**There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.**

~Daniel Bernoulli

The 29th day of the year; 2

^{29}=

**536870912**a nine-digit number with no digit repeated. Is it possible to create a power of a single digit number that has ten distinct digits?

The digits of 29 appear in one of the most unusual un-mistake I can imagine in numbers, if you inadvertently wrote the exponents of on the same line as the bases you get 2592 which is = . It is believed that this is the only such example.

28 is a perfect number, and I think it is interesting that we have proven that if there is ever an odd perfect number it will have at least 29 prime factors, the largest will be greater than 10

^{8}

There are only two prime day numbers that can be the hypotenuse of a primitive Pythagorean Triangle with consecutive integer legs, 3,4,5; and 20, 21, 29. The next prime hypotenuse for these is 5741. Can you find the legs?***

And I like this "Euler-like" function from Legendre in 1798, 2n

^{2}+ 29 is prime for all n from 0 through 28.

Note:

*A blog page with an expanded version of the daily Math Facts for each day is posted for days 1-30 at*https://mathdaypballew.blogspot.com/

**EVENTS**

**1697**(o.s.) Newton received two challenge problems from Johann Bernoulli, one being the Brachistochrone problem published in Acta eruditorum the previous June and addressed “to the shrewdest mathematicians in the world.” The next day Newton posted his solution to the Royal Society. When Bernoulli saw the anonymous solution he recognized it as “ex ungue leonem” (as the lion is recognized by his paw). *Westfall, Never at Rest, pg 581

**1769**"On the morning of the 29 January 1769, seven ‘transit’ (of Venus) astronomers went to Catherine the Great’s Winter Palace in St Petersburg because the Empress had requested to meet her astronomical army before they set out to their destinations across the Russian empire. The German Georg Moritz Lowitz and his assistant, the Russian Pjotr Inochodcev were going to Guryev, Russia (modern Atyrau, Kazakhstan), the Russian Stepan Rumovsky and the Swiss Jacques André Mallet and Jean-Louis Pictet were all travelling to different locations on the Kola peninsula, the Germans Christoph Euler was ordered to Orsk and Wolfgang Ludwig Krafft to Orenburg. *Andrea Wulf, Transit of Venus Web Site

**1824**Even right at the end of his life, former President Thomas Jefferson was still reporting on the current news in mathematics. On this day he writes to Patrick K. Rogers concerning the abandonment of fluxional calculus at Cambridge in favor of the Leibnizian notation , "The English generally have been very stationary in later times, and the French, on the contrary, so active and successful, particularly in preparing elementary books, in mathematics and natural sciences, that those who wish for instruction without caring from what nation they get it, resort universally to the latter language. Besides the earlier and invaluable works of Euler and Bezout, we have latterly that of Lacroix in mathematics, of Legendre in geometry, . . . to say nothing of the many detached essays of Monge and others, and the transcendent labors of Laplace, and I am informed by a highly instructed person recently from Cambridge, that the mathematicians of that institution, sensible of being in the rear of those of the continent, and ascribing the cause much to their long-continued preference of the geometrical over the analytical methods, which the French have so long cultivated and improved, have now adopted the latter; and that they have also given up the fluxionary, for the differential calculus. " *John Fauval, Lecture at Univ of Va.

**1886**Karl Benz finished his motorcar in 1885 and named it "

*Benz Patent-Motorwagen*".The Motorwagen was patented on 29 January 1886 as DRP-37435: "automobile fueled by gas". *Wik

**1939**J. Robert Oppenheimer hears about the discovery of fission. Within a few minutes, he realizes that excess neutrons must be emitted, and that it might be possible to build a bomb. Fission was discovered on December 17, 1938 by German Otto Hahn and his assistant Fritz Strassmann, but Oppenheimer probably hear about it through the publications which explained it (and named it) theoretically in January 1939 by Lise Meitner and her nephew Otto Robert Frisch. Frisch named the process by analogy with biological fission of living cells. *Wik

**1957**SRI and GE Meet to Choose a Place for ERMA's MICR Encoding

ERMA (Electronic Recording Machine - Accounting), developed by SRI and General Electric for the Bank of America in California, employed Magnetic Ink Character Recognition (MICR) as a tool that captures data from checks. IBM was making a strong case to place the encoding at the top of a check. SRI and GE conducted a series of tests that clearly demonstrated the advantage of the bottom-of-the-check encoding. *CHM

**1970**Yuri Matiyasevich presents proof of Hilbert's 10th Problem. Having been frustrated by the problem, he had given up hope of solving it. In December of the previous year after having been asked to review an article by Julia Robinson, he was inspired by the novelty of her approach and went back to work on H10. By Jan 3, 1970 he had a proof. He would present the proof on January 29, 1970

**1996**

**"I am not a crank." The lawsuit by William Dilworth, an engineer who (the complaint alleges) has published a half dozen articles in mathematics journals, including A Correction in Set Theory,” published in 1974 in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, was settled for the defense. The defendant, Underwood Dudley, a professor of mathematics at DePauw University had listed Dilworth amonst the "cranks" in a 1992 entitled Mathematical Cranks. One of these “cranks” was the plaintiff, William Dilworth. Dilworth, according to Dudley, “chose to prove that Cantor's diagonal process is a snare and a delusion.” His article reads as if it is by someone convinced, whose mind is not going to be changed by anything. It is, in two words, a crank, and it is no credit to the state of [Wisconsin].”**

The court's decision for the defense, "We hold only that where one scholar calls another a “crank” for having taken a position that the first scholar considers patently wrongheaded, the second does not have a remedy in defamation."

**BIRTHS**

**1688 Emanuel Swedenborg**(29 Jan 1688; 29 Mar 1772) Swedish scientist, philosopher and theologian. While young, he studied mathematics and the natural sciences in England and Europe. From Swedenborg's inventive and mechanical genius came his method of finding terrestrial longitude by the Moon, new methods of constructing docks and even tentative suggestions for the submarine and the airplane. Back in Sweden, he started (1715) that country's first scientific journal, Daedalus Hyperboreus. His book on algebra was the first in the Swedish language, and in 1721 he published a work on chemistry and physics. Swedenborg devoted 30 years to improving Sweden's metal-mining industries, while still publishing on cosmology, corpuscular philosophy, mathematics, and human sensory perceptions. *TIS

**1700 Daniel Bernoulli**(29 January 1700 (

*8 Feb new style*), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.

He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.

In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.

One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

**1761 Josef (also José or Joseph) de Mendoza y Ríos**(29 January 1761; Sevilla, Spain - 4 March 1816 Brighton, England) was a Spanish astronomer and mathematician of the 18th century, famous for his work on navigation. The first work of Mendoza y Ríos was published in 1787: his treatise, Tratado de Navegación, about the science and technique of navigation in two tomes. He also published several tables for facilitating the calculations of nautical astronomy and useful in navigation to calculate the latitude of a ship at sea from two altitudes of the sun, and the longitude from the distances of the moon from a celestial body. In the field of the nautical instruments, he improved the reflecting circle.

In 1816, he was elected a foreign member of the Royal Swedish Academy of Sciences. @Wik

**1810 Ernst Eduard Kummer**(29 Jan 1810; 14 May 1893) He was professor at the University of Breslau(now Wroclaw, Poland) in 1842-1855 and developed his theory of ideals here. Kronecker studied with him. Later he replaced Dirichlet at The University of Berlin. He died at age 83, after a short attack of inﬂuenza. German mathematician whose introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic to complex number fields. He worked on Function theory, and extended Gauss's work on hypergeometric series, giving developments that are useful in the theory of differential equations. He was the first to compute the monodromy groups of these series. Later. Kummer devoted himself to the study of the ray systems, but treated these geometrical problems algebraically. He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent planes. *TIS and others An oft told, and almost certianly untrue anecdote is told about Kummer: Kummer was so inept at simple arithmetic that he often asked students to help him in class. On one occasion, Kummer sought the result of a simple multiplication. "Seven times nine," he began. "Seven times nine is er - ah - ah - seven times nine is..." "Sixty-one," a mischievous student suggested and Kummer wrote the "answer" on the blackboard. "Sir," another one interjected, "it should be sixty-seven." "Come, gentlemen, it can't be both," Kummer exclaimed. "It must be one or the other!" According to Erdos, Kumer reasoned out the answer as follows, -It can't be 61 as that is prime, as is 67, and 65 is a multiple of five, and 69 is too big, so it must be 63.

**1817 William Ferrel**(29 Jan 1817; 18 Sep 1891) American meteorologist who was an important contributor to the understanding of oceanic and atmospheric circulation. He was able to show the interrelation of the various forces upon the Earth's surface, such as gravity, rotation and friction. Ferrel was first to mathematically demonstrate the influence of the Earth's rotation on the presence of high and low pressure belts encircling the Earth, and on the deflection of air and water currents. The latter was a derivative of the effect theorized by Gustave de Coriolis in 1835, and became known as Ferrel's law. Ferrel also considered the effect that the gravitational pull of the Sun and Moon might have on the Earth's rotation and concluded (without proof, but correctly) that the Earth's axis wobbles a bit. *TIS (A more complete biography is here)

**1838 Edward Williams Morley**(29 Jan 1838; 24 Feb 1923) American chemist who is best known for his collaboration with the physicist A.A. Michelson in an attempt to measure the relative motion of the Earth through a hypothetical ether (1887). He also studied the variations of atmospheric oxygen content. He specialized in accurate quantitative measurements, such as those of the vapour tension of mercury, thermal expansion of gases, or the combining weights of hydrogen and oxygen. Morley assisted Michelson in the latter's persuit of measurements of the greatest possible accuracy to detect a difference in the speed of light through an omnipresent ether. Yet the ether could not be detected and the physicists had seriously to consider that the ether did not exist, even questioning much orthodox physical theory. *TIS

**1888 Sydney Chapman**(29 Jan 1888; 16 Jun 1970) English mathematician and physicist noted for his research in geophysics. After graduation (1910) he worked at the Greenwich Observatory, but returned to Cambridge upon the outbreak of WW I. Between 1915 and 1917 he completed a series of important papers on thermal diffusion and the fundamentals of gas dynamics. He developed systematic approximations to the Maxwell-Boltzmann formulation for the velocity distribution function for interacting particles under general force laws. During WW II he worked on military operational research and incendiary bomb problems. Chapman's main area of research was geomagnetism, beginning in 1913 and extending to terrestrial and interplanetary magnetism, the ionosphere and the aurora borealis.*TIS

**1894 Miss Helen Almira Shaffer**, A. M., LL. D., President of Welleslev College,

died of pneumonia at the college, on January 29, aged 54 years. She was chief teacher

of Mathematics for ten years in the St. Louis High School. In 1877 she accepted the

professorship of Mathematics in Wellesley, which she filled until 1888, when she became

president of that institution. *The American Mathematical Monthly Vol. 1, No. 2, Feb., 1894

**1926 Abdus Salam**(29 Jan 1926; 21 Nov 1996) Pakistani-British nuclear physicist who shared the 1979 Nobel Prize for Physics with Steven Weinberg and Sheldon Lee Glashow. Each had independently formulated a theory explaining the underlying unity of the weak nuclear force and the electromagnetic force. His hypothetical equations, which demonstrated an underlying relationship between the electromagnetic force and the weak nuclear force, postulated that the weak force must be transmitted by hitherto-undiscovered particles known as weak vector bosons, or W and Z bosons. Weinberg and Glashow reached a similar conclusion using a different line of reasoning. The existence of the W and Z bosons was eventually verified in 1983 by researchers using particle accelerators at CERN. *TIS

**1928 O. Timothy O’Meara**born in South Africa. This expert in quadratic forms is now Provost at the University of Notre Dame. *VFR On October 8, 2008, the Mathematics Library at Notre Dame was rededicated and named for Prof. O. Timothy O’Meara. Prof. O’Meara is a noted Mathematician, who has been on the faculty of the Mathematics Department since 1962, and twice served as its chairman. In 1976 he was named to the Kenna Endowed Chair in Mathematics. He is noted for serving as the first lay Provost of the University, 1978-1996. He is now an emeritus faculty member, but still very active and interested in the library *ND Web Site

**1928 Joseph Bernard Kruskal, Jr**. (January 29, 1928 – September 19, 2010) was an American mathematician, statistician, computer scientist and psychometrician. He was a student at the University of Chicago and at Princeton University, where he completed his Ph.D. in 1954, nominally under Albert W. Tucker and Roger Lyndon, but de facto under Paul Erdős with whom he had two very short conversations.Kruskal has worked on well-quasi-orderings and multidimensional scaling.

He was a Fellow of the American Statistical Association, former president of the Psychometric Society, and former president of the Classification Society of North America.

In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. In combinatorics, he is known for Kruskal's tree theorem (1960), which is also interesting from a mathematical logic perspective since it can only be proved nonconstructively. Kruskal also applied his work in linguistics, in an experimental lexicostatistical study of Indo-European languages, together with the linguists Isidore Dyen and Paul Black.

Kruskal was born in New York City to a successful fur wholesaler, Joseph B. Kruskal, Sr. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of Origami during the early era of television. He died in Princeton. *Wik

**DEATHS**

**1707 Otto Mencke**(

*22 March (OS)*April 2, 1644 –

*18 Jan (OS)*29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.

He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

**1715 Bernard Lamy**(15 June 1640, in Le Mans, France – 29 January 1715, in Rouen, France) was a French Oratorian mathematician and theologian. He wrote on geometry and mechanics and developed the idea of a parallelogram of forces at about the same time as Newton and Verignon. The Law of Sines as applied to three static forces in mechanics is sometimes called Lamy's Rule. (

*Would provide an interesting variation for Pre-calc classes*)

**1859 William Cranch Bond**(9 Sep 1789, 29 Jan 1859) American astronomer who, with his son, George Phillips Bond (1825-65), discovered Hyperion, the eighth satellite of Saturn, and an inner ring called Ring C, or the Crepe Ring. While W.C. Bond was a young clockmaker in Boston, he spent his free time in the amateur observatory he built in part of his home. In 1815 he was sent by Harvard College to Europe to visit existing observatories and gather data preliminary to the building of an observatory at Harvard. In 1839 the observatory was founded. He supervised its construction, then became its first director. Together with his son he developed the chronograph for automatically recording the position of stars. They also took some of the first recognizable photographs of celestial objects.*TIS

**1864 Benoît "Claudius" Crozet**(December 31, 1789; Villefranche, France – January 29, 1864) was an educator and civil engineer.

After serving in the French military, in 1816, he immigrated to the United States. He taught at the U.S. Military Academy at West Point, New York, and helped found the Virginia Military Institute at Lexington, Virginia. He was Principal Engineer for the Virginia Board of Public Works and oversaw the planning and construction of canals, turnpikes, bridges and railroads in Virginia, including the area which is now West Virginia. He became widely known as the "Pathfinder of the Blue Ridge."

On June 7, 1816, in Paris, Crozet married Agathe Decamp.

Late in fall of 1816, Crozet and his bride headed for the United States. Almost immediately after arriving, Crozet began work as a professor of engineering at the U.S. Military Academy at West Point, New York.

While at West Point, Crozet is credited by some as being the first to use the chalkboard as an instructional tool. He also designed several of the buildings at West Point. Thomas Jefferson referred to Claudius Crozet as "by far the best mathematician in the United States." He also published A Treatise on Descriptive Geometry while at West Point, a copy of which was sent to Jefferson. Jefferson's response on Nov 23, 1821 began, "I thank you, Sir, for your kind attention in sending me a copy of your valuable treatise on Descriptive geometry." He continued the messsage with praise for the work, and the instructor both. The dining hall at the Virginia Military Institute is named in his honor. It has been affectionately nicknamed "Club Crozet" by the Cadets. * Wik & Natl. Archives

**1905 Robert Tucker**(26 April 1832 in Walworth, Surrey, England - 29 Jan 1905 in Worthing, England) A major mathematical contribution made by Tucker was his work as editor of William Kingdon Clifford's papers. Fifty-seven of Clifford's papers were collected and edited by Tucker and published in 1882 as Mathematical Papers. Tucker also wrote many biographies including those of Gauss, Sylvester, Chasles, Spottiswoode, and Hirst, all of which appeared in Nature. But, like a number of schoolmaster's at this time, he also made a contribution to research in geometry. He wrote over 40 research papers which were published in leading journals. These papers, although sometimes not of the highest quality, do contain a number of interesting ideas. Hill specially singles out for special mention his work on the Triplicate-Ratio Circle, the group of circles sometimes known as Tucker Circles, and the Harmonic Quadrilateral. *SAU

**1984 John Macnaghten Whittaker**I(7 March 1905 in Cambridge, England - 29 Jan 1984 in Sheffield, England) was the son of Edmund Whittaker. He studied at Edinburgh University and Cambridge. After posts at Edinburgh and Cambridge he became Professor at Liverpool though his tenure was interrupted by service in World War II. He left Liverpool to become Vice-Chancellor of Sheffield University. He worked in Quantum Mechanics and Complex Analysis. *SAU

**1999 Viktor Aleksandrovich Gorbunov**(17 Feb 1950 in Russia - 29 Jan 1999 in Novosibirsk, Russia) He published his first paper in 1973 being a joint work with A I Budkin entitled Implicative classes of algebras (Russian). The implicative class of algebras is a generalisation of quasivarieties. The structural characteristics of the implicative class are studied in this paper. A second join paper with Budkin On the theory of quasivarieties of algebraic systems (Russian) appeared in 1975. In the same year he published Filters of lattices of quasivarieties of algebraic systems (Russian), this time written with V P Belkin. In fact he had written six papers before his doctoral thesis On the Theory of Quasivarieties of Algebraic Systems was submitted. He received the degree in 1978. Gorbunov continued working at Novosibirsk State University, being promoted to professor. He also worked as a researcher in the Mathematics Institute of the Siberian Branch of the Russian Academy of Sciences. *SAU

*** the legs are 4059 and 4060.

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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