**"Life is good for only two things, discovering mathematics and teaching mathematics"**

Siméon Poisson

**The 245th day of the year**; 245 is the fifth StellaOctangula number. The sum of the 5th octahedral number (85) and eight of the fourth tetrahedral numbers (20). 245 =85 + 8 (20)

245 is also the sum of three consecutive squares, \(245 = 8^2 + 9^2 + 10^2 \)

There are 245 odd entries in the first 33 rows of the Arithmetic Triangle.

245 is also the 46th prime plus 46, 199+46=245

**1488**The Plimpton Library has a copy of Anianus, Computus Manualis combined with Boethius, Arithmetica, which is probably the first book on mathematics printed in Strasburg. It DIDN'T happen on this date but I include it here because it has the first known printing of the little mnemonic that begins, “Thirty days bath September,”

*historyofscience.com

**1672**Hooke's diary records " Calculated lengths of Glasses." from Hooke's Journal *Robert Hooke @HookesLondon This was done using Hookes "musical cylinder" or string phone. In July 1664 Hooke produced an experiment to show the number of vibrations of an extended String, made in a determinate time, requested to give a certain Tone or Note, by which it was found that "a Wire making two hundred seventy two vibrations in one second of time sounded G Sol Re Vt. in the Scale of all Musick". Hooke had found that middle C had 272 beats a second, and on 1st September 1672 Hooke noted the he had invented an easy way for "a musical cylinder with pewter tips pinched between cylindrick rings". *Daniel P McVeigh, "An Early History of the Telephone 1664-1865"

**1698**The last Russian year to begin on September 1. January 1, 1699 began a new year. *VFR but still on the Julian Calendar. Russia would not switch to the Gregorian calendar until 24 January 1918 when the Council of People's Commissars issued a Decree that Wednesday, 31 January 1918 was to be followed by Thursday, 14 February 1918, thus dropping 13 days from the calendar. *Wik

1742 a letter from Euler to Niklaus I Bernoulli on pentagonal number theorem. Euler also notes in this letter that the coefficients of the terms in the series

1 + 1n + 2n

2 + 3n

3 + 5n

4 + 7n

5 + 11n

6 + 15n

7 + 22n

8 + 30n

9 + 42n

10 + 56n

11 + etc.

give the number of different ways in which the exponent of the term can be made by addition, i.e. that it is the generating function for the (unrestricted) partition function. Euler then writes: “This series moreover arises from division, if unity were divided by \((1 − n)(1 − n^2)(1 − n^3)(1 − n^4)(1 − n^5 )\) etc., which product if expanded gives this expression \( 1 − n − n^2 + n^5 + n^7 − n^{12} − n^{15} + n^{22} + n^{26} − n^{35} − etc\) . where the precise way in which the exponents proceed I have not been able to penetrate, although by induction(

*Euler means experimentation and extrapolation of a pattern, not the proof by induction we use today*) I have concluded for no other exponents to occur, unless they are contained in the formula (3xx ± x)/2; and this is such that the powers of n have the + sign if the exponents arise with an even number substituted for x”. *Jordan Bell, Euler and the Pentagonal Number Theorem

**1849**On the night of September 1, 1849, the nearly full Moon appeared over the town of Canandaigua, New York. At 10:30 P.M., Samuel D. Humphrey slid a highly polished, silver-plated copper sheet measuring

**2¾x1¾**inches into his camera, which was pointed at the Moon. After developing the plate with mercury vapor, he sent his daguerreotype to Harvard College. This is believed to be the oldest existing photo of the moon.

Many sources (Wikipedia, for instance) claim this is actually the first known photo of the moon was taken on March 23, 1840 (see my page for that date) by John W. Draper of New York City. Draper is credited with making a clearer daguerreotype of the (full) Moon in March 1840, and he sent a letter with a copy of the image to John Herschel. Others believe his original photo was destroyed in a fire. This may be due to some confusion about a photo taken the previous year by Daguerre, which burned in his laboratory fire. *PB notes

**1854**It was on this day that John Snow became aware of the cholera epidemic, and began his studies leading to the isolation of the Broad Street Pump. "Early on the morning of September 1st, 1854, in the Berwick Street district of St. James's, Westminster, where I had spent some hours of the preceding day without hearing any mention of cholera-and where, in former epidemics, the mortality from that disease had been inconsiderable-I was asked to visit a house in which lay, already collapsed, four persons who had been seized with cholera during the night; and, on leaving this house, whichever way I turned, I came upon similar scenes. At noon, when I met my brother curate and the Scripture-reader for a short time in the vestry of St. Luke's, Berwick Street, I learned that they had each been occupied all the morning in the same way as myself. The rest of the day was spent in the same manner; and, as an indication of the severity of the outbreak, I record that, of all the cholera patients visited by me on that day, only one recovered." *The John Snow Archives, For those who are unfamiliar with the case, a beautiful book:

**1859**First recorded observation of a solar flare. Richard Christopher Carrington English astronomer was the first to map the motions of sunspots and thus discover from them that the Sun rotates faster at the equator than near the poles (equatorial acceleration). He observed that the sunspots were not attached to any solid object, and also discovered the movement of sunspot zones toward the Sun's equator as the solar cycle progresses. On 1 Sep 1859, Carrington was the first to record the observation of a solar flare. *TIS Richard Hodgson, another English amateur astronomer, independently made the observations of the same solar flare. *Wik He reported his Description of a Singular Appearance seen in the Sun in the Monthly Notices of the Royal Astronomical Society (1860), "While engaged in the ... observation of ... solar spots ... two patches of intensely bright and white light broke out. ... I therefore noted down the time, ... and seeing the outburst to be very rapidly on the increase ... I hastily ran to call some one to witness ... and on returning within 60 seconds, was mortified to find that it was already much changed and enfeebled. Very shortly afterwards the last trace was gone. In this lapse of 5 minutes, the two patches of light traversed a space of about 35,000 miles."*TIS

**1861**(Sept ?) Sir Charles Bright and Mr. Latimer Clark proposed the names of ohm, volt, and farad for the practical units based on the centimetre-gramme-second absolute system, Sir William Thomson gave a cordial support; and on his initiative was formed the famous Committee of Electrical Standards of the British Association, which year by year has done so much to carry to perfection the standard and the methods of electrical measurement. *IEC History This seems to have been the first time a unit of measure was named for a famous scientist.

**In 1869**, Cleveland Abbe began a weather reporting system in Cincinnati, Ohio and published a weather bulletin which contained his first weather forecast on September 1, 1869. In the United States, on October 21, 1743, Benjamin Franklin had tracked a hurricane for the first time. It was the first recorded instance in which the progressive movement of a storm system was recognized. A photo gallery of the development of the US Weather Bureau is available here:

In 1847, the first weather warnings were issued via telegraph. In 1870, the National Weather Service was born. *Weather.about.com

**1902**The French film pioneer George Méliès presented the very first science fiction movie to the stunning public of the Paris Olympia theater. *Yovisto

1916 The first (late) summer meeting of the MAA was held at MIT, September 1-2, 1916. *MAA

**1920**The central limit theorem didn't get it's name until 1920 even though the first version of the theorem was published in 1733. *Probability Fact @ProbFact,

The first version of this theorem was postulated by Abraham de Moivre who used the normal distribution to approximate the distribution of the number of heads resulting from many tosses of a fair coin. The actual term "central limit theorem" (in German: "zentraler Grenzwertsatz") was first used by George Pólya in 1920 in the title of a paper, "Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem", in Mathematische Zeitschrift. (9/1/1920) Pólya referred to the theorem as "central" due to its importance in probability theory. According to Le Cam, the French school of probability interprets the word central in the sense that "it describes the behaviour of the centre of the distribution as opposed to its tails". *Wik

**1922**British chemist and physicist Francis W. Aston was awarded the Nobel Prize in Chemistry. He developed the mass spectrometer, a device that separates molecular fragments of different mass and measures them with remarkable accuracy. Using the spectrometer, Aston discovered that neon had two isotopes, \(^{20} \)Ne and \(^{21} \)Ne, and was awarded the 1922 Nobel Prize for this work. *RSC.org

**1936**The ﬁrst meeting of the Association for Symbolic Logic was held in Cambridge, Massachusetts. Rudolf Carnap presented an invited address, “Truth in Mathematics and Logic,” to an audience of three hundred. *VFR

**1939**Robert Oppenheimer wrote a seminal paper on black holes that went mostly overlooked and is still relatively un-noted because it was published on the same day that WWII began with German invasion of Poland.

**1939**World War II began, as German troops marched into Poland.

1963 The scientific community learned about rotating black holes in general relativity #OTD in 1963, when Roy Kerr's groundbreaking paper appeared in Physical Review Letters. hat tip @RobertMcNees

**1964**The Ryukyu Islands issued a stamp commemorating the opening of the Ryukyu Islands–Japan microwave system for telephone and telegraph messages. Pictured is a parabolic antenna, one of the many applications of the reﬂective properties of the conics. [Scott #123] *VFR

**1967**Harvey Friedman was appointed Assistant Professor of Mathematics at Stanford University, just three weeks before his nineteenth birthday. This is the youngest at which anyone has begun a university career. He is now a distinguished logician at The Ohio State University. (Guinness) See September 23, 1948, September 30, 1717, and November 19, 1982. *VFR

**In 1997**, the discovery of a new sub-atomic particle was announced, called the "exotic meson." Scientists speculated that the exotic meson might comprise four quarks, unlike all other known particles, which have three. The research team included physicists at Brookhaven National Laboratory, Upton, N.Y., and other facilities in the U.S. and Russia.*TIS

**1994**U.S. Library of Congress starts "Virtual Library" project.The LOC holds the first of several meetings to plan a project to convert its materials to digital form so they will be accessible via computer networks to students and researchers around the world. The "virtual library" project could also save rare materials that are degrading or have been vandalized, as well as saving space for the library, whose belongings fill up 575 miles of shelving. At the time of the initial meeting -- at which librarians and technical experts from several major computer companies discussed strategy and funding -- the library hoped to have its most vulnerable materials digitized by the year 2000. *CHM

**2008**John D. Barrow is appointed Gresham Professor of Geometry. He had previously held the Gresham chair in Astronomy, (2003-2007). *Wik

**1659 Joseph Saurin**(September 1, 1659 at Courtaison – December 29, 1737 at Paris) . In the early seventeenth century he defended the calculus against the criticisms of Michael Rolle. *VFR He became friends with de L'Hôpital, Malebranche and Varignon but, by 1702, he was in dispute with Rolle over the calculus. This came about because of his role as mathematics editor of the Journal des Sçavants. He appealed to the Académie Royal des Sciences but, although Saurin was correct, they had no wish to come out against Rolle who was a member. Perhaps to be diplomatic, Saurin was elected to the Académie Royal des Sciences in 1707. *SAU In the Paris Académie Royale des Sciences in July of 1700, Michel Rolle voiced opposition to the use of infinitesimal magnitudes.Rolle was not alone in this project, for he allied himself with several mathematical conservatives, including the Abbé Jean Gallois and the Abbé Thomas Gouye, both of whom venerated the Greek standards of rigor and had significant reservations about the use of infinitesimal methods. Rolle's criticisms were later published in the memoir Du nouveau systême de l'infini, which he opened by declaring that

We have always regarded geometry as an exact science, and also as the source of the exactness which is spread throughout all the other parts of mathematics. We see among its principles only true axioms: all the theorems and all the problems proposed here are either solidly demonstrated or capable of a solid demonstration. And if it should happen that any false or less certain principles slip in, they should be at once banished from this science.*Leibniz on the Foundations of the Calculus:

But it seems that this character of exactitude no longer reigns in geometry, ever since we became entangled in the new system of the infinitely small. For myself, I do not see that it has produced any new truth, and it seems to me that it often leads to error.

The Question of the Reality of Infinitesimal Magnitudes, Douglas M. Jesseph

**1826 Alfred Ely Beach**(1 Sep 1826; 1 Jan 1896) American inventor and publisher, whose Scientific American helped stimulate 19th-century technological innovations and became one of the world's most prestigious science magazines. Beach himself invented a tunneling shield and built the pneumatic tube subway (1870). In 1856 he won First Prize and a gold medal at New York's Crystal Palace Exhibition. Beach had invented a typewriter for the blind. It resembled the modern typewriter in the arrangement of its keys and typebars, but embossed its letters on a narrow paper strip instead of a sheet. *TIS Beach purchased SA while the paper was still a small weekly journal with a circulation less than 300. It was bought for $800 in July 1846 by 20-year-old Beach as editor, and Orson Desaix Munn.

**1835 William Stanley Jevons**,(1 September 1835 – 13 August 1882) Political economist. He did early work in symbolic logic and built an early logic machine, the ﬁrst that could solve complicated problems faster than they could be solved by hand.*VFR Irving Fisher described his book The Theory of Political Economy (1871) as beginning the mathematical method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons had written in his Principles of Science, p. 123, "Can the reader say what two numbers multiplied together will produce the number 8616460799 ? I think it unlikely that anyone but myself will ever know." This became known as Jevons' Number and was factored by Derrick Norman Lehmer in 1903. (Reader, try your hand.)

In economics, the Jevons paradox (sometimes Jevons effect) is the proposition that technological progress that increases the efficiency with which a resource is used tends to increase (rather than decrease) the rate of consumption of that resource. *Wik

**1902 Dirk Brouwer**(1 Sep 1902; 31 Jan 1966) Dutch-born U.S. astronomer and geophysicist known for his achievements in celestial mechanics, especially for his pioneering application of high-speed digital computers for astronomical computations. While still a student he determined the mass of Titan from its influence on other Saturnian moons. Brouwer developed general methods for finding orbits and computing errors and applied these methods to comets, asteroids, and planets. He computed the orbits of the first artificial satellites and from them obtained increased knowledge of the figure of the earth. His book, Methods of Celestial Mechanics, taught a generation of celestial mechanicians. He also redetermined astronomical constants.*TIS

**1648 Marin Mersenne**died (8 September 1588 – 1 September 1648).Often called the center of the scientific world in the early 17th century for his communication with and between many of the most prominent scientific minds of the period. He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, reported in his

*Cogitata Physico-Mathematica*in 1644. He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings. *Wik

**1687 Henry More**(October 12, 1614 – September 1, 1687) was an English philosopher of science whose ideas may have influenced Newton. One other thing about Henry More which we should discuss is his relation to Newton. Newton was born close to Grantham and attended the Free School in Grantham. In fact he had lodgings in Grantham for seven years with a Mr Clark, the brother of a teacher at the Free School. More, who was about 30 years older than Newton, often returned to his home town of Grantham and when he did so he lived with one of the two Clark brothers. Therefore when More was a major figure at Cambridge he must have got to know the young pupil Newton. We certainly know that there was contact between Newton and More up till the time More was around 70 years of age.

Did More's ideas of space influence Newton? It is impossible to say with any certainty, but we can certainly note that Newton's idea of absolute space and time was crucial to his physics and that this notion of space is closely related to that put forward by More in his arguments against Descartes. Also in terms of gravity, for Descartes it was necessary to have an interaction through matter between the bodies. For Newton gravity was a force which acted through empty space and although he does not appear to have identified space with God as More did, nevertheless the spiritual aspect of space supported Newton's gravitational theories. *SAU

**1716 Heinrich Meissner**(April 20th 1644 in Hamburg - September 1 1716 Hamburg) was a co-founder of the Hamburg Masters and computing Mathematical Society in Hamburg. This is the oldest existing mathematical society in the world.

From 1688 until shortly before his death he was "writing, arithmetic and upper-master" of the parish school of St. Jacobi .

Meissner founded (Jan 2, 1690) along with Valentin Heins 'art-accounting practicing Society ", which became Hamburg Mathematical Society .

Meissner published a whole series of books and magazines. Worth mentioning are especially the key star and Algebrae, a textbook on algebra in the German language, and the Teutsche Euclid, a translation of the first two books in the "Elements" of Euclid with extensive annotations. *Wik

**1908 Aleksandr Nikolayevich Korkin**(3 March [O.S. 19 February] 1837–September 1, 1908) was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School*Wik

**1982 Haskell Brooks Curry**(12 Sep 1900, 1 Sep 1982)American mathematician who was a pioneer of modern mathematical logic. His research in the foundations of mathematics led him to the development of combinatorial logic. Later, this seminal work found significant application in computer science, especially in the design of programming languages. Curry worked on the first electronic computer, called ENIAC, during WW II. He also formulated a logical calculus using inferential rules. In 1942, he published Curry's paradox, which occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules. *TIS

**1982 Ludwig Georg Elias Moses Bieberbach** (4 December 1886, 1 September 1982 wrote a habilitation thesis in 1911 about groups of Euclidean motions – identifying conditions under which the group must have a translational subgroup whose vectors span the Euclidean space – that helped solve Hilbert's 18th problem. He worked on complex analysis and its applications to other areas in mathematics. He is known for his work on dynamics in several complex variables, where he obtained results similar to Fatou's. In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic function to map the open unit disc injectively into the complex plane in terms of the function's Taylor series.*Wik

**1988 Luis Walter Alvarez**(June 13, 1911 – September 1, 1988) was an American experimental physicist, inventor, and professor who was awarded the Nobel Prize in Physics in 1968. The American Journal of Physics commented, "Luis Alvarez was one of the most brilliant and productive experimental physicists of the twentieth century.

In 1940 Alvarez joined the MIT Radiation Laboratory, where he contributed to a number of World War II radar projects, from early improvements to Identification Friend or Foe (IFF) radar beacons, now called transponders, to a system known as VIXEN for preventing enemy submarines from realizing that they had been found by the new airborne microwave radars. The radar system for which Alvarez is best known and which has played a major role in aviation, most particularly in the post war Berlin airlift, was Ground Controlled Approach (GCA). Alvarez spent a few months at the University of Chicago working on nuclear reactors for Enrico Fermi before coming to Los Alamos to work for Robert Oppenheimer on the Manhattan project. Alvarez worked on the design of explosive lenses, and the development of exploding-bridgewire detonators. As a member of Project Alberta, he observed the Trinity nuclear test from a B-29 Superfortress, and later the bombing of Hiroshima from the B-29 The Great Artiste.

After the war Alvarez was involved in the design of a liquid hydrogen bubble chamber that allowed his team to take millions of photographs of particle interactions, develop complex computer systems to measure and analyze these interactions, and discover entire families of new particles and resonance states. This work resulted in his being awarded the Nobel Prize in 1968. He was involved in a project to x-ray the Egyptian pyramids to search for unknown chambers. With his son, geologist Walter Alvarez, he developed the Alvarez hypothesis which proposes that the extinction event that wiped out the dinosaurs was the result of an asteroid impact. *Wik

**1982 Haskell Brooks Curry**(12 Sep 1900; 1 Sep 1982)American mathematician who was a pioneer of modern mathematical logic. His research in the foundations of mathematics led him to the development of combinatory logic. Later, this seminal work found significant application in computer science, especially in the design of programming languages. Curry worked on the first electronic computer, called ENIAC, during WW II. He also formulated a logical calculus using inferential rules. In 1942, he published Curry's paradox, which occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules.*TIS

**2006 Warren J. Mitofsky**, (17 September 1934 - 1 September 2006)While working at the Census Bureau in the 1960s, he and a colleague, Joseph Waksberg, began to devise a random-digit dialing (RDD) system that now bears both their names.

Mr. Mitofsky went to work at CBS News in 1967. Not long afterwards, he organized the first "exit poll" in a Kentucky gubernatorial election, with his first national exit poll being in 1972. He directed the CBS News Election and Survey Unit until 1990, leading, in 1975, to the joint effort with the NYTimes, the CBS News/New York

Times Poll (which The Times calls the New York Times/CBS News Poll),

which he directed until 1990.

Since 2003, Mitofsky, considered the "Father of Exit Polling" by many, led election-night analysis for the News Election Pool, providing exit-poll results and projections. (Mitofsky disliked the term "exit poll"; he preferred "Election Day survey".)

In exit polls on Election Day in 2004, Mitofsky's early exit polls found Senator John Kerry leading over President Bush, which led some in the news media to prepare for Senator Kerry becoming President Kerry. But such was too premature, as Mitofsky readily acknowledged, later discovering that the pro-Kerry exit-poll lead was caused by Republicans refusing to participate at a greater rate than Democrats in the exit polls. [Guess this shows the importance of not ignoring nonresponse.]

However, despite all this, Mitofsky will probably be best remembered by many for his efficient method of sampling telephone numbers using random-digit dialing (RDD), which is now known as the Mitofsky-Waksberg Method. In 1970, Mitofsky wrote an unpublished CBS News memorandum titled "Sampling of Telephone Households" that helped make his name a household word in public-opinion polling. Eight years later, Joseph Waksberg published an analogous paper, "Sampling Methods for Random Digit Dialing", in the prestigious Journal of the American Statistical Association (JASA), thus resulting in the Mitofsky-Waksberg Method appellation.

The Mitofsky-Waksberg Method of RDD is a cluster-sampling method

for sampling residential telephone numbers that greatly increases

the percentage of calls that do reach residential households. *David Bee

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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