1947 with an MA in mathematics.

After two years wherein he did actuarial work, he also attended Trinity College, Cambridge. He had a scholarship to do so, and graduated in 1951 with a BA focused on statistics. The year after he graduated, he joined the Department of Applied Economics at Cambridge as a statistician. He continued his work at Cambridge until 1956, when he was offered the position of Lecturer of Statistics at the University of Glasgow. During his time at Glasgow, he wrote The Lognormal Distribution, With Special Reference to its Uses in Economics (1957) with J A C Brown (who he met at Cambridge).

However, he left Glasgow in 1962, when the University of Liverpool offered him the positions of Senior Lecturer and head of Mathematical Statistics. In 1964, he was promoted to Reader.

From 1966 to 1976 he was Titular Professor of Statistics and Mitchell Lecturer in Statistics at the University of Glasgow. He was made a Fellow of the Royal Society of Edinburgh in 1968. He began writing student level books, Solving Problems in Statistics (Volume 1 in 1968, Volume 2 in 1972)  and Choice Against Chance: An Introduction to Statistical Decision Theory (1970).

In 1976 he joined the University of Hong Kong as a Chaired Professor of Statistics. He resigned from the University of Glasgow the year after and founded the Hong Kong Statistical Society. He was the President of the Society during 1977 to 1979.

In 1986 he published the book The Statistical Analysis of Compositional Data, an important resource on the analysis of compositional data.

On his retirement from the University of Hong Kong in 1989, he joined the University of Virginia as Professor and Chairman of the Division of Statistics, which he retired from in 1994. After this, he returned to the University of Glasgow as an Honorary Senior Research Fellow in the Department of Statistics.



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:
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:
Theorem 
2. A torsion-free, finitely generated group, containing a free subgroup of finite index, is itself free.
Theorem 
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






DEATHS

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




1824 Robert Patterson (May 30, 1743 – July 22, 1824) was an Irish-American mathematician and director of the United States Mint from 1806 to 1824. He was a professor of mathematics at the University of Pennsylvania from 1779 to 1810, professor of natural history and mathematics and vice provost from 1810 to 1813. At the request of Thomas Jefferson, he advised Meriwether Lewis on the purchase and usage of navigational equipment for the Lewis and Clark Expedition.
He taught at schools in Hinkletown and Northampton, Pennsylvania. He moved to Philadelphia and opened a school to teach navigational mathematics to ship captains. One of his students was Andrew Ellicott who became a notable surveyor. He operated a country store in Bridgeton, New Jersey for two years.

In 1774, he became principal of Wilmington Academy in Wilmington, Delaware. Classes were suspended at the outbreak of the American Revolutionary War and he served in the war for about three years as a military instructor, an assistant surgeon, adjutant to the 1st Delaware Regiment under John Haslet,  and as a brigade major.

He worked as a professor of mathematics at the University of Pennsylvania from 1799 to 1810 as well as professor of natural history and mathematics and vice provost from 1810 to 1813. He was elected president of Philadelphia's Select Council in 1799.

He was elected a member of the American Philosophical Society in 1783, served as secretary in 1784, vice-president in 1799 and president from 1819 to 1823. He published The Newtonian System (1808) and edited various works on mathematics and physics.

In 1803, Thomas Jefferson wrote a letter to Patterson requesting that he meet with Meriwether Lewis and provide further instruction and advice on calculating latitude and longitude during the Lewis and Clark Expedition. Patterson was one of five American Philosophical Society members who were consulted by Lewis prior to the expedition. In anticipation of the visit from Lewis, Patterson began to calculate astronomical formulas for usage on the expedition for the calculation of longitude from lunar observations and for altitude and time.

Patterson advised Lewis on the navigational equipment to purchase for the expedition and trained him on their usage. Jefferson recommended that Lewis use a theodolite for the calculation of latitude and longitude, however Patterson recommended usage of a sextant instead since it would handle better under the rigors of field work. Patterson advised Lewis on the purchase of a chronometer necessary for calculation of latitude and longitude as well as other techniques in case the chronometer malfunctioned. The chronometer was purchased in Philadelphia for $250, the most expensive single item purchased for the expedition.

Patterson was interested in ciphers and regularly exchanged coded correspondence with Thomas Jefferson. One of Patterson's ciphers included in a December 19, 1801, dated letter to Jefferson was decoded in 2007 by Lawren Smithline. The cipher consists of 7 digit pairs and is decoded by decrypting 7 blocks at a time. The cipher was of the Declaration of Independence, of which Jefferson was the primary author. Patterson called it his "perfect cipher" and Jefferson considered adopting it for government use.

Jefferson appointed Patterson as director of the United States Mint in 1805 and he served in this role until his death. Patterson was one of the founders of the Franklin Institute in Philadelphia and served as the first chairman of their board of managers.

He died on July 22, 1824, and was initially interred in a churchyard in Philadelphia and reinterred in 1844 at Laurel Hill Cemetery along with his wife after her death.





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

“Suspension Bridge Grand March,” sheet music cover, commemorating the opening of the Ohio River suspension bridge, designed and built by John A. Roebling, Cincinnati, 1867, Library of Congress (loc.gov)

*Linda Hall Org




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



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