Gauss-Weber Monument in Gotttingen |

**Now it is quite clear to me that there are no solid spheres in the heavens, and those that have been devised by authors to save the appearances, exist only in their imagination, for the purpose of permitting the mind to conceive the motion which the heavenly bodies trace in their courses.**

~Tycho Brahe

^{10}

^{2}= 88209 and 88+209 = 297. (Numbers that have this property are a type of Kaprekar number; there are only three such numbers of three digits, now you know one of them.)

And this one from * Jim Wilder @wilderlab 297

^{3}=26,198,073 and 26+198+073=297

**EVENTS**

**1676**Newton summarized the stage of development of his method in the “Epistola posterior,” which he sent to Oldenburg to transmit to Leibniz. *VFR (see Oct 26, 1676) This may be the first time Newton used irrational exponents in communication to others. It is one of the earlier uses by anyone. In the letter to Oldenburg, Newton remarks that Leibniz had developed a number of methods, one of which was new to him. Newton had sent (June 13, 1676) Oldenburg his “Epistola prior” . Among other things it contained the ﬁrst statement of the binomial theorem for negative and fractional exponents. This may be the first use of fractional and negative exponents in the modern sense (cajori, 308 pgs 370-371)

The idea and limited use had been mentioned by Viete, but in a rhetorical manner. Wallis, twenty years earlier, had mentioned both negative and fractional "indices" and gives an example using 1/sqrt(2) has index (-1/2). Oresme was The first to use fractional and irrational powers to explore his knowledge of music, but he did not write them as raised numbers.

*Arithmetica Infinitorum,*a seminal work of 17th-century math. Wallis included a novel and inductive method of determining the value of pi, and Newton wanted to devise something similar. He started with the problem of finding the area of a “circular segment” of adjustable width

*x*. This is the region under the unit circle, defined by y=√1−x2, that lies above the portion of the horizontal axis from 0 to

*x*. Here

*x*could be any number from 0 to 1, and 1 is the radius of the circle. The area of a unit circle is pi, as Newton well knew, so when

*x=1*, the area under the curve is a quarter of the unit circle, π4. But for other values of

*x*, nothing was known.

*Getty |

**1729**Euler mentioned the gamma function in a letter to Goldbach. In 1826 Legendre gave the function its symbol and name. * F. Cajori, After earlier giving him the definition as an integral, he presents the function as Γ(1) = 1, Γ(x + 1) = xΓ(x) , History of Mathematical Notations, vol. 2, p. 271 (the Oct 13 date is for the Julian Calendar still used in Russia when Euler wrote from there. It was the 24th in most of the rest of the world using the Gregorian Calendar.)

**1826**Abel wrote Holmboe his impressions of continental mathematics and mathematicians.

Upon reaching Paris from Berlin, he worked on what would be called the Paris Treatise that he submitted to the Academy in October 1826. In this memoir, Abel obtained among other things, an important addition theorem for algebraic integrals. It is also in this treatise that we see the first occurrence of the concept of the genus of an algebraic function. Cauchy and Legendre were appointed referees of this memoir. In Paris, Abel was disappointed to find little interest in his work, which he had saved for the Academy. He wrote to Holmboe, “I showed the treatise to Mr. Cauchy, but he scarcely deigned to glance at it."*Krishnaswami Alladi, NEILS HENRIK ABEL, Norwegian mathematical genius (paper on UFL website)

**1844**Michael Faraday in a letter (his first?) to Ada Lovelace declines an invitation to be her tutor, and in response to her questions about his religion, he describes himself as, "of a small and despised sect of Christians, known, if they are known at all, as Sandemanian." Michael Brooks, in his book Free Radicals, describes the sect as responsible for Faraday's lack of much interest in the applications of his scientific discoveries; "It was his calling, as he saw it, to study nature, which was 'written by the finger of God', and make clear the eternal power and divine nature of the creator."

**In 1851**, William Lassell discovered Ariel and Umbriel, satellites of Uranus. All of Uranus's moons are named after characters from the works of William Shakespeare or Alexander Pope's The Rape of the Lock. The names of all four satellites of Uranus then known were suggested by John Herschel in 1852 at the request of Lassell. Ariel has an approx. diameter of 1160-km, an orbital period of 2.52 days, and orbital radius of 191,240-km from Uranus. The name Umbriel comes from Alexander Pope's The Rape of the Lock. Umbriel has a diameter of 1170-km, an orbital period of about 4 days and orbit radius of 266,000-km. Lassell, a British astronomer, had previously also discovered Neptune's largest satellite, Triton and (with Bond) discovered Saturn's moon Hyperion. He was a successful brewer before turning to astronomy.*TIS *Wik

**1902**In Science, George Bruce Halsted wrote that his student R. L. Moore, who had proved that one of Hilbert’s betweenness axioms was redundant, “was displaced in favor of a local schoolmarm,” Miss Mary E. Decherd. *VFR Dechard was a well-connected but, perhaps, less qualified candidate with roots in the area.

**1904**Emmy Noether matriculated at the University of Erlangen. *VFR The University was only yards from her house. Images of both are at this site from The Renaissance Mathematicus.

**1927**From the 24th to 29th October 1927 in Brussels, the fifth Solvay Conference took place, Perhaps the most famous science conference in history. 17 of the 29 attendees were or became Nobel Prize winners. It is also famously remembered for it was at this conference that Einstein, who liked to invent catchy phrases, uttered his, "God does not play dice" . Bohr replied, "Einstein, stop telling God what to do". Of the attendees, only two were American Born. The influence of USA in Physics was just beginning.

A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. de Donder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin; P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr; I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch.-E. Guye, C.T.R. Wilson, O.W. Richardson |

1956

**Time Magazine doews a feature "Close-Up" on Danish Scientist/Mathematician/poet Piet Hein, "A Poet with a Slide Rule." Hein was the creator of the term Super Ellipse, which already had the perfectly good name of Lame curve, after Gabriel Lame.**

**1989**“Welcome to the White House on this glorious fall day. I’m sorry if I’m just a little bit late. I was sitting in there trying to solve a few quadratic equations. [Laughter] Somewhat more difficult than balancing the budget, I might say. And then I thought it might be appropriate to have a moment of silence in memory of those substitute teachers back home. [Laughter].” Remarks by President George Bush (the elder) at the Presentation Ceremony for the Presidential Awards for Excellence in Science and Math Teaching. (A few years later when I won the award, he and Barbara walked by the group and gave us a wave. )

1994 Lynchburg College Professor Thomas Nicely, Reports a flaw in the Pentium chip by Intel that he discovered while he was trying to calculate Brun's constant,(The sum of the reciprocals of all the twin primes, 1/3+1/5+1/5+1/7+1/11+1/13.... which converges to about 1.902).

The Pentium chip occasionally gave wrong answers to a floating-point (decimal) division calculations due to errors in five entries in a lookup table on the chip. Intel spent millions of dollars replacing the faulty chips.

Nicely first noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors until October 19, 1994. On October 24, 1994 he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro. *Wik

**BIRTHS**

**1632 Antonie van Leeuwenhoek**(24 Oct 1632; 26 Aug 1723.) Dutch microscopist who was the first to observe bacteria and protozoa. His researches on lower animals refuted the doctrine of spontaneous generation, and his observations helped lay the foundations for the sciences of bacteriology and protozoology.*TIS "The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite. "

**1804 Wilhelm Eduard Weber**(24 Oct 1804; 23 Jun 1891) German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

**1821 Philipp Ludwig von Seidel**(23 October 1821, Zweibrücken, Germany – 13 August 1896, Munich)

**formulated the notion of uniform convergence.*VFR**

Lakatos credits von Seidel with discovering, in 1847, the crucial analytic concept of uniform convergence, while analyzing an incorrect proof of Cauchy's.

^{ }In 1857, von Seidel decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations. The Gauss–Seidel method is a useful numerical iterative method for solving linear systems. *Wik

**1853 Heinrich Maschke**(24 October 1853 in Breslau, Germany (now Wrocław, Poland) – 1 March 1908 Chicago, Illinois, USA) was a German mathematician who proved Maschke's theorem.*Wik

**1873 Sir Edmund Taylor Whittaker**(24 Oct 1873; 24 Mar 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS

**1898 Lillian Rose Vorhaus Kruskal Oppenheimer**(October 24, 1898 in New York City – July 24, 1992) was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis. Lillian taught origami to Persi Diaconis when he was working as a magician;

She was the mother of three sons William Kruskal(developed the Kruskal-Wallis one-way analysis of variance), Martin David Kruskal(co-inventor of solitons and of surreal numbers), and Joseph Kruskal ( Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph) who all went on to be prominent mathematicians. Her grandson Clyde P. Kruskal (son of Martin) is an American computer scientist,working on parallel computing architectures, models, and algorithms. *Wik

**1906 Aleksandr Osipovich Gelfond**(24 Oct 1906; 7 Nov 1968) Russian mathematician who originated basic techniques in the study of transcendental numbers (numbers that cannot be expressed as the root or solution of an algebraic equation with rational coefficients). He profoundly advanced transcendental-number theory, and the theory of interpolation and approximation of complex-variable functions. He established the transcendental character of any number of the form ab, where a is an algebraic number different from 0 or 1 and b is any irrational algebraic number, which is now known as Gelfond's theorem. This statement solved the seventh of 23 famous problems that had been posed by the German mathematician David Hilbert in 1900. *TIS

**1908 John Tuzo Wilson,**CC, OBE, FRS, FRSC, FRSE (October 24, 1908 – April 15, 1993) the world-renowned Canadian geophysicist, served as Director General of the Ontario Science Centre from 1974 to 1985. He was instrumental in developing the theory of Plate Tectonics in the 1960s. This theory describes the formation, motion and destruction of the Earth's crust, the origin of volcanic eruptions and earthquakes, and the growth of mountains. Dr. Wilson's significant contributions to this theory revolutionized Earth Sciences. He proposed the existence of transform faults to explain the numerous narrow fracture zones and earthquakes along oceanic ridges. He also showed that rising magma plumes beneath the Earth's crust could create stationary hot spots, leading to the formation of mid-plate volcanic chains like the Hawaiian Islands.

The first graduate of geophysics from the University of Toronto in 1930, Dr. Wilson went on to study at Cambridge and Princeton, earning his doctorate in 1936. After spending two years with the Geological Survey of Canada and almost a decade with the Canadian Military Engineers, he accepted the position of Professor of Geophysics at the University of Toronto in 1946. Internationally recognized for his major contributions as a research scientist, educator and visionary, Dr. Wilson received many prestigious

awards, including the Vetlesen Prize, the Earth Sciences equivalent of the Nobel Prize.*THE HISTORICAL MARKER DATABASE

**1922 Werner Buchholz**(24 October 1922 – 11 July 2019) He was a member of the teams that designed the IBM 701 and Stretch models. Buchholz used term byte to describe eight bits—although in the 1950s, when the term first was used, equipment used six-bit chunks of information, and a byte equaled six bits. Buchholz described a byte as a group of bits to encode a character, or the numbers of bits transmitted in parallel to and from input-output. *CHM

**1932 Pierre-Gilles de Gennes**(24 Oct 1932; 18 May 2007) French physicist who was awarded the 1991 Nobel Prize for Physics for "discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers." He described mathematically how, for example, magnetic dipoles, long molecules or molecule chains can under certain conditions form ordered states, and what happens when they pass from an ordered to a disordered state. Such changes of order occur when, for example, a heated magnet changes from a state in which all the small atomic magnets are lined up in parallel to a disordered state in which the magnets are randomly oriented. Recently, he has been concerned with the physical chemistry of adhesion. *TIS

**DEATHS**

**1601 Tycho Brahe**(14 December 1546 – 24 October 1601) Kepler inherited his vast accurate collection of astronomical data. He used this to derive his laws of planetary motion. *VFR In 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point. He always carried a small box of glue in his pocket for use when the new nose became wobbly. Tycho Brahe was famous for the most accurate and precise observations achieved by any astronomer before the invention of the telescope. Born to an aristocratic family in Denmark in 1546, he was one of twin boys – the other twin was still-born – and while still a baby Tycho was stolen from his parents by a rich, childless uncle, who paid for his education and sent him to Leipzig University to study law. His imagination had been fired, however, by a total eclipse of the sun in 1560 and he was determined to be an astronomer. He found that the existing tables recording the positions of planets and stars were wildly inaccurate and dedicated himself to correcting them. *History Today Was Tycho Murdered? Read an excellent blog on "The crazy life and crazier death of Tycho Brahe, history’s strangest astronomer".

**1635 Wilhelm Shickard**(22 April 1592 – 24 October 1635) He invented and built a working model of the ﬁrst modern mechanical calculator. *VFR

Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables.

In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize the designs or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed the calculator based upon Schickard's original plans; it is still on display there today.

He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.

**1655 Pierre Gassendi**(22 Jan 1592, 24 Oct 1655) French scientist, mathematician, and philosopher who revived Epicureanism as a substitute for Aristotelianism, attempting in the process to reconcile Atomism's mechanistic explanation of nature with Christian belief in immortality, free will, an infinite God, and creation. Johannes Kepler had predicted a transit of Mercury would occur in 1631. Gassendi used a Galilean telescope to observed the transit, by projecting the sun's image on a screen of paper. He wrote on astronomy, his own astronomical observations and on falling bodies. *TIS

**1870 Charles Joseph Minard**(27 Mar 1781; 24 Oct 1870 at age 89) French civil engineer who made significant contributions to the graphical representations of data. His best-known work, Carte figurative des pertes successives en hommes de l'Armee Français dans la campagne de Russe 1812-1813, dramatically displays the number of Napoleon's soldiers by the width of an ever-reducing band drawn across a map from France to Moscow. At its origin, a wide band shows 442,000 soldiers left France, narrowing across several hundred miles to 100,000 men reaching Moscow. With a parallel temperature graph displaying deadly frigid Russian winter temperatures along the way, the band shrinks during the retreat to a pathetic thin trickle of 10,000 survivors returning to their homeland. *TIS Minard advocated the graphing idea that the ratio of information to ink should be as high as possible.

**1930 Paul Emile Appell**(27 Sept 1855 in Strasbourg, France - 24 Oct 1930) Appell's first paper in 1876 was based on projective geometry continuing work of Chasles. He then wrote on algebraic functions, differential equations and complex analysis. In 1878 he noted the physical significance of the imaginary period of elliptic functions in the solution of the pendulum which had been though to be purely a mathematical curiosity. He showed that the double periodicity follows from physical considerations. *SAU

**1940 Pierre-Ernest Weiss**(25 Mar 1865, 24 Oct 1940) French physicist who investigated magnetism and determined the Weiss magneton unit of magnetic moment. Weiss's chief work was on ferromagnetism. Hypothesizing a molecular magnetic field acting on individual atomic magnetic moments, he was able to construct mathematical descriptions of ferromagnetic behaviour, including an explanation of such magnetocaloric phenomena as the Curie point. His theory succeeded also in predicting a discontinuity in the specific heat of a ferromagnetic substance at the Curie point and suggested that spontaneous magnetization could occur in such materials; the latter phenomenon was later found to occur in very small regions known as Weiss domains. His major published work was Le magnetisme ( 1926).*TIS

**1927 John McCarthy** (September 4, 1927 – October 24, 2011) was an American computer scientist and cognitive scientist. He was one of the founders of the discipline of artificial intelligence. He co-authored the document that coined the term "artificial intelligence" (AI), developed the programming language family Lisp, significantly influenced the design of the language ALGOL, popularized time-sharing, and invented garbage collection.

McCarthy spent most of his career at Stanford University. He received many accolades and honors, such as the 1971 Turing Award for his contributions to the topic of AI, the United States National Medal of Science, and the Kyoto Prize.

**1952 Ida Martha Metcalf**(August 26, 1857 – October 24, 1952) was the second American woman to receive a PhD in mathematics. She was born in Texas to Charles A. and Martha C. (Williams) Metcalf. During her youth, her family moved about the south. After her father’s death, she moved to New England with her mother and siblings. By 1870, she was living in Massachusetts, where she taught school for many years.

**1966 ****Sofya Aleksandrovna Yanovskaya **(also Janovskaja; 31 January 1896 – 24 October 1966) was a Soviet mathematician, philosopher and historian, specializing in the history of mathematics, mathematical logic, and philosophy of mathematics. She is best known for her efforts in restoring the research of mathematical logic in the Soviet Union and publishing and editing the mathematical works of Karl Marx. *Wik

**2014 Johanna Weber **(8 August 1910 – 24 October 2014) was a German-born British mathematician and aerodynamicist. She is best known for her contributions to the development of the Handley Page Victor bomber and the Concorde.

In 1939, Weber joined the Aerodynamics Research Institute (Aerodynamische Versuchsanstalt Göttingen) in Göttingen. She was part of a small theoretical team, and her initial training in aerodynamics consisted of wind tunnel corrections. Here she met and began her lifelong collaboration with Dietrich Küchemann.

Scientists at Institute had by then worked out a consistent theory of flow around an aircraft. This was, however, an approximation, using singularities to represent the vortices that generated lift, and Weber was given the task of improving it. She realised that some of her work overlapped with Küchemann's research on jet engine intakes. They teamed up, with Weber doing the theoretical development and wind tunnel testing, and Küchemann setting the direction of their research based on his consultation with manufacturers. Over the period of the Second World War, they created a substantial body of work.

Weber also began her research into supersonic transport. In 1955, she showed that a thin delta wing with a high angle of attack could generate sufficient lift to provide the take-off and landing capability, while simultaneously enabling efficient supersonic performance. Küchemann then advocated this wing configuration with the UK Government, resulting in the support for a Mach 2 airliner by the Supersonic Transport Advisory Committee (STAC) in 1956.

In 1961, a prototype aircraft, the Handley Page HP.115, was built to test the low speed performance of the slender delta wing.*Wik

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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