**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 (above 1) for which the arithmetic, geometric, and harmonic means of φ(n)(Tne umber 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.

248 = 2

^{8}- 2

^{3}

248 is the only number such that its unique prime factorization is of the form \(p^{p+1}[p^{p+3}-1]\) *Prime Curios

**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

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

**1877**"marked a turning point in the cartography of Mars. On 5 September of that year, Earth and Mars stood in “perihelic opposition,” as Earth came into line between Mars and the sun when the two planets were also nearest to the sun and to each other along their respective elliptical orbits. With the disk of Mars fully illuminated by the sun during this close approach, terrestrial astronomers enjoyed incomparable views, not only on the day of the opposition itself but also in the days and weeks leading up to and following the event. Taking advantage of this rare occurrence, the English amateur astronomer Nathaniel Green departed from his usual observing station—in the back garden of his home in St. John’s Wood, a suburb of London—and traveled with his 13‐inch reflecting telescope all the way to the Portuguese island of Madeira in search of good atmospheric conditions for extended observations. Over two months, Green’s effort was rewarded with forty‐seven nights suitable for Mars observation, sixteen of which he termed “good,” “excellent,” or “superb”; this was fewer than expected but “considerably in excess of the average of an English climate.” During his expedition he produced a series of exquisite sketches that he later compiled into the most detailed map of Mars to date (see Figure 1). The expedition to Madeira was a major event in Green’s avocational career, cementing his status as a serious amateur." *K Maria D Lane,Isis,Vol. 96, No. 4, December 2005

*Mercator and planar projection maps by Nathaniel Green, 1877. Originally published (using reddish‐orange color tones) in Memoirs of the Royal Astronomical Society, 1877–1879, p. 44.

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 an 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

1923 Minor planet (1005) Arago Discovered 1923 September 5 by S. I. Belyavskij at Simeis. Named in honor of François Arago (1786-1853) *NSEC

**1935**“Emmy Noether’s career was full of paradoxes, and will always stand as an example of shocking stagnancy and inability to overcome prejudice 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 University 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

**1637 Ignace-Gaston Pardies**(September 5, 1636 – April 22, 1673) was a French scientist. He died of fever contracted whilst ministering to the prisoners of Bicêtre Hospital, near Paris.

He was born in Pau, the son of an adviser at the local assembly. He entered the Society of Jesus 17 Nov., 1652 . After his ordination he taught philosophy and mathematics at the Lycée Louis-le-Grand in Paris. His earliest scientific work is the Horologium Thaumanticum Duplex (Paris, 1662), in which is described an instrument he had invented for constructing various kinds of sundials. Three years later appeared his Dissertatio de Motu et Natura Cometarum,

published separately in Latin and in French (Bordeaux, 1665). His La Statique (Paris, 1673) argued that Galileo's theory was not exact. This, along with Discours du mouvement local (Paris, 1670), and the manuscript Traité complet d'Optique, in which he followed the undulatory theory of light (which identifies it as a harmonic vibration), form part of a general work on physics which he had planned. Traité complet d'Optique had been studied by Pierre Ango (1640-1694) a confrere of Pardies for his Book L`Optique[1] which he published in 1682 after Pardies early death. The Manuscript has also been mentioned by Christiaan Huygens in his 'Treatise on Light'. Huygens himself mentioned in 1668 that it has been Pardies Theory that the Speed of Light is finite.

He opposed Isaac Newton's theory of refraction and his letters together with Newton's replies (which so satisfied Pardies that he withdrew his objections) are found in the Philosophical Transactions of the Royal Society for 1672 and 1673. A proponent of Mechanism, his Discours de la Connaissance des Bestes (Paris, 1672) combatted Descartes's views on animals, but did so so weakly that many looked on it as a covert defence rather than a refutation, an impression which Pardies himself afterwards endeavoured to destroy. His Elémens de Géométrie (Paris, 1671) was translated into Latin and English. He left in manuscript a work entitled Art de la Guerre and a celestial atlas comprising six charts, published after his death (Paris, 1673–74). His collected mathematical and physical works were published in French (The Hague, 1691) and in Latin (Amsterdam, 1694). He was a member of the academy of anatomist Pierre Michon Bourdelot. *Wik

In the course of the correspondence between Pardies and Newton published in the TRS, Pardies takes his arguments from Grimaldi. Pardies had argued that such a drastic departure from the accepted theory should not be entirely founded on the one experiment of the prism since the radical implication of Newton's paper would overthrow the accepted foundations of geometrical optics. But Pardies gradually comes to Newton's position, making a rather generous admission of error, which precipitated this reply from Newton:

In the observations of Reverend Fr. Pardies, one can hardly determine whether there is more of humility and candor in allowing my arguments their due weight, or penetration and genius in stating objections. *Joseph MacDonnell, S.J. Fairfield Univ Website

Pardies created a series of six beautiful star and constellation maps in the late 17th century. All six map plates join together to make a unified view of the Heavens as seen from the Earth. Plate 5, is shown at right. All six plates and several assembled views are available at *David Rumsey Map Collection

**1667 Girolamo Saccheri**born (September 5, 1667, Sanremo – October 25, 1733). 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

The Renaissance Mathematicus has a great post on how Saccheri stood at the door to fame and turned away.

1725 Jean-Étienne Montucla (5 September 1725 – 18 December 1799) 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

**1946 Kyongae Chang**(September 5, 1946, ) is a South Korean astrophysicist. She is best known for her work on gravitational lensing, including the Chang-Refsdal lens.

Chang was born in Seoul. She worked as a research associate on astrometric binaries with Professors van de Kamp and Heintz at Sproul Observatory from 1969 till 1971. From 1975 until 1980 she worked on a Dr. rer. nat. at Hamburg University, graduating with her work on the Chang-Refsdal lens. The main result was published in Nature in 1979 immediately after the discovery of the first gravitational lens.

She returned to Korea in 1985 and became a professor at Cheongju University. *Wik

Federico Commandino (1509 – September 5, 1575) was an Italian humanist and mathematician.

Born in Urbino, he studied at Padua and at Ferrara, where he received his doctorate in medicine. He translated the works of ancient mathematicians and was responsible for the publication of the works of Archimedes. He also translated the works of Aristarchus of Samos (On the masses and distances of the Sun and the Moon), Pappus of Alexandria (Mathematical collection), Hero of Alexandria (Pneumatics), and Euclid (Elements). Among his pupils was Guidobaldo del Monte. Commandino maintained a correspondence with the astronomer Francesco Maurolico. The proposition known as Commandino's theorem first appears in his work on centers of gravity.(VFR has this date listed as Sep 3). Commandino's Theorem is a nice extension of the concentric properties of medians in a triangle. "The four medians of a tetrahedron concur in a point which divides each tetrahedron median in the ratio 1:3, the longer segment being on the side of the vertex of the tetrahedron." (A proof appropriate for good HS students well versed in 3-D coordinate geometry)

**1667 Henry Oldenburg**died (c. 1619 – 5 September 1677). 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 behavior of atoms and molecules with the large scale properties and behavior 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.

Ważewski 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

Ważewski studied at the Jagiellonian University in 1914–1920. He started from physics but very quickly turned to mathematics. Ważewski was a pupil of Zaremba.

He spent three years in Paris and got a doctoral diploma from Sorbona.

In his doctoral dissertation he obtained interesting results on dendrites (locally connected continua not containing simple closed curves). *Ciesielski & Pogoda, EMS Newsletter December 2012

**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 :

*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