Pat'sBlog

Wednesday, 2 September 2026

A Bird in the Hand is worth... a Pigeon Hole Principle

Sometimes problems that seem very hard, can be very easy if they are viewed in the right way, and one of those easy ways to make some hard problems manageable is the Pigeon-Hole Principle. Over the last few weeks seems like lots of problems involving this idea have shown up, so I thought I would bring it to you.
The basic idea is so easy any sixth grader would agree; if you have two boxes, and you are going to put three balls in the boxes, then at least one box will get more than one ball..... "well, Duh!" they answer... and yet... it seems easier to apply than it might be. Now that you know the secret, try these two problems. I'll post the answer down lower on the page where you must not look until you take a few minutes to ponder the problems.
Here is the first from a recent blog I read: "39 people are attending a large, formal dinner, which must of course occur at a single, circular table. The guests, after milling about for a while, sit down to eat. It is then pointed out to them that there are name cards labeling assigned seats, and not a single one has sat in the seat assigned to them. Prove that there is some way to rotate the table so that at least two people are in the correct seats."
This one seems tougher, but really isn't, it just requires a different way of thinking. "Suppose you pick six unique integers from 1 to 1000. Prove that at least two of them must have a difference that is a multiple of five.
Before I give you the answers, I will throw in a little cultural information that may amuse and entertain you. The same axiom is often named in honor of Dirichlet who used it in solving Pell's equation. In a discussion on a history group a few years ago Julio Cabillon added that there are a variety of names in different countries for the idea. His list included "le principe des tiroirs de Dirichlet", French for the principle of the drawers of Dirichlet, and the Portuguese "principio da casa dos pombos" for the house of pigeons principle and "das gavetas de Dirichlet" for the drawers of Dirichlet. It also is sometimes simply called Dirichlet's principle and most simply of all, the box principle. Jozef Przytycki wrote me to add, "In Polish we use also:"the principle of the drawers of Dirichlet" that is 'Zasada szufladkowa Dirichleta' ". You just can't have TOO many names for a really useful idea.
Ok, The Proofs... for number one... Suppose you handed each person a number that was how many seats they needed to move to the right to find their assigned seat. Since no one is at the right seat, the number can not be zero or thirty-nine. SO each of the people has a number between 1 and 38...wait, there are 39 people...two of them (at least) must be the same distance away from their assigned seats.... admit it…..that’s pretty cool. (I have a slight question about whether this actually proves the solution of "rotating the table" to put two in their correct seats. Suppose we know that persons A and B are in each others seats and 5 seats apart. Rotating the table five seats in either direction would only put one of them in their correct seat. Maybe all we proved is that there are , at least, two people who are the same distance from their seat. If we had specified how far away in a clockwise direction they are from their correct seat, we would have a solution to the rotation of the table problem.)
For number two it is sort of the same idea, but you have to think about how much each number would have for a remainder if you divided them by five. The only possible choices are 0, 1, 2, 3, or 4... , five different remainders, but there are six numbers, so two of them have the same remainder...and two numbers that have the same remainder on division by five, are a multiple of five apart.... think of 1,6, 11, etc for remainders of one. If you want to read more about how remainders can play a part in solving problems, see my blog on "casting out sevens" (And other primes)

And for some history about this beautiful problem solving idea, see this.

On This Day in Math - September 2

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

D MacHale, Comic Sections (Dublin 1993)
(I realize that a whole generation has grown up who have no idea what "New Mathematics" means, my apologies to them for a dated quote)

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 , 199+46=245 (is there a mathematical significance for these numbers, or just a nice curiosity? Serious question.)

See Math Facts for every Year Day here.

EVENTS

1666 Five days previously Wren had visited Old St. Paul's Cathedral to determine the reconstruction needs for the decaying old building. During the night of Sep 2, and for the next five days, the Great Fire of London will burn out about 7/8 of the city of London and greatly alter Wren's work at St Paul's. [The Great Fire of is supposed to have started in the house of King Charles II's baker on Pudding Lane near London Bridge.*@History Magazine]

Image from Wikipedia,

In 1752, today was the last day of the Julian calendar in Great Britain and the British colonies; the Gregorian Calendar designed to correct the extra leap year day problem went into effect the next day with tomorrow being September 14, hence 11 days were dropped. Most other countries made the adjustment in 1582. *TIS

Some historians suggested there had been riots, the oft called the Calendar Riots of 1752. These claims of civil unrest and rioters demanding “Give us our eleven days” may have arisen through a misinterpretation of a contemporary painting by William Hogarth. His 1755 painting entitled: “An Election Entertainment” refers to the elections of 1754 and depicts a tavern dinner organised by Whig candidates. A stolen Tory campaign banner with the slogan, “Give us our Eleven Days” can be seen lower right (on the black banner on the floor under the seated gentleman’s foot). The Tories can be seen outside the window, demonstrating.Claims of civil unrest and rioters demanding “Give us our eleven days” may have arisen through a misinterpretation of a contemporary painting by William Hogarth. His 1755 painting entitled: “An Election Entertainment” refers to the elections of 1754 and depicts a tavern dinner organised by Whig candidates. A stolen Tory campaign banner with the slogan, “Give us our Eleven Days” can be seen lower right (on the black banner on the floor under the seated gentleman’s foot). The Tories can be seen outside the window, demonstrating.

1808 Gauss writes Wolfgang Bolyai: “It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.” * Mathematical Circles Squared,Howard Eves, pg 113

1885 Gunshots rang out on the afternoon of September 2, 1885, in Rock Springs, Wyoming Territory. Home to hundreds of Chinese coal miners who had come to the United States for work, the settlement’s Chinatown was facing impending bloodshed. After a morning of violence against Chinese workers in one of the nearby mines, more than a hundred white men armed with guns and other weapons had surrounded the neighborhood.

Tensions between Chinese and white coal miners in Rock Springs had been growing for a long time. White miners, organized under the Knights of Labor union, sought to improve workers’ conditions through unionizing and striking against the giant Union Pacific Railroad Company. Fed up with the company’s proposals to cut pay and its requirement that miners buy necessities at its overpriced stores, the Knights of Labor demanded negotiations with the miners’ employers. The union represented the will of oppressed workers, but it also represented a racist sentiment: the Knights of Labor argued that a large part of the miners’ problems was being caused by an influx of Chinese immigrants who were willing to work for less pay than white workers. When the Chinese workers at Rock Springs refused to strike with the white miners, tensions between the groups reached a breaking point. After returning from the mines to their homes to retrieve their weapons, white men, as well as women, stormed Chinatown that September afternoon. Their violent crusade, now known as the Rock Springs Massacre, resulted in the deaths of 28 Chinese people and the injury of 15, making it one of the bloodiest racially motivated massacres against Chinese immigrants in America.

What happened at Rock Springs was symptomatic of much wider racist sentiment in the United States at the time. Anti-Chinese views had existed since the first major waves of Chinese workers had arrived in North America to build the transcontinental railroad. Such workers represented a relatively cheap source of labour willing to work in dangerous conditions, and they soon replaced many of their white counterparts. In fact, the racist expression “not a Chinaman’s chance” is believed to derive from the dangerous working conditions Chinese workers typically found themselves in, such as being lowered along cliff faces to detonate explosives.*Britannica

1905 While a student at Kumbakonam, Ramanujan was so obsessed with his math studies that he failed all his other classes. It seems after a conflict at home, he ran away, causing his mother to send a missing-person letter to the newspaper:

1958 The National Defense Education act was passed in response to Sputnik (4 October 1957). $840 million was appropriated to improve the teaching of mathematics, science, and foreign languages. *VFR

The year 1957 also coincided with an acute shortage of mathematicians in the United States. The electronic computer created a demand for mathematicians as programmers and it also shortened the lead time between the development of a new mathematical theory and its practical application, thereby making their work more valuable. The United States could no longer rely on European refugees for all of its mathematicians, though they remained an important source, so it had to drastically increase the domestic supply. At the time, "mathematics" was interpreted as pure mathematics rather than applied mathematics. The problem in the 1950s and 1960s was that industry, including defense, was absorbing the mathematicians who were also needed at high schools and universities training the next generation. At the university level, even more recently, there have been years when it was difficult to hire applied mathematicians and computer scientists because of the rate that industry was absorbing them.

This chart shows the number of PhDs in the US by year from 1900. The linearity across the 20th Century of the semi-log graph may make one wonder if the program really had much impact. In fact the slope of growth rate drops significantly around the 70's (Which could be from age distribution in the country or numerous other causes.)

1997 After its Deep Blue chess-playing computer defeated human world chess champion Gary Kasparov in a closely watched match in May, the pioneering computer company decided to make the machine even faster and stronger. On September 2, IBM announced that its RS/6000 SP model, a parallel supercomputer, was now 58 percent faster thanks to a new microprocessor and some software refinements. Kasparov was not available for comment.*CHM

a Deep Blue Processor, *Wik

2023 Dennis Austin, the principal software developer of PowerPoint, passed away from lung cancer on Sept. 1. He was 76. The Washington Post reports:

Released in 1987 by Forethought, a small software firm, PowerPoint was the digital successor to overhead projectors, transforming the labor-intensive process of creating slides -- a task typically assigned to design departments or outsourced -- to one where any employee with a computer could point, click and rearrange information with a mouse. "Our users were familiar with computers, but probably not graphics software," Mr. Austin wrote in an unpublished history of the software's development. "They were highly motivated to look their best in front of others, but they weren't savvy in graphics design."

Working alongside Robert Gaskins, the Forethought executive who conceived the software, it was Mr. Austin's job as the software engineer to make PowerPoint (originally called Presenter) easy to operate. He accomplished this with a "direct-manipulation interface," he wrote, meaning that "what you are editing looks exactly like the final product." Originally targeted for Macintosh computers, which had a graphical interface, Presenter included ways for users to incorporate graphics, clip art and multiple fonts. In addition, the slides could be uniform with graphic borders, corporate logos and slide numbers. The goal, Mr. Austin wrote, was "to create presentations -- not simply slides."

In his book "Sweating Bullets: Notes about Inventing PowerPoint" (2012), Gaskins wrote that "Dennis came up with at least half of the major design ideas," and was "completely responsible for the fluid performance and the polished finish of the implementation." "It's a good bet," Gaskins added, "that if Dennis had not been the person designing PowerPoint, no one would ever have heard of it."

BIRTHS

1841 Paul Matthieu Hermann Laurent born (2 September 1841 Luxembourg City – 19 February 1908 Paris, France). He developed statistical formulas for the calculation of actuarial tables and studied heat conduction. *VFR

In 1883 he became an examiner at the École Polytechnique. Because examiners were forbidden from publishing textbooks on the very subjects they examined, Laurent found a workaround—he published under pseudonyms! In 1895 he released Traité d’arithmétique, attributing it to his friends C. A. Laisant and Émile Lemoine to comply with the rules while still sharing his knowledge

Despite his large body of works, Laurent series expansions for complex functions were not named after him, but after Pierre Alphonse Laurent.

1850 Alfred Pringsheim born (2 September 1850 – 25 June 1941), a German mathematician who worked on real and complex functions. *SAU Pringsheim's theorem concerns the convergence of a power series with non-negative real coefficients. Pringsheim and Ivan Śleszyński, working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions.*Wik

1856 Wilhelm Franz Meyer born (2 September 1856 in Magdeburg; 11 April 1934 in Königsberg . Meyer studied algebraic geometry, algebraic curves and invariant theory.*SAU He was a Founding member of the German Mathematical Society. *Wik

1877 Frederick Soddy (2 September 1877 – 22 September 1956) was an English radiochemist and monetary economist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also proved the existence of isotopes of certain radioactive elements. He received the Nobel Prize for Chemistry in 1921, and named after him is small crater on the far side of the Moon and the radioactive Uranium mineral, Soddyite. He rediscovered the Descartes' theorem in 1936 and published it as a poem. The kissing circles in this problem are sometimes known as Soddy circles.
The Poem begins,

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.

The entire poem is found here, along with a story about how, In a strange "chain reaction" of ideas, Soddy played a part in the US developing an atomic bomb. *(Assorted notes)

1878 (René-)Maurice Fréchet (2 Sep 1878; 4 June 1973) was a French mathematician known chiefly for his contribution to real analysis. He is credited with being the founder of the theory of abstract spaces, which generalized the traditional mathematical definition of space as a locus for the comparison of figures; in Fréchet's terms, space is defined as a set of points and the set of relations. In his dissertation of 1906, he investigated functionals on a metric space and formulated the abstract notion of compactness. In 1907, he discovered an integral representation theorem for functionals on the space of quadratic Lebesgue integrable functions. He also made important contributions to statistics, probability and calculus. *TIS

1891 Ivan Matveyevich Vinogradov (2 Sep 1891[OS? SAU gives 14 Sep], 20 Mar 1983)Soviet mathematician known for his contributions to the analytical theory of numbers, including a partial solution of the Goldbach conjecture proving that every sufficiently large odd integer can be expressed as the sum of three odd primes. He described his methods in his most celebrated piece of work Some Theorems Concerning the Theory of Prime Numbers (1937)*TIS

1892 Frank Wilcoxon, (2 September 1892 - 18 November 1965) whose name should be familiar to anyone who has used classic nonparametric (distribution-free) tests, was born in County Cork, Ireland, to American parents. He spent much of his early life in the Hudson River Valley region of New York. Sometime around 1908 he ran away to sea, jumped ship after a week of chipping paint when the ship failed to sail, and hid out for years from the imagined consequences of this desertion in the back country of West Virginia, first as an oil well worker, then as a tree surgeon. A trip to Boston to hone the latter skills at a forestry school fizzled when it turned out that the school had closed. Finally returning home, he was sent to the Pennsylvania Military College in 1917, another totally incompatible environment. His twin sister died in childbirth in 1918.

After a WW1 job with the Atlas Powder Company in Michigan, Wilcoxon entered Rutgers in 1920, and completed an MS in chemistry in 1921; he then shifted to Cornell and physical chemistry, and got his PhD in 1924.

Much of his early work was in research related to chemistry, with his interest in statistics resulting from reading Fisher's well-known book Statistical Methods for Research Workers (which I recall reading somewhere was for some time the most cited book in all of science). During the 1940s Dr. Wilcoxon was perhaps most instrumental in the growth of the fledgling field of nonparametric or distribution-free statistics, introducing his signed-rank test for paired samples and his famous two-sample rank-sum test as an alternative to Student's unpaired two-sample t-test, each of which carry Wilcoxon's name in its appellation. (Wilcoxon's 1945 paper introducing these two tests was titled "Individual Comparisons by Ranking Methods".)

At the time of his death, Wilcoxon was working on a multivariate generalization of his two-sample rank sum test. His proposals were described posthumously (by Bradley, 1967). They have not been taken up by the statistical community.

For a good description of how outliers led the chemist Wilcoxon to develop these tests, read Chapter 16, "Doing Away With Parameters", in David Salsburg's book The Lady Tasting Tea, in which Salsburg writes in a footnote that "the nonparametric approach was not fully understood to be such a drastic revolution until Wilcoxon's work in this field" *David Bee

1909 Deane Montgomery (2 Sept 1909 - 15 March 1992 in Chapel Hill, North Carolina, USA) was a mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.
Born in the small town of Weaver, Minnesota, he received his B.S. from Hamline University in St. Paul, MN and his Masters and Ph.D. from the University of Iowa in 1933; his dissertation advisor was Edward Chittenden.
In 1941 Montgomery was awarded a Guggenheim Fellowship. In 1988, he was awarded the American Mathematical Society Leroy P. Steele Prize for Lifetime Achievement.*Wik

1913 Israel Moiseevich Gelfand, (2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow.

His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand.

Gelfand is known for many developments including:

the book Calculus of Variations (1963), which he co-authored with Sergei Fomin;

Gelfand's formula, which expresses the spectral radius as a limit of matrix norms.

the Gelfand representation in Banach algebra theory;

the Gelfand–Mazur theorem in Banach algebra theory;

the Gelfand–Naimark theorem;

the Gelfand–Naimark–Segal construction;

Gelfand–Shilov spaces;

the Gelfand–Pettis integral;

the representation theory of the complex classical Lie groups;

contributions to the theory of Verma modules in the representation theory of semisimple Lie algebras (with I. N. Bernstein and S. I. Gelfand);

contributions to distribution theory and measures on infinite-dimensional spaces

the first observation of the connection of automorphic forms with representations (with Sergei Fomin);

conjectures about the Atiyah–Singer index theorem;

ordinary differential equations (Gelfand–Levitan theory);

work on calculus of variations and soliton theory (Gelfand–Dikii equations);

contributions to the philosophy of cusp forms;

Gelfand–Fuchs cohomology of Lie algebras;

Gelfand–Kirillov dimension;

integral geometry;

combinatorial definition of the Pontryagin class;

Coxeter functors;

general hypergeometric functions;

Gelfand–Tsetlin patterns;

Gelfand–Lokutsievski method;

and many other results, particularly in the representation theory of classical groups.

1923 René Thom (September 2, 1923 – October 25, 2002) is known for his development of catastrophe theory, a mathematical treatment of continuous action producing a discontinuous result. *SAU
Born in Montbeliard, France. In 1958 he received a Fields Medal for his 1954 creation of cobordism in algebraic topology. His classiﬁcation of manifolds used homotopy theory in a fundamental way and this work became an important example of general cohomology theory. *VFR Thom is also known for his later work developing the catastrophe theory (1972), a mathematical treatment of continuous action producing a discontinuous result. Thom's theory is an attempt to describe, in a way that is impossible using differential calculus, those situations in which gradually changing forces lead to so-called catastrophes, or abrupt changes. The theory has widespread application in the physical and biological sciences and in the social sciences, but eventually fell from favour.*TIS

1925 Roy Jay Glauber (September 1, 1925 – December 26, 2018) was an American theoretical physicist. He was the Mallinckrodt Professor of Physics at Harvard University and Adjunct Professor of Optical Sciences at the University of Arizona. Born in New York City, he was awarded one half of the 2005 Nobel Prize in Physics "for his contribution to the quantum theory of optical coherence", with the other half shared by John L. Hall and Theodor W. Hänsch.
In this work, published in 1963, he created a model for photodetection and explained the fundamental characteristics of different types of light, such as laser light (see coherent state) and light from light bulbs (see blackbody). His theories are widely used in the field of quantum optics. *Wik

1948 Christa McAuliffe (2 Sep 1948; died 28 Jan 1986) Astronaut, first teacher in space, who died on

the Challenger Space Shuttle when 73 seconds into its 10th launch, Challenger (STS-51L) exploded in midair, killing its crew of seven. Space shuttle flights were suspended until 1988. An independent U.S. commission blamed the disaster on unusually cold temperatures that morning and the failure of the O-rings, a set of gaskets in the rocket boosters. *TIS

DEATHS

1764 Nathaniel Bliss (28 November 1700 – 2 September 1764) was an English mathematician and astronomer who went on to become Astronomer Royal. He succeeded Edmond Halley as professor of geometry at Oxford University in 1742 and was elected a Fellow of the Royal Society the same year. He succeeded James Bradley to become the fourth Astronomer Royal in 1762, but held the post for too short a period to make a significant impact (1762-1764).*Wik

1768 Antoine Deparcieux (October 28, 1703 – September 2, 1768) was a French mathematician who is best known for an early work on annuities and mortality.*SAU In 1746, he published Essai sur les probabilités de la durée de la vie humaine (An Essay on the Probabilities of the Duration of Human Life). Deparcieux analyzed in detail empirical observations. As a mathematician and physicist, he can be considered, after Halley and Struyck, one of the founders of the estimation of longevity and all the issues surrounding that concept. *Wik

1832 Franz Xaver von Zach (4 June 1754, 2 Sep 1832) German-Hungarian astronomer patronized by Duke Ernst of Saxe-Gotha-Altenburg. Director of observatory near Gotha (1787-1806). There he organized in 1798 the first congress of astronomers with Josef Lalande (1732-1807) as celebrated guest. In last years of the 18th century he formed a group of 24 astronomers chosen from throughout Europe to track down a "missing" planet between the orbits of Mars and Jupiter, where they instead discovered the asteroids. His greatest contribution was in the organizational area, for he maintained an enormous correspondence with all the astronomers of his time, and edited 28 volumes of Monatliche Korrespondenz zur Beforderung der Erd- und Himmelskunde (1800-13).*TIS

1834 Thomas Telford (9 August 1757 Glendinning, Westerkirk, Eskdale, Dumfriesshire, Scotland - 2 September 1834 (aged 77) 24 Abingdon Street, Westminster, London) He is the founder of modern bridge construction, his crowning achievement being the Menai suspension bridge in Wales. Do you know the shape of the cables on a suspension bridge? *VFR

Menai Suspension Bridge *Wik

Telford's reputation in Shropshire led to his appointment in 1793 to manage the detailed design and construction of the Ellesmere Canal, linking the ironworks and collieries of Wrexham via the north-west Shropshire town of Ellesmere, with Chester, utilising the existing Chester Canal, and then the River Mersey.

Among other structures, this involved the spectacular Pontcysyllte Aqueduct over the River Dee in the Vale of Llangollen, where Telford used a new method of construction consisting of troughs made from cast iron plates and fixed in masonry. Extending for over 1,000 feet (300 metres) with an altitude of 126 ft (38 m) above the valley floor, the Pontcysyllte Aqueduct consists of nineteen arches, each with a 45 ft (14 m) span. Being a pioneer in the use of cast-iron for large scaled structures, Telford had to invent new techniques, such as using boiling sugar and lead as a sealant on the iron connections. Eminent canal engineer William Jessop oversaw the project, but he left the detailed execution of the project in Telford's hands. The aqueduct was designated a UNESCO World Heritage Site in 2009. *Wik

A canal boat traverses the Pontcysyllte aqueduct in North Wales

1836 William Henry FRS (12 December 1774 – 2 September 1836) was an English chemist. He was the son of Thomas Henry and was born in Manchester England. He developed what is known today as Henry's Law.

William Henry was apprenticed to Thomas Percival and later worked with John Ferriar & John Huit at the Manchesters Infirmary. He began to study medicine at University of Edinburgh in 1795, taking his medical in 1807, but ill-health interrupted his practice as a physician, and he devoted his time mainly to chemical research, especially with regard to gases. One of his best-known papers (published in Philosophical Transactions of the Royal Society, 1803) describes experiments on the quantity of gases absorbed by water at different temperatures and under different pressures. His results are known today as Henry's law. His other papers deal with gas-analysis, fire-damp, illuminating gas, the composition of hydrochloric acid and of ammonia, urinary and other morbid concretions, and the disinfecting powers of heat. His Elements of Experimental Chemistry (1799) enjoyed considerable vogue in its day, going through eleven editions in 30 years. He was one of the founders of the Mechanics' Institute, the original precursor of University of Manchester Institute of Science and Technology.

He was elected a Fellow of the Royal Society in February 1809, having been awarded their prestigious Copley Medal in 1808.

He shot himself in his private chapel at Pendlebury, near Manchester, in 1836.

1865 Sir William Rowan Hamilton (4 Aug 1805, 2 Sep 1865) Irish mathematician in the fields of optics, geometrics, and classical mechanics. By age 12, Hamilton had already learned fourteen languages when he met the American, Zerah Colburn, who could perform amazing mental arithmetical feats, and they joined in competitions. It appears that losing to Colburn sparked Hamilton's interest in mathematics. At 15, he began studied the works of LaPlace and Newton so by age 17 had become the greatest living mathematician. He contributed to the development of optics, dynamics, and algebra. His invention of the calculus of quaternions enabled a three-dimensional algebra or geometry which provided a basis for the later development of quantum mechanics. *TIS

2002 Sheila Edmonds (1 April 1916 – 2 September 2002) was one of the last of the old-style Cambridge dons who devoted their lives to teaching and to their colleges.
Sheila had an excellent undergraduate career ending up a `Wrangler', as students who are placed first class in the examinations for the Mathematical Tripos are called - though this did not result in a Cambridge BA degree because women were ineligible until 1947. The following year, she was awarded a distinction in the notoriously demanding Part III of the Tripos. In a speech she gave at her 80th birthday dinner, she acknowledged that a key to her success was the thorough mathematical training she received from her Director of Studies at Newnham, Margaret Grimshaw, who was 11 years her senior and another of the old-style dons. *Newnham College web page

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

Tuesday, 1 September 2026

On This Day in Math- September 1

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

The 244th day of the year; 244 is the smallest number (besides 2) that can be written as the sum of 2 squares or the sum of two 5th powers. *What's Special about this number

244 is anti-perfect. The proper divisors are 1, 2, 4, 61, and 122, & adding their reversal is 1 + 2 + 4 + 16 + 221 = 244. *Jim Wilder ‏@wilderlab (244 is the smallest multi-digit anti-perfect number; There is one more year day which is anti-perfect.... don't just sit there, go find it!)

244 is also the sum of three cubes, $ 244 = 1^3 + 3^3 + 6^3 $

244 is "power friendly" with 136. $244 =1 ^3 + 3^3 + 6^3$ and $136 = 2^3 + 4^3 + 4^3$

See More Math Facts for every Year Day here.

EVENTS

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 hath 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"

Today if we saw this device we would call it a string phone, although it was not clear from Hooke's notes that his intention was to speak through the device. What is clear is that the device was created for the purpose of making music.

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.

The first photographer is widely acknowledged to be a French inventor named Joseph Nicéphore Niépcethe. He started experimenting with ways to record light in 1814. One of the oldest surviving photos of any kind was taken in 1825 when Niépce captured the black-and-white image of an engraving of a boy pulling a horse. However, this method required a full eight hours of exposure.

*PB notes

A different photo that is claimed to be the oldest surviving photograph: View from the Window at Le Gras (French: Point de vue du Gras) is a heliographic image and the oldest surviving camera photograph. It was created by French inventor Nicéphore Niépce in 1826 in Saint-Loup-de-Varennes, France, and shows parts of the buildings and surrounding countryside of his estate, Le Gras [fr], as seen from a high window.

below: The original plate (left) and colorized reoriented enhancement (right). The photo was found to be taken at his home from a second-story south-facing bedroom window.

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:

John Snow Pub, and the notorious pump

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

a modern image of a solar flare

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.

Sir William Thomson, Lord Kelvin

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

1885 On September 5, 1885, Scientific American published a photograph depicting a “streak of real ‘Jersey lightning,’” taken by William Nicholson Jennings (1860-1946) at 10:30 p.m. on the first of August that same year. Captured on the roof of Jennings’ house in North Philadelphia and later reproduced as a lantern slide, the photograph reveals a flash of lightning traveling diagonally from the upper left corner of the frame to the horizon, illuminating the tops of trees and a line of row house roofs in the foreground. Regional and national newspapers soon proclaimed Jennings as the first to successfully photograph lightning with a camera.

The Today in Science claims an earlier occurrence. " In 1884, the first photograph of a lightning flash made in the U.S. was made by W. C. Gurley of the Marietta Observatory, Ohio. The flash was about 3 miles away." I don't have a picture of that one (but am willing to post one if someone can find it) so Jennings gets the plug.

*Panaroma

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

https://youtu.be/xLVChRVfZ74

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 behavior of the center 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

BIRTHS

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.
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.

*Leibniz on the Foundations of the Calculus:
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

DEATHS

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 is perhaps best known today among mathematicians for Mersenne prime numbers, those which can be written in the form Mn = 2^p − 1 for some prime integer p.

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

1662 Paul Halcke (also: Halcken or Halke), (1662 in Elmshorn, 1731 in Buxtehude) was a German mathematician, writer, computer, and calendar maker.

He was the brother of writer and computer Johann Halcke and founded, in 1690, together with Heinrich Meißner, the Hamburgischen Kunst-Rechnungs lieb- und übenden Societät, today's Hamburg Mathematical Society. Since about 1687 he was writer and calculator at the city school of Buxtehude.

In 1694 he issued a solution's book to a collection of exercises by Heinrich Meißner, and later he published his own collection of 574 exercises from mathematics and astronomy, entitled Mathematischer Sinnen-Confect ("mathematical mind candy"), which was translated in various languages and remained a seminal textbook for more than a century. The exercises were enriched by poems and descriptions of the solving methods. In particular, exercise 289 on page 256 consists in finding the smallest Euler brick, for which Paul Halcke is most well-known today. This cuboid has sides and face diagonals of integer lengths {44, 117, 240} and {125, 244, 267}.

Halcken was also the first (1729) to show that the product of the aliquot divisors of 24, equals its cube, $1*2*3*4*6*8*12 = 13824=24^3$ and that the same fact is true about 40.

He also edited several popular calendars for the years 1705, 1707, 1715, 1716 and 1725.

An Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.

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 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