**Errors using inadequate data are much less than those using no data at all.**

~Charles Babbage

The 248th day of the year; 248 is the smallest number n>1 for which the arithmetic, geometric, and harmonic means of φ(n)(

*The number of positive integers less than n that are relatively prime to it, 120*) and σ(n) (

*the sum of positive integers less than n that are factors of n, 480*) are all integers.

**EVENTS**

**1666**The ﬁre of London was extinguished after four days and nights. Some 13,000 buildings were destroyed. It took a lot of architects to rebuild. Sadly for mathematics, a talented young mathematician, who was also something of an architect was available. This explains how mathematics lost Christopher Wren. *VFR

1777 In a memoir written on this day, Lavoisier introduced the term "Oxygine" (from the Greek for acid former) into scientific language. *Brody & Brody, The Science Class You Wish You Had

In

**1857**, Charles Darwin, now 48 years old, had not yet published his theory of evolution. On this day, he sent a letter to Asa Gray, a Harvard botanist, discussing his theory. The encouragement which followed from Gray and others, and new knowledge that Alfred Wallace had independently developed the same theory, prompted Darwin to end 20 years of indecision and publish his ideas.*TIS

1883 An aging Sylvester,longing for the security of his homeland sent a letter to Cayley, "If I am not accepted at Oxford, I shall buy and annuity or study abroad or go into business with my small acquired capital. He would write President Gilman of Johns Hopkins to resign a week later, to take effect Jan 1 of the following year. *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900

**1935**“Emmy Noether’s career was full of paradoxes, and will always stand as an example of shocking stagnancy and inability to overcome preudice on the part of the Prussian academic and civil service bureaucracies. Her appointment as Privatdozent in 1919 was only possible because of the persistence of Hilbert and Klein, who overcame some extreme opposition from reactionary university circles. The basic formal objection was the sex of the candidate: ‘How can we allow a woman to become a Privatdozent! after all, once she is a Privatdozent, she may become a Professor and member of the Uiversity Senate; is it permissible for a woman to enter the Senate?’ This provoked Hilbert’s famous reply: ‘Meine Herren, der Senate is ja keine Badenanstalt, warum darf eine Frau nicht dorthin! [Gentlemen, the Senate is not a bathhouse, so I do not see why a woman cannot enter it!]’”—from an address, “In Memory of Emmy Noether,” delivered by P. S. Alexandrov, then president of the Moscow Mathematical Society. Quoted from Emmy Noether: 1882–1935, by Auguste Dick. Birkh¨auser, 1981. *VFR

**1945**Romania issued two postage stamps to commemorate the 50th anniversary of the mathematics journal Gazeta Mathematica. Editors I. N. Ionescu (1870–1948), Gheorge Titeica (1873–1939), A. O. Idachimescu (1895–1943), and Vasile Cristescu 1869–1929) are pictured on the ﬁrst of them. [Scott #596-7]. *VFR

**1980**The last IBM 7030, or STRETCH, mainframe computer is decommissioned at Brigham Young University. STRETCH was the result of an intensive R&D project started at IBM in 1955. The goal: build a super-computer 100 to 200 times as powerful as anything yet yet built. The premier customer: Los Alamos Scientific Laboratory (run by the Atomic Energy Commission), which was designing atomic weapons. *CHM

**1667 Girolamo Saccheri**born. He was the ﬁrst to publish the eﬀects of denying Euclid’s ﬁfth postulate. *VFR He tried to prove the fifth postulate of Euclid, which can be stated as, "Through any point not on a given line, one and only one line can be drawn that is parallel to the given line." Euclid saw the proof was not self-evident, yet neither did he provide one; instead he accepted it as an assumption. Subsequently many mathematicians tried to prove this fifth postulate from the remained axioms - and failed. Saccheri took the novel approach of first assuming that the postulate was wrong, then followed the all consequences seeking any one contradiction that then leaves the only original postulate as the only possible solution. In the process, he came close to discovering non-Euclidian geometry, but gave up too early. *TIS

**1725 Étienne Montucla**was a French historian of mathematics who wrote in 1754 a history of the problem of squaring the circle. He also wrote the first truly comprehensive classical history of mathematics,Histoire des mathématiques. Late in his life, Montucla's friends persuaded him to work on a new edition of his famous Histoire des mathématiques. In August 1799 Montucla published new editions through Agasse in Paris of the two volumes originally published in 1758. Montucla extensively revised and enlarged the two volumes. He had intended to extend his cover of history to the end of the 18th century and part of the third volume on this topic was printed by the time he died, four months after the publication of the new editions of 1799. Lalande, with the help of some other scientists, completed volumes three and four to give the coverage that Montucla had intended. Volume three covered 18th century pure mathematics, optics and mechanics in 832 pages, while the fourth volume covered 18th century astronomy, mathematical geography and navigation in 688 pages.*SAU

**1850 Eugen Goldstein**(5 Sep 1850; 25 Dec 1930)physicist who discovered and named canal rays (1886) which emerge through holes in the anodes of low-pressure electrical discharge tubes (later shown to be positively charged particles). Earlier, he coined the term "cathode ray" (1876) emitted from a cathode. He was the first to see that they could cast a shadow, and were emitted at right angles to the surface. He also investigated the wavelengths of light emitted by metals and oxides when canal rays impinge on them. When the Berlin Urania, opened in 1889 it had five scientific departments and a "science theatre", it was Goldstein who had recommended the "hall of physics in which the visitor could experiment on his own". Students of his that continued his work included Wien and Stark. *VFR

**1879 Frank Baldwin Jewett**(5 Sep 1879; 18 Nov 1949) the U.S. electrical engineer who directed research as the first president of the Bell Telephone Laboratories, Inc., (1925-40). Jewett believed that the best science and technology result from bringing together and nurturing the best minds. Under his tenure Bell Labs laid the foundation for a new scientific discipline, radio astronomy, and transformed movies by synchronizing sound to pictures. Bell Labs was the first to transmit television over a long distance in the U.S. and designed the first electrical digital computer. Bell Labs won its first Nobel Prize in physics for fundamental work demonstrating the wave nature of matter.*TIS

**1927 William Moser**(5 Sep 1927;28 Jan 2009) My mathematical interests are: presentations for finite groups; combinatorial enumerations (e.g., counting restricted permutations and combinations); problems in discrete and combinatorial geometry. *From his page at McGill Univ.

In March 2003 Moser was interviewed by Siobhan Roberts who was working on her major work on Coxeter King of Infinite space. He recounted the following story

"Donald made many great contributions to mathematics. I made one great contribution," recounted Moser. Moser's opportunity came at the end of Coxeter's 1955 summer of roving lectures, after his session in Stillwater, at Oklahoma State University. Moser drove down to meet Coxeter and serve as his assistant, taking detailed notes of the well-polished lectures. "At the end of the summer we drove north, to civilisation," said Moser wryly. "We were in my car and Donald asked me if he could drive. It was a new car. Indeed it was the first car I had ever purchased, a green 1955 Plymouth 2-door. I paid $2,000 for it and drove it to Oklahoma. But I agreed. I was surprised to see that he was an aggressive driver. At one point he was trying to pass a car while driving up a hill on a 2-lane highway. I immediately perceived that this was not a prudent thing to do. He tried to coax the car to go faster but it wouldn't respond. At the last moment I shrieked at him, 'Pull back, pull back'. I was probably his only student to shriek at him. He began to pull back and at that moment a truck came over the hill. He managed to get back in the right lane just in time. I HAD SAVED HIS LIFE! And mine. But saving Coxeter's life was my greatest contribution to mathematics."*SAU

**1575 Frederico Commandino**was an Italian mathematician who published important translations of works of the Ancient Greek mathematicians.*SAU (VFR has this date listed as Sep 3).

**1667 Henry Oldenburg**died. He was one of the foremost intelligencers of Europe of the seventeenth century, with a network of correspondents to rival those of Fabri de Peiresc, Marin Mersenne and Ismaël Boulliau. After the Restoration he became an early member (original fellow) of the Royal Society (founded in 1660), and served as its first secretary along with John Wilkins, maintaining an extensive network of scientific contacts through Europe. He also became the founding editor of the Philosophical Transactions of the Royal Society. Oldenburg began the practice of sending submitted manuscripts to experts who could judge their quality before publication. This was the beginning of both the modern scientific journal and the practice of peer review. He was interred on 7 September at St Mary the Virgin, Bexley. His widow died ten days later. *Wik

**1857 Isidore Auguste Marie François Xavier Comte**(17 Jan 1798, 5 Sep 1857)French philosopher and mathematician. a founder of the discipline of sociology and of the doctrine of positivism. He may be regarded as the first philosopher of science in the modern sense of the term. *Wik

**1906 Ludwig Eduard Boltzmann**(February 20, 1844 – September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory at a time when that scientific model was still highly controversial. *Wik Trivia: Boltzmann's famous equation S = K log W (where S = entropy, K = Boltzmann's constant, and W = probability of a particular state) was inscribed as an epitaph on Boltzmann's tombstone. *Wik After obtaining his doctorate, he became an assistant to his teacher Josef Stefan. Boltzmann's fame is based on his invention of statistical mechanics, independently of Willard Gibbs. Their theories connected the properties and behaviour of atoms and molecules with the large scale properties and behaviour of the substances of which they were the building blocks. He also worked out a kinetic theory of gases, and the Stefan-Boltzmann law concerning a relationship between the temperature of a body and the radiation it emits. His firm belief and defense of atomism (that all matter is made of atoms) against hostile opposition to this new idea, may have contributed to his suicide in 1906. *TIS

**1917 Marian Smoluchowsk**i (28 May 1872 - 5 September 1917) was an ethnic Polish scientist in the Austro-Hungarian Empire. He was a pioneer of statistical physics and an avid mountaineer. Smoluchowski scientific output included fundamental work on the kinetic theory of matter. In 1904 he was the first who noted the existence of density fluctuations in the gas phase and in 1908 he became the first physicist to ascribe the phenomenon of critical opalescence to large density fluctuations. His investigations also concerned the blue colour of the sky as a consequence of light dispersion on fluctuations in the atmosphere, as well as explanation of Brownian motion of particles. At that time Smoluchowski proposed formulae which presently carry his name.

In 1906, independently of Albert Einstein, he described Brownian motion. Smoluchowski presented an equation which became an important basis of the theory of stochastic processes. *Wik

**1930 Johann Georg Hagen**(6 Mar 1847, 5 Sep 1930) Austrian Jesuit priest and astronomer who made a catalog of variable stars (1890-1908). Working at the Vatican Observatory he reexamined for accuracy the listing of all of the NGC (New General Catalogue of Nebulae and Star Clusters) objects north of about -30 degrees. He published lists of errata in the NGC. During his observations, he observed dark nebulae, tenuous dark clusters of interstellar matter sometimes known as Hagen's clouds. These strange clouds have not been recorded by others, and are now attributed to optical illusions associated with visual observations. Jesuits have been involved in astronomy since 1551 when Fr. Christoph Clavius, SJ, a mathematician and astronomer helped Pope Gregory XIII reform the calendar.*TIS

**1948 Richard C(hace) Tolman**(4 Mar 1881, 5 Sep 1948) was an American physicist and chemist who demonstrated that electrons are the charge-carrying entities in the flow of electricity, and also made a measurement of its mass. During the Manhattan Project of WW II, he was the chief scientific adviser to Brig. General Leslie Groves, the head of military affairs overseeing the development of the atomic bomb. After the war he was adviser to the U.S. representative to the United Nations Atomic Energy Commission. *TIS

**1972 Tadeusz Ważewski**(24 September 1896 – 5 September 1972) was a Polish mathematician who made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. He is most famous for applying the topological concept of retract, introduced by Karol Borsuk to the study of the solutions of differential equations.*Wik

**1994 Shimshon Avraham Amitsur**(August 26, 1921 – September 5, 1994) was a Jewish mathematician. He is best known for his work in ring theory, in particular PI rings, an area of abstract algebra.*Wik

Credits

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum