## Saturday 20 July 2024

### On This Day in Math - July 20

The greatest discoveries of science have always been
those that forced us to rethink our beliefs
about the universe and our place in it.

-Robert L. Park

The 201st day of the year; 201 is a Harshad number... A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997. (Can you find the string of three consecutive Harshad numbers smaller than 201?)

A 3x3 magic square with a magic constant for each row/column of 201 can be created by taking the basic n= 1-9 digits and replacing them with 13n+2

54  119  28

41   67  93

106 15  80

201 is also a lucky number, a number that survives from the sieve process created about 1955 by Stanislaw Ulam, the great Polish mathematician who coinvented the H-bomb and was the father of cellular automata theory. Students who are familiar with the way the Sieve of Erathosthenes produces the primes may wish to compare the lucky numbers produced by this sieve. "Start wtih the odd numbers.The first odd number >1 is 3, so strike out every third number from the list (crossing out the 5, 11,17 etc): 1, 3, 7, 9, 13, 15, 19, .... The first odd number greater than 3 in the list is 7, so strike out every seventh number: 1, 3, 7, 9, 13, 15, 21, 25, 31, .... The numbers that remain are the so called "lucky numbers". Look for similarities to the primes. *Martin Gardner, Mathworld

201 has a largest factor of 67, so a palindrome of 201 with only 6 and 7, 6 x 7 + 7 x 6 + 7 + 6 + 7 + 6 + 7 + 6 x 7 + 7 x 6 = 201

201 is the the difference of two squares, 201 = 101^2 - 100^2=35^2 - 32^2, and just to break the rules, it's also 22.6^2 - 17.6^2

And Wikipedia tells me that Star Trek had an episode with the title, 11001001, which is 201 in binary.
Notice the base four unit digits all appear 3,0,2,1

EVENTS

1632 Pierre de Carcavi became a member of the parliament of Toulouse. His friendship with Fermat dates from this time.*VFR  He was a secretary of the National Library of France under Louis XIV.

Carcavi is known for his correspondence with Pierre de Fermat, Blaise Pascal, Christiaan Huygens, Galileo Galilei, Marin Mersenne, Evangelista Torricelli and René Descartes.

Fermat sent many of his works to Carcavi after he moved to Paris in 1636. In 1650 he sent Carcavi a treatise entitled Novus secundarum et ulterioris radicum in analyticis usus Ⓣ. This work contained the first known method of elimination and Fermat wanted it published. Both Pascal and Carcavi were asked to find a publisher for the work, Fermat writing to Carcavi on 9 August 1654:-

"I was overjoyed to have had the same thoughts as those of M Pascal, for I greatly admire his genius and I believe him capable of solving any problem he attempts. The friendship he offers is so dear to me and so precious that I shall not scruple to take advantage of it in publishing an edition of my Treatises. If it does not shock you, you could both help in bringing out this edition, and I suggest that you should be the editors; you could clarify or augment what seems too brief and thus relieve me of a care which my work prevents me from taking. I would like this volume to appear without my name even, leaving to you the choice of designation which would indicate the author, whom you could qualify simply as a friend."

Carcavi approached Huygens, trying to publish the papers which Fermat had sent him. Unfortunately neither Carcavi nor Pascal succeeded and Fermat's papers were never published. The most important of the letters that Fermat sent Carcavi was dated 14 August 1659. In it Fermat claimed to be able to prove the following five theorems by the method of infinite descent :

(1) The area of a right-angled triangle whose sides are integers cannot be a square number.

(2) The equation x^3 + y^3 = z^3 has no solutions in integers.

(3) The equation y^2 + 2 = x^3 admits no solutions in integers except  x=3,y=5.

(4) The equation y^2 +4=x^2  admits no solutions in integers except x=2,y=2 and x=5,y=11.

(5) Each prime number of the form  p=4n+1 is uniquely expressible as the sum of two squares.

He ends his letter to Carcavi as follows:-

Here you have a summary account of my dreams on the subject of numbers. I have only written it because I fear I will lack the leisure to fully express myself and to lay out the entirety of my demonstrations and methods; in any case, this outline will serve the savants to be able to prove for themselves that which I have not filled out, especially if MM de Carcavi and Frenicle give them some demonstrations by descent that I have sent them on the subject of some negative propositions. And perhaps posterity will be thankful for my having let them know that which the Ancients did not ...

*SAU *Wik

 Carcavi

1676 Reverend Thomas Baker responds to message from John Collins and mentions a problem proposed by James Gregory that Collins had proposed a method to solve by "Billy's Method" (Jacques de Billy). Baker says he had solved the same problem when it had been proposed to him "Michaelmass last". "The sum of the squares and the sum of the cubes of four proportionals being given, to find the proportions themselves." Baker does not supply his method because, "I presumed I would but light a candle to the sun.' (The kind of compliment no one would disagree with.)

1714 Just twelve days before her death, Queen Anne signs "An Act for Providing a Publick Reward for such Person or Persons as shall Discover the Longitude at Sea". *Derek Howse, Britain's Board of Longitude:the Finances 1714-1828

1795 James Woodhouse was elected professor of "Chymistry" at the University of Pennsylvania.
The American Chemist founded the Chemical Society of Philadelphia and authored numerous works on chemistry, including the first book of directed chemical experiments.*rsc.org

At the University, Woodhouse worked in a small but well-equipped laboratory, from which he produced a number of research findings and publications. Priestley, the discoverer of oxygen, was a frequent visitor of the laboratory. Priestley was an adherent of the phlogiston theory, believing in the existence of a flammable principle contained in materials that burn; Woodhouse, however, had produced some of the most telling arguments and demonstrations against the phlogiston theory. These were published in the Transactions of the American Philosophical Society, of which he became a member in 1796. After such presentations by Woodhouse and others, the phlogiston theory became effectively dead in the United States.

Priestly had turned down the professorship, and after a second choice for the position, Woodhouse was selected.

Ticket for a Woodhouse Lecture

1798 The Battle of the Pyramids during Napoleon’s Egyptian campaign. It is a myth that his troops damaged the Sphinx by using it for target practice. *VFR (I'm afraid it is a myth I have shared, sorry kids!)

 The Meteor of 1860 by Frederic Church

1860 Great Meteor Procession of 1860 occurred on the evening of July 20. Unlike early morning meteors that are more frequent and run into the Earth head-on as it plows along in its orbit, evening meteors are rarer and have to approach the Earth from behind. In contrast, these often leave slow and stately trains as they move across the evening sky, struggling to keep up with the Earth. *David Dickinson, Universe Today

1925 Clarence Darrow calls William Jennings Bryan, counsel for the prosecution, to the stand as a witness for the defense in the Scopes Trial on the teaching of Evolution in Dayton, Tennessee, USA. Bryan testified to his literal interpretation of the Bible. He called the questioning a ridiculing of god. *Des Moines Register, July 21, 1925

Scopes is buried in Paducah, Kentucky.

 *John T Scopes

1959 The ﬁrst “International Mathematical Olympiad” began in Brasov, Romania. It lasted until 30 July and involved teams from seven Eastern European countries. [The College Mathematics Journal, 16 (1985), p. 333] *VFR A comment from J. points out that the IMO site gives dates one day later for start and finish, "first IMO was organised between 21,July to 31,July." Thanks

Maryam Mirzakhani (Iran), the first woman to be honored with a Fields Medal, won 2 gold medals in 1994 and 1995, getting a perfect score in the second year.

1969 Neil Armstrong, now of Lebanon, OH, was the ﬁrst man on the moon; Edwin Aldrin was a close second. Armstrong all but quoted what D. T. Whiteside wrote two years earlier about Isaac Newton: “May this present edition be a small step towards that long-overdue monument to a man who in so many areas of human thought himself took a giant’s leap.” See The Mathematical Papers of Isaac Newton, I, xxxvi and VIII, xxix. *VFR In 1969, Apollo XI astronauts Neil Armstrong and Edwin "Buzz" Aldrin became the first men to walk on the moon, after their lunar module separated from the command module and landed on the lunar surface at 09:18 GMT/4:18 EDT on the Sea of Tranquillity. Neil Armstrong and Edwin Aldrin establish Tranquility Base while Michael Collins orbited above. Armstrong stepped on the lunar surface at 10:56 ET and proclaimed, "That's one small step for a man, one giant leap for mankind." Internationally, nearly 700 million television viewers witnessed the event live as it happened.*TIS

 Armstrong on moon

1969 The mineral armalcolite was found on the moon, before it was known to exist on the earth. Named for the first letters of the Apollo 11 astronauts who found it, ARMstrong, COLlins, and ALDrin, the mineral was later found in Montana, South Africa, Greenland, and the Ukraine. *FFF pg 220 Then the name should be changed to UkeAfrGreMont.

1976  Viking I landed on Mars to explore the surface of the Red Planet. The first robots on Mars, Viking I and its successor gave scientists their first information about the planet's surface, including information they hoped would allow people to walk there. Although the Viking probes found no evidence of life on Mars, they returned detailed pictures of the planet and information about the soil's composition. *CHM

 *CHM

2017  To celebrate the 48th anniversary of the Apollo 11 lunar landing, Sotheby’s New York held a special space exploration-themed auction on July 20th. One of the hot-ticket items, a zippered bag laced with moon dust, sold for $1.8 million. The bag’s previous owner is likely thrilled, but NASA certainly isn’t celebrating. The agency recently fought, and lost, a bitter court battle to retrieve the artifact from a private collection. The bag, which is stamped with the words “Lunar Sample Return,” was used by Neil Armstrong during the first manned mission to the moon in 1969. He had packed the bag with moon rocks so he could transport them back to Earth. NASA accidentally sold it to a private collector three years before. Investigators had found the bag while searching through the belongings of Max Ary, the former president of the Kansas Cosmosphere. In 2005, Ary was indicted of stealing and selling museum artifacts, including ones that had been loaned out by NASA. Due to an error in NASA’s system, the bag was confused with another space bag from a later lunar landing, and was then accidentally sold to an Illinois woman for just$995 at auction,

The buyer, one Nancy Carlson, knew that the bag had been used during a space flight, but she wasn’t sure which one. So she sent the bag of to NASA for testing. The agency, realizing its cosmic goof, refused to return the bag. The item “belongs to the American people,” NASA said in a statement at the time.  But U.S. District Judge J. Thomas Marten ruled in Carlson's favor. He said that while the bag should never have been put up for sale, he had no recourse to reverse the transaction. NASA was forced to return the artifact in February of 2017.

BIRTHS

1789 Antonio Maria Bordoni (19 July 1789 – 26 March 1860) was an Italian mathematician who did research on mathematical analysis, geometry, and mechanics. Joining the faculty of the University of Pavia in 1817, Bordoni is generally considered to be the founder of the mathematical school of Pavia. He was a member of various learned academies, notably the Accademia dei XL. Bordoni's famous students were Francesco Brioschi, Luigi Cremona, Eugenio Beltrami, Felice Casorati and Delfino Codazzi.

On 1 November 1817 he became full professor of Elementary Pure mathematics at the University and in 1818 he held the chair of Infinitesimal Calculus, Geodesy and Hydrometry, a discipline he taught for 23 years.

In 1827 and 1828 he was dean of the University itself. In 1854, as the Faculty of Mathematics of the University of Pavia (it previously belonged to the one of the Philosophy) was established, he was elected Director of Mathematical Studies and held such office until his death, which occurred 26 March 1860, just one month after being appointed senator. *Wik

1805 Ormbsy MacKnight Mitchel (July 20, 1805 – October 30, 1862) American astronomer and major general in the American Civil War.
A multi-talented man, he was also an attorney, surveyor, and publisher. He is notable for publishing the first magazine in the United States devoted to astronomy. Known in the Union Army as "Old Stars", he is best known for ordering the raid that became famous as the Great Locomotive Chase during the Civil War. He was a classmate of Robert E. Lee and Joseph E. Johnston at West Point where he stayed as assistant professor of mathematics for three years after graduation.
The U.S. communities of Mitchell, Indiana, Mitchelville, South Carolina, and Fort Mitchell, Kentucky were named for him. A persistently bright region near the Mars south pole that was first observed by Mitchel in 1846 is also named in his honor. *TIA

1806 Alexander (Dallas) Bache (July 19, 1806 – February 17, 1867) was Ben Franklin's great grandson. A West Point trained physicist, Bache became the second Superintendent of the Coast Survey (1844-65). He made an ingenious estimate of ocean depth in 1856. He studied records of a tidal wave that had taken 12 hours to cross the Pacific. Knowing that wave speeds depend on depth, he calculated a 2 1/5-mile average depth for the Pacific (within 15% of the right value). Bache created the National Academy of Sciences, securing greater government involvement in science. Through the Franklin Institute he instituted boiler tests to promote safety for steamboats.*TIS

1820 James Dunwoody Brownson De Bow (July 20, 1820 – February 27, 1867) American statistician and editor, who is regarded as a pioneer of economic statistics for the U.S. Census Office. As a young man, he moved in 1820 to New Orleans, and there began publishing his periodical, DeBow’s Review, on business and the economy. By 1848, he became professor of commerce and statistics at the University of Louisiana, and was appointed some months later to head Louisiana’s new Bureau of Statistics. President Franklin Pierce turned to DeBow to be Superintendent (1853-55) of the Seventh U.S. Census, for which he produced a full report, and also Statistical View of the United States, a summary subsequently known as the Compendium, which was popular for the usefulness of its economic statistics.« *TiS

1855 Pierre Henri Puiseux, a French astronomer, was born July 20, 1855. He began working at the Paris Observatory in 1885, where he soon teamed up with Maurice Loewy, an Austrian Jew who had left Vienna seeking a country more hospitable for a Jewish astronomer. Puiseux and Loewy initially worked on a project known as the Cartes du Ciel, which intended to provide a complete photographic atlas of the stars, but the project, after some initial enthusiasm, withered and died. So the two decided to use the large astrograph (photographic telescope) at the Observatory to record images of the moon, and this enterprise was much more successful. They started taking photographs in 1894, and in 1896, they issued the first fascicule of their Atlas photographique de la lune. Each fascicule had 5-6 heliogravure prints of a section of the Moon and a descriptive text. *Linda Hall Org.

1873 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

1876 Ludwig Otto Blumenthal (20 July 1876 – 12 November 1944) was a German mathematician and professor at RWTH Aachen University.
He was born in Frankfurt, Hesse-Nassau. A student of David Hilbert, Blumenthal was an editor of Mathematische Annalen. When the Civil Service Act of 1933 became law in 1933, after Hitler became Chancellor, Blumenthal was dismissed from his position at RWTH Aachen University. He was married to Amalie Ebstein, also known as 'Mali' and daughter of Wilhelm Ebstein.

Blumenthal, who was of Jewish background, emigrated from Nazi Germany to the Netherlands, lived in Utrecht and was deported via Westerbork to the concentration camp, Theresienstadt in Bohemia (now Czech Republic), where he died.

In 1913, Blumenthal made a fundamental, though often overlooked, contribution to applied mathematics and aerodynamics by building on Joukowsky's work to extract the complex transformation that carries the latter's name, making it an example of Stigler's Law of eponymy.  *Wik

1894 Georges Henri Joseph Édouard Lemaître (17 July 1894 – 20 June 1966) was a Belgian priest, astronomer and professor of physics at the Catholic University of Leuven. He proposed the theory of the expansion of the universe, widely misattributed to Edwin Hubble. He was the first to derive what is now known as Hubble's law and made the first estimation of what is now called the Hubble constant, which he published in 1927, two years before Hubble's article. Lemaître also proposed what became known as the Big Bang theory of the origin of the universe, which he called his "hypothesis of the primeval atom" or the "Cosmic Egg" *Wik

1894 Errett Lobban Cord (20 July 1894 – 2 January 1974) U.S. automobile manufacturer, advocate of front-wheel-drive vehicles. Cord, still in his twenties when he arrived at the Auburn Automobile Company, had a talent for seeking and hiring young, innovative minds, full of drive and ambition. Cord was a brilliant, complex industrialist who helped personal and public transportation come of age. He is best known today for Auburn, Cord and Duesenberg automobiles, Cord's greatest talent may have been his unparalleled ability to construct an automotive empire durable enough to thrive during the darkest years of the Great Depression. Photo: 1929 Cord L-29 Sedan, America's first front-drive production car. Built by the Auburn Automobile Company, Auburn, Indiana. *TIS

1996 Tadeusz Reichstein (20 July 1897 – 1 August 1996) was a Polish-born Swiss chemist, botanist and Nobel laureate.

Reichstein, with Philip S. Hench and Edward C. Kendall, received the Nobel Prize for Physiology or Medicine in 1950 for his discoveries concerning hormones of the adrenal cortex, their structure and biological effects. With his co-workers, Reichstein accomplished the first isolation of four active hormones from the adrenal cortex, the first synthesis of one of them, the proof of the steroid nature of said hormones, and numerous details on the structure and properties of these important bodies. This made synthesis possible, leading to the creation of new medications *TiS *Wik

1924 Robert D. Maurer (born July 20, 1924, ) was born. Maurer is an American physicist who co-invented the optical fiber with Donald Keck and Peter Schultz . Optical fiber is a fiber made of glass or plastic that can carry light along its length. They are used in telecommunications and information technology or even illumination. They work as a waveguide because the core keeps the light by total internal reflection. The light bounces off the edges and is reflected back into the fiber without any loss out the side.*Today in History

1947 Gerd Binnig (20 July 1947, ) German-born physicist who co-invented the scanning tunneling microscope with Heinrich Rohrer. They shared the 1986 Nobel Prize for Physics with Ernst Ruska, who designed the first electron microscope. This instrument is not a true microscope ( i.e. an instrument that gives a direct image of an object) since it is based on the principle that the structure of a surface can be studied using a stylus that scans the surface at a fixed distance from it. Vertical adjustment of the stylus is controlled by means of what is termed the tunnel effect - hence the name of the instrument.*TIS

DEATHS

1819 John Playfair (10 March 1748 – 20 July 1819) Scottish mathematician, physicist, and geologist who is remembered for his axiom that two intersecting straight lines cannot both be parallel to a third straight line. His Illustrations of the Huttonian Theory of the Earth (1802) gave strong support to James Hutton's principle of uniformitarianism, essential to a proper understanding of geology. Playfair was the first scientist to recognize that a river cuts its own valley, and he cited British examples of the gradual, fluvial origins of valleys, to challenge the catastrophic theory (based on the Biblical Flood in Genesis) that was still widely accepted. He was also the first to link the relocation of loose rocks to the movement of glaciers. Playfair published texts on geometry, physics, and astronomy. *TIS

I have Playfair's 1802 Elements of Geometry, Second Edition, enlarged.  Signed inside "James Norgate, Caius College, 1808.  It's not too valuable, but earlier than this one at MAA

1866 Georg Friedrich Bernhard Riemann died in Bolzano, Italy, at age 39 (September 17, 1826 – July 20, 1866). The inscription on his tombstone (translated from the German) reads: “All things work together for good to them that love the Lord.” *VFR Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics.
Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier series—a first step in generalized function theory—and studied the Riemann–Liouville differintegral.
He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he introduced the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.
He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities.*Wik

1937 Guglielmo Marconi (25 April 1874 – 20 July 1937)Italian inventor, born in Bologna. He was a physicist, who invented the wireless telegraph in 1935 known today as radio. Nobel laureate (1909). In 1894, Marconi began experimenting on the "Hertzian Waves" (the radio waves Hertz first produced in his laboratory a few years earlier). Lacking support from the Italian Ministry of Posts and Telegraphs, Marconi turned to the British Post Office. Encouraging demonstrations in London and on Salisbury Plain followed. Marconi obtained the world's first patent for a system of wireless telegraphy, in 1897, and opened the world's first radio factory at Chelmsford, England in 1898. In 1900 he took out his famous patent No. 7777 for "tuned or syntonic telegraphy."*TIS

1922 Andrey Andreyevich Markov (14 June 1856 N.S. – 20 July 1922) Russian mathematician who helped to develop the theory of stochastic processes, especially those called Markov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors. (For example, the probability of winning at the game of Monopoly can be determined using Markov chains.) His work based on the study of the probability of mutually dependent events has been developed and widely applied to the biological and social sciences.*TIS - Simple Markov chain problem for students, The probability of Events A, B and C are 1/2, 1/3, and 1/6 respectively.  If one of these events occurs on each trial, what is the probability that it takes six or less trials to get all three outcomes?

1997 Eric Charles Milner, FRSC (May 17, 1928–July 20, 1997) was a mathematician who worked mainly in combinatorial set theory.
A former London street urchin, Milner attended King's College London starting in 1946, where he competed as a featherweight boxer. He graduated in 1949 as the best mathematics student in his year, and received a masters degree in 1950 under the supervision of Richard Rado and Charles Coulson. Partial deafness prevented him from joining the Navy, and instead, in 1951, he took a position with the Straits Trading Company in Singapore assaying tin. Soon thereafter he joined the mathematics faculty at the University of Malaya in Singapore, where Alexander Oppenheim and Richard K. Guy were already working. In 1958, Milner took a sabbatical at the University of Reading, and in 1961 he took a lecturership there and began his doctoral studies; he obtained a Ph.D. from the University of London in 1963. He joined his former Singapore colleagues Guy and Peter Lancaster as a professor at the University of Calgary in 1967, where he was head of the mathematics department from 1976 to 1980. In 1973, he became Canadian citizen, and in 1976 he became a fellow of the Royal Society of Canada.
In 1954, while in Singapore, Milner married Esther Stella (Estelle) Lawton, whom he had known as a London student; they had four children. Estelle died of cancer in 1975, and in 1979 Milner remarried Elizabeth Forsyth Borthwick, with whom he had another son.
Milner's interest in set theory was sparked by visits of Paul Erdős to Singapore and by meeting András Hajnal while on sabbatical in Reading. He generalized Chang's ordinal partition theorem for arbitrary finite k. He is also known for the Milner–Rado paradox. *Wik

2007 Kai Manne Börje Siegbahn (20 April 1918 – 20 July 2007) Swedish physicist who shared (with Nicolaas Bloembergen and Arthur L.Schawlow) the 1981 Nobel Prize for Physics for “his contribution to the development of high-resolution electron spectroscopy.” He analyzed the resulting electrons that were knocked out from the interior of an atom by a high energy X-ray photons. Thus he could measure the binding energy of atomic electrons with higher accuracy than was previously possible. Furthermore, since that binding energy was somewhat dependent upon the chemical environment of the atom, this provided a new tool of chemical analysis—ESCA (Electron Spectroscopy for Chemical Analysis). ESCA is now used by hundreds of laboratories around the world to investigate surface reactions, such as corrosion or catalytic reactions, and others also of great important in industrial chemistry. His father, Karl Manne Georg Siegbahn, received the 1924 Nobel Prize in Physics. *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