On This Day in Math - April 2

  

12th century copy of Gerber's De geometria. *Wik

The notion of a set is too vague for the continuum hypothesis to have a positive or negative answer.
~Paul Cohen

The 92nd day of the  year; 92 is the smallest composite number for which the reverse of its digits in hexadecimal, decimal, octal, and binary are all prime.  *Prime Curios (Is there a smaller Prime that could also be prime when reversed in all these bases?)

And... There are exactly 92 Johnson Solids: The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" Archimedean solids, and the two infinite families of prisms and antiprisms). *Geometry Fact ‏@GeometryFact
and a related point, The snub dodecahedron has 92 faces (80 triangular, 12 pentagonal), the most an Archimedean solid can have.

92 is the number of different arrangements of 8 non-attacking Queens on an 8 by 8 chessboard (i.e. no two Queens should share the same row, column, or diagonal)

92= 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 the sum of eight consecutive integers

92 is a palindrome in bases 6 (232₆), and 7 (161₇)

Unlike 91 (and lots of other numbers) 92 can not be written as the sum of three positive squares.

Because 92 is divisible by four, it is the difference of two squares, 24^2 - 22^2

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EVENTS

999   Gerbert was elected Pope Sylvester II. He introduced into the West the practice of making calculations by using marked discs (apices). This method, which has nearly all the advantages of positional arithmetic, was used in abacus calculations throughout the eleventh and twelfth centuries.  *VFR More about Pope Sylvester's Abacus.  The previous page at this site shows the arabic letters in use at this time, 10th-11th centuries.

MAA

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1792   U.S. Mint established. It was Jefferson who suggested decimal coinage. *VFR After the U.S. Constitution was ratified, Congress passed the "Mint Act" of April 2, 1792, which established the coinage system of the United States and the dollar as the principal unit of currency. By this Act the U.S., became the first country in the world to adopt the decimal system for currency.  United States money is expressed in dollars, dimes or tenths, cents or hundredths,1 and mills or thousandths. A dime is a tenth of a dollar, a cent is a hundredth of a dollar, and a mill is a thousandth of a dollar.  

 On May 8, 1792 an act was passed to make copper coins, "On the reverse of the copper coins, there express the denomination of the coin as one-cent or half-cent."  Half cents were made by the Philadelphia mint from 1793 - 1857. That same year they discontinued both the half cents and the large cents (cents back then were about the size of a quarter) and started minting pennies that are the same size as today's pennies.

The Nickname "Pennies" comes from the English unit of money worth 1/12 of a shilling.  The English pennies was a plural term for the singular unit of pence.

The first silver dollars, precisely 1,758 of them, were coined on October 15, 1794, and were immediately delivered to Mint Director David Rittenhouse for distribution to dignitaries as souvenirs. Thereafter, until 1804, they were struck in varying quantities.

1794 Liberty head cent, and 1794 "flowing hair dollar

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1827  lead pencils were first manufactured by Joseph Dixon, who built his factory in Salem, Mass. Dixon was responsible for the development of the graphite industry in the U.S. In 1859 he patented graphite crucibles. When he died, the Joseph Dixon Crucible Company was the largest manufacturer of graphite products in the world. The first* pencil factory in the U.S. however, was started earlier by William Monroe of Concord, Mass., in Jun 1812. His first 30 pencils were bought by Benjamin Adams, a hardware dealer in Boston, Mass. The first pencils made in Great Britain (1584) used graphite from Borrowdale, Cumberland. *TIS
The Pencil, A History of Design and Circumstance

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1845 Fizeau and Foucault take the first successful photograph of the sun. *VFR
"Taking advantage of a relatively new technology, the daguerreotype, French physicists Louis Fizeau and Leon Foucault made the first successful photographs of the sun on April 2, 1845. The original image, taken with an exposure of 1/60th of a second, was about 4.7 inches (12 centimeters) in diameter and captured several sunspots, visible in this reproduction. "( I find it interesting that the first photo of the sun was over five years after the first photo of the moon.  Can you think why ?)

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1921 Einstein made it known that he would arrive in New York harbor on April 2, 1921 for his first trip to the United States. A crowd of thousands gathered in Battery Park to await his arrival, while reporters and dignitaries interested in his theory of relativity came aboard the ship to meet Dr Einstein. City officials, including Mayor John Francis Hylan, were eager to greet Dr. Einstein. Mayor Hylan bestowed the honorary award the 'freedom of the city' on Dr. Einstein and chemist Dr. Chaim Weizmann.

Albert Einstein arrived in New York on the SS Rotterdam IV;

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1933 Emmy Noether's right to teach at Gottingen was withdrawn because of her Jewish ancestry. The resulting infusion of scientists played a major role in transferring mathematical leadership from Germany to the United States. See AMM, 90(1983), 717. *VFR  Thony Christie  sent me a note assuring me that it was not her religion, but her politics. Seems she had Marxist leanings. Many others in her department were discharged at the same time. After the sweeping removal of "undesirables" Minister of Education Bernhard Rust supposedly had the following conversation with  David Hilbert.

Rust: “I hear you have some problems in the mathematics department at Göttingen Herr Professor”.
Hilbert: “No, there are no problems; there is no mathematics department in Göttingen”.

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1935 Sir Robert Watson-Watt received a patent on a radio device for detecting and locating an aircraft. He had submitted the idea to the Air Ministry in secret memo, Detection and location of aircraft by radio methods on Feb 12 of the same year. The method was tested on Feb 26 in a field just off the present day A5 in Northamptonshire near the village of Upper Stowe. *Wik

The story is told that years later while traveling across Canada, he was caught speeding with a radar gun.  As the officer was writing up the ticket, Watson-Watt said, "If I knew you were going to use it for this, I would never have invented it."

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1948 Kurt Godel became a United States citizen. Being the diligent individual that he was, he studied the constitution carefully beforehand and felt that he had found a contradiction. On the way to the ceremony Einstein and Oskar Morgenstern tried to keep his mind on other issues, but when the judge called them into his chambers (so that he could meet Einstein) he asked Godel if he had anything to say. It was only with considerable effort that his friends were able to change the subject when Godel brought up the contradiction. *VFR 
Paul O'Malley directed me to a site where a more complete version of this anecdote is spelled out by writer Jeffrey Kegler. I've included here a link to a source that has a draft recollection of the story from Morgenstern.

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1953 the journal Nature published a paper with this date from Francis Crick and James Watson, titled Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid, in which they described a double helix structure for DNA. The diagram published with the paper was captioned, "The figure is purely diagrammatic. The two ribbons symbolize the phosphate-sugar chains, and the horizontal rods the pairs of bases holding the chains together. The vertical line marks the fibre axis." *TIS

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1980  Microsoft Corporation announces the Z80 SoftCard--their first and (for many years) only hardware product--a microprocessor on a printed circuit board that plugged into the Apple II personal computer. It retailed for $349.00. The SoftCard allowed programs running under the CP/M operating system (included with the card, as was Microsoft BASIC) to run on the 6502-based Apple II with only minor modifications. In particular, the word processor WordStar was so popular that people bought the SoftCard and a companion "80-column card" just to run it. At one time, SoftCard brought in about half of Microsoft's total revenue. It was discontinued in 1986.

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BIRTHS

1618 – Francesco Maria Grimaldi (2 April 1618 – 28 December 1663) was an Italian Jesuit priest, mathematician and physicist who taught at the Jesuit college in Bologna.
Between 1640 and 1650, working with Riccioli, he investigated the free fall of objects, confirming that the distance of fall was proportional to the square of the time taken. In astronomy, he built and used instruments to measure geological features on the Moon, and drew an accurate map or selenograph which was published by Riccioli. He was the first to make accurate observations on the diffraction of light (although by some accounts Leonardo da Vinci had earlier noted it), and coined the word 'diffraction'. Later physicists used his work as evidence that light was a wave, and Isaac Newton used it to arrive at his more comprehensive theory of light.  *Wik
Thony Christie has a nice post about his influential work in the early investigation of refraction that is well worth reading.

In the late 1640s, he produced a large and detailed map of the moon, based on his own observations. His fellow Jesuit and Bolognese, Giambattista Riccioli, then invented a naming system for the various craters and seas, and published Grimald's map with his own names in his Almagestum Novum (1651). The map is especially noteworthy because Riccioli’s lunar nomenclature – one of several then available – turned out to be the one we still use. So the Sea of Tranquility (Mare tranquilitatis), where Apollo 11 landed, first appeared with that name on the Grimaldi/Riccioli map. *Wik

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1878 Edward Kasner (April 2, 1878 – January 7, 1955) was an American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jewish person appointed to a faculty position in the sciences at Columbia University.[1] Subsequently, he became an adjunct professor in 1906, and a full professor in 1910, at the university. Differential geometry was his main field of study. In addition to introducing the term "googol", he is known also for the Kasner metric and the Kasner polygon.

In 1940, with James R. Newman, Kasner co-wrote a non-technical book surveying the field of mathematics, called Mathematics and the Imagination (ISBN 0-486-41703-4). It was in this book that the term "googol" was first popularized:

Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was suggested that a googolplex should be 1, followed by writing zeros until you get tired. This is a description of what would happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number is a googol. A googolplex is much bigger than a googol. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way. *Wik  

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1888 Antonio Signorini (2 April 1888 – 23 February 1963) was an influential Italian mathematical physicist and civil engineer of the 20th century. He is known for his work in finite elasticity, thermoelasticity and for formulating the Signorini problem.
The Signorini problem is the first variational inequality problem, : it consists in finding the elastic equilibrium configuration of an anisotropic non-homogeneous elastic body, resting on a rigid frictionless surface and subject only to its mass forces. The name was coined by Gaetano Fichera to honour his teacher, Antonio Signorini: the original name coined by him is problem with ambiguous boundary conditions.   The problem was posed by Antonio Signorini during a course taught at the Istituto Nazionale di Alta Matematica in 1959. The problem was taken up, in particular, by one of his students,  Gaetano Fichera.
On the first days of January 1963, Fichera was able to give a complete proof of the existence and uniqueness of a solution for the problem with ambiguous boundary condition, which he called "Signorini problem" to honour his teacher. The preliminary note later published as Fichera 1963 was written up and submitted to Signorini exactly a week before his death: He was very satisfied to see a positive result.

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1906 Shokichi Iyanaga (April 2, 1906 – June 1, 2006) was a Japanese mathematician. Iyanaga published many papers which arose through several courses such as algebraic topology, functional analysis, and geometry, which he taught. He became Professor at the University of Tokyo in 1942. It was during World War II. Towards the end of the war, many Japanese cities were bombarded and he had to find refuge in the countryside. He was busy in editing textbooks from primary and secondary schools and he continued to give courses and organise seminars.*Wik

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1923 – George Spencer-Brown (April 2, 1923, Grimsby, Lincolnshire, England, August 25, 2016  ) is a polymath best known as the author of Laws of Form. He describes himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, consulting psychotherapist, author, and poet.",*Wik
In a 1976 letter to the Editor of Nature, Spencer-Brown claimed a proof of the four-color theorem, which is not computer-assisted. The preface of the 1979 edition of Laws of Form repeats that claim, and further states that the generally accepted computational proof by Appel, Haken, and Koch has 'failed' (page xii). Spencer-Brown's claimed proof of the four-color theorem has yet to find any defenders; Kauffman provides a detailed review of parts of that work. *VFR

During his time at Cambridge,[clarification needed] Spencer-Brown was a chess half-blue. He held two world records as a glider pilot, and was a sports correspondent to the Daily Express.[9] He also wrote some novels and poems, sometimes employing the pen name James Keys.

Spencer-Brown died on 25 August 2016. He was buried at the London Necropolis, Brookwood, Surrey.

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1934  Paul Joseph Cohen (2 Apr 1934, March 23, 2007 )American mathematician who received the Fields Medal (1966) for his fundamental work on the foundations of set theory. Cohen invented a technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalised continuum hypothesis. The continuum hypothesis problem was the first of Hilbert's famous 23 problems delivered to the Second International Congress of Mathematicians in Paris in 1900. Hilbert's famous speech The Problems of Mathematics challenged (then and now) mathematicians to solve these fundamental questions and Cohen has the distinction of solving Problem 1. He also worked on differential equations and harmonic analysis. *TIS

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DEATHS

1952 Bernard(-Ferdinand) Lyot (27 Feb 1897; 2 Apr 1952 at age 55) French astronomer who invented the coronagraph (1930), an instrument which allows the observation of the solar corona when the Sun is not in eclipse. Earlier, using his expertise in optics, Lyot made a very sensitive polariscope to study polarization of light reflected from planets. Observing from the Pic du Midi Observatory, he determined that the lunar surface behaves like volcanic dust, that Mars has sandstorms, and other results on the atmospheres of the other planets. Modifications to his polarimeter created the coronagraph, with which he photographed the Sun's corona and its analyzed its spectrum. He found new spectral lines in the corona, and he made (1939) the first motion pictures of solar prominences.*TIS

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1902 Thomas Gerald Room FRS FAA (10 November 1902 – 2 April 1986) was an Australian mathematician who is best known for Room squares. He was a Foundation Fellow of the Australian Academy of Science.He studied mathematics in St John's College, Cambridge, and was a wrangler in 1923. He continued at Cambridge as a graduate student, and was elected as a fellow in 1925, but instead took a position at the University of Liverpool. He returned to Cambridge in 1927, at which time he completed his PhD, with a thesis supervised by H. F. Baker.  Room remained at Cambridge until 1935, when he moved to the University of Sydney, where he accepted the position of Chair of the Mathematics Department, a position he held until his retirement in 1968.

During World War II he worked for the Australian government, helping to decrypt Japanese communications.

Room's PhD work concerned generalizations of the Schläfli double six, a configuration formed by the 27 lines on a cubic algebraic surface.

In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press. Nearly 500 pages long, the book combines methods of synthetic geometry and algebraic geometry to study higher-dimensional generalizations of quartic surfaces and cubic surfaces. It describes many infinite families of algebraic varieties, and individual varieties in these families, following a unifying principle that nearly all loci arising in algebraic geometry can be expressed as the solution to an equation involving the determinant of an appropriate matrix.

Room invented Room squares in a brief note published in 1955.

A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that:

Each cell of the array is either empty or contains an unordered pair from the set of symbols

Each symbol occurs exactly once in each row and column of the array

Every unordered pair of symbols occurs in exactly one cell of the array.

An example, a Room square of order seven, if the set of symbols is integers from 0 to 7:

(It is known that a Room square (or squares) exist if and only if n is odd but not 3 or 5.)

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1995 Hannes Olof Gösta Alfvén (30 May 1908, 2 Apr 1995 at age 86) was a Swedish astrophysicist who was one of the founders of the field of plasma physics (the study of ionized gases). He shared the 1970 Nobel Prize in Physics (with Frenchman Louis Néel). Alfvén was recognized “for fundamental work in magnetohydrodynamics with fruitful applications in different parts of plasma physics.” He conceived plasma cosmology as an alternative to the Big Bang theory of the origin of the universe. In the concept of plasma cosmology, the universe has no specific beginning nor has any forseeable end. Instead of a dominance by gravitational forces, the theory maintains that it is the electromagnetic forces of plasma throughout the universe that organizes the matter of the universe into its observed structure of stars. *TIS

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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

On This Day in Math - April 1

   

first newspaper weather map - The Times, London, England

We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about `and'.
~Arthur Eddington


The 91st day of the year; 10ⁿ + 91 and 10ⁿ + 93 are twin primes for n = 1, 2, 3 and 4. (For n less than ten, one of these expressions is prime for some other values of n, which?)

91 and it's reversal 19 are related to Ramanujan's Taxi-cab number, 1729 = 19x91, a palindrome product.  Note that the sum of the digits of 1729 are 19.

91 is : The sum of thirteen consecutive integers = 1 + 2 + 3 + ... + 11 + 12 + 13, the thirteenth triangular number.
and of six consecutive squares= 1² + 2² + 3² + 4² + 5² + 6²
    two consecutive cubes = 3³ + 4³ and the difference of two consecutive cubes = 6³ - 5³

The sum of one of each US coin less than a Silver Dollar is 91 cents.

     

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EVENTS

1700 It was the English, it seems, who are responsible for all the mischief you will have to put up with on "April Fools Day". English pranksters begin popularizing the annual tradition of April Fool's Day by playing practical jokes on one another. * Tweet from @Historymag

Historians have also linked April Fools' Day to festivals such as Hilaria (Latin for joyful), which was celebrated in ancient Rome at the end of March by followers of the cult of Cybele. It involved people dressing up in disguises and mocking fellow citizens and even magistrates and was said to be inspired by the Egyptian legend of Isis, Osiris and Seth *History com

In 1508, French poet Eloy d'Amerval referred to a poisson d'avril (April fool, literally "April's fish"), possibly the first reference to the celebration in France. Some historians suggest that April Fools' originated because, in the Middle Ages, New Year's Day was celebrated on 25 March in most European towns, with a holiday that in some areas of France, specifically, ended on 1 April, and those who celebrated New Year's Eve on 1 January made fun of those who celebrated on other dates by the invention of April Fools' Day.

In 1686, John Aubrey referred to the celebration as "Fooles holy day", the first British reference. On 1 April 1698, several people were tricked into going to the Tower of London to "see the Lions washed". *Wik

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1737 Euler Reads his instrumental paper, ‘De fractionibus continuis dissertatio’ (‘Essay on continued fractions’), to the St Petersburg Academy of Sciences, which had been presented with the document on March 7. "With the exception of a few isolated results which appeared in the sixteenth and seventeenth centuries, most of the elementary theory of continued fractions was developed in a single paper written in 1737 by Leonhard Euler." *Rosanna Cretney, The origins of Euler's early work on continued fractions. Historia Mathematica, Vol 41, issue 2

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.[1] In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression. In either case, all integers in the sequence, other than the first, must be positive. The integers are called the coefficients or terms of the continued fraction.

Every infinite continued fraction is irrational, and every irrational number can be represented in precisely one way as an infinite continued fraction. *Wik

A infine regular continued fraction, 

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1741 In a letter to Goldbach, Euler demonstrates for all n less than 300, that the sum of the digits of a number n, $\sigma(n)= \sigma(n-1) + \sigma(n-2) - \sigma(n-5) - \sigma(n-7) + \sigma(n-12)....$ where the signs pattern two positive, two negative, repeating and the numbers are the pentagonal numbers. *L E Dickson, History of the Theory of Numbers

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1764 Nichole-Reine Lapaute, wife of the famous clock maker, publishes her own map of the annular eclipse across North Africa and Europe in two colors (rare for the period). The cartouche design was by another talented female, Madame Lattre, wife of the mapmaker-to-the king, Jean Lattre.

,

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1801 Gauss records in his diary that he extended his "purely analytical formula" for Easter to the Passover date. [Dunningham, p. 69] *VFR  

Not sure most folks are aware that Easter is not calculated based on the actual moon phases; instead, it is based on a calculated "ecclesiastical full moon," which is a mathematical approximation of the first full moon occurring on or after the spring equinox, meaning it doesn't always perfectly align with the actual astronomical moon phases. *PB

An ecclesiastical full moon is formally the 14th day of the ecclesiastical lunar month (an ecclesiastical moon) in an ecclesiastical lunar calendar. The ecclesiastical lunar calendar spans the year with lunar months of 30 and 29 days which are intended to approximate the observed phases of the Moon. Since a true synodic month has a length that can vary from about 29.27 to 29.83 days, the moment of astronomical opposition tends to be roughly 14.75 days after the previous conjunction of the Sun and Moon (the new moon). The ecclesiastical full moons of the Gregorian lunar calendar tend to agree with the dates of astronomical opposition, referred to a day beginning at midnight at 0 degrees longitude, to within a day or so. However, the astronomical opposition happens at a single moment for the entire Earth: The hour and day at which the opposition is measured as having taken place will vary with longitude. In the ecclesiastical calendar, the 14th day of the lunar month, reckoned in local time, is considered the day of the full moon at each longitude.*Wik

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1803 John Dalton makes the first entry in his first meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816.  By September 3, 1803 he made a logbook entry that day titled, “Observations on the Ultimate Particles of Bodies and their Combinations.” It was the first use of symbols to represent the elements of modern chemistry.

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1824 Instrument maker Peter Barlow is paid 500 Pounds from the Board of Longitude for his "Iron Plate to improve ships compasses." Barlow had studied the "local attraction" or influence on the compass by iron on-board the ship and achieved a way of using an iron plate to minimize the deviation. *Derek Howse, Britain's Board of Longitude, The Finances. 

Barlow, from Norfolk, was an optician and mathematician who invented two varieties of achromatic (non-colour-distorting) telescope lenses known as Barlow lenses.

Self-educated, he became assistant mathematics master at the Royal Military Academy, Woolwich, in 1801. He published numerous mathematical works, including New Mathematical Tables (1814). The latter became known as Barlow's Tables and gives squares, cubes, square roots, cube roots, and reciprocals of all integer numbers from 1 to 10,000. *Wik

In 1823, he was made a fellow of the Royal Society. Two years later, he received its Copley Medal for his work on correcting the deviation in ship compasses caused by the presence of iron in the hull.

Essay on magnetic attractions, and on the laws of terrestrial and electro-magnetism, 1824

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In 1875, Sir Francis Galton published the first newspaper weather map - in The Times, London, England - now a standard feature in newspapers worldwide. He was the first to identify the anticyclone (as opposed to the cyclone), and introduced the use of charts showing areas of similar air pressure, as used on the modern weather map. Galton also devised several novel and ingenious mechanical instruments for recording information about the weather, while working at the Kew Observatory. He was also active as an explorer, anthropologist, statistician and criminologist. Galton was the first to place the study of fingerprints for identification on a scientific basis and so lay the groundwork for their use in criminal cases. *TIS

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1876 The New-England Journal of Education (vol. 3, p. 161), in its weekly mathematics column, published a proof of the Pythagorean theorem by General James A. Garfield, Member of Congress from Ohio, and later President of the United States. They refer to the theorem as the pons asinorum, though today that term is reserved for Euclid I.5 which states that the base angles of an isosceles triangle are equal.
Garfield was a professor of mathematics (and languages) at Hiram College in Ohio for several years before being elected to the Ohio Senate in 1859. For more notes about his proof, and some other tidbits on mathematical Presidents see this blog.

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1878   From Greg Ross at Futility Closet 

The April 1, 1878, issue of the New York Daily Graphic announced that Thomas Edison had invented a “victuals machine” that would feed the human race:

I made all this food out of the dirt taken from the cellar and water that runs through these pipes. … I believe that in ten years my machines will be used to provide the tables of the civilized world. … I can make cabbages and oranges that have never felt the rain. Nature is full of surprises. Bananas and chocolate can be made out of the very same ingredients, and the methods of combining differ only a trifle.

The last paragraph revealed that the story was a hoax, but many readers didn’t get that far — several newspapers picked up the news, and some readers even tried to order the device. Reporter William Augustus Croffut, who’d concocted the tale, wrote diffidently to Edison on April 4, “Did you see my hoax? And are you in a state of fiery wrath? Or how is it?”

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1939 To commemorate the New York World's Fair the U.S. issued a postage stamp picturing a trylon and perisphere. This was the 1st stamp in the world to picture geometric objects. Can you identify these shapes? They are not in my dictionaries. [Scott #853] *VFR (To answer Professor Rickey, they were photographed at the fair (above). The names were for the structures, not a particular geometric shape-The word Perisphere was coined using the Greek prefix peri-, meaning all around, about, or enclosing, surrounding. The word Trylon was coined from the phrase "triangular pylon". )

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1948 Physicists Hans Bethe and George Gamow become acquainted with a bright young physicist with such an unusual name that they decided to write a joint paper, which was submitted to The Physical Review on this date. Its only unusual feature was its by-line, "by Alpher, Bethe, and Gamow." [Eves, Revisited, 268] *VFR  The article, about the possibility that the elements Carbon and Nitrogen were formed during the big  bang, which were needed for the creation of heavier elements in the centers of stars under the current theories.  The article is frequently called the "alphabet article."

*HT to Paul Abbott who wrote to add that, "That’s not really what happened…

“Hans Bethe hadn't really contributed to the work and Alpher, at the time only a graduate student, was generally dismayed by the inclusion of Bethe's name on this paper. He felt that the inclusion of another eminent physicist would overshadow his personal contribution to this work and prevent him from receiving proper recognition for such an important discovery. He expressed resentment over Gamow's whimsy as late as 1999.”

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1960 First televisioin picture of earth from space. It was taken by TIROS 1.*NASA History Office ‏@NASAhistory  

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1975 Martin Gardner announced that in November 1974, William McGregor, a graph theorist of Wappingers Falls, N.Y., discovered a counterexample to the four-color conjecture. He produced a map containing 110 regions that requires five colors. This "Mathematical Games" column provoked over one thousand letters including a threatened lawsuit from Ivan Guffvanoff III at the University of Wisconsin who destroyed his disproof after reading of this counterexample in The New York Times. The mathematics students at the University of Warwick realized that the column was an April Fool's joke, for they published this poem in Manifold, a journal of mathematical humor:

Oh Mr. Gardner,
What have you done?
You've started up a rumour
You should never have begun!
A four-colour hoax can't
Be undone so quick . . .
Oh Mr. Gardner, what
A bloody silly trick!"

For more details see Time Travel and Other Mathematical Bewilderments by Martin Gardner,
1988, pp. 134, 135
[  The actual map he claimed required five colors can be seen at the Math Forum site.]
   Gardner also presented another Aprils Fool Joke in that article by claiming that Ramanujan had conjectured, and it had been proved, that $e^{\pi \sqrt{163}}$ was an integer.  The "almost integer" became known as Ramanujan's constant.  The value is approximately 262,537,412,640,768,743.999999999992

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1976 The Jovian–Plutonian gravitational effect, a hoax phenomenon stated to cause a noticeable short-term reduction in gravity on Earth, was an invention for April Fools' Day by the English astronomer Patrick Moore broadcast on BBC Radio 2 on 1 April 1976.
Moore stated to radio listeners that an astronomical event would take place at 9:47 a.m. that day, a conjunction of Jupiter and Pluto, which was expected to have an effect observable everywhere. As Pluto passed behind Jupiter, it would briefly cause a powerful combination of the two planets' gravitation which would noticeably decrease gravity on Earth. If listeners were to jump into the air at that exact moment, they would find they felt a floating sensation.
Soon after 9:47 on that morning, the BBC began to receive hundreds of telephone calls from people reporting they had observed the decrease in gravity. One woman who called in even stated that she and eleven friends had been sitting and had been "wafted from their chairs and orbited gently around the room".
Interestingly, in 1980, Moore collaborated with Clyde Tombaugh, the man who had discovered Pluto in 1930, to publish a new book about the dwarf planet.*Wik (ht to David Dickinson @Astroguyz)

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1997 The Great Comet of 1997, comet Hale–Bopp passed perihelion. It had been discovered on July 23, 1995, independently by two observers, Alan Hale and Thomas Bopp, both in the United States. Hale–Bopp's orbital position was calculated as 7.2 astronomical units (AU) from the Sun, placing it between Jupiter and Saturn and by far the greatest distance from Earth at which a comet had been discovered by amateurs. It was discovered at  (such a great distance from the Sun that it raised expectations that the comet would brighten considerably by the time it passed close to Earth. Although predicting the brightness of comets with any degree of accuracy is very difficult, Hale–Bopp met or exceeded most predictions when it passed perihelion.

The beautiful illustration below is displayed proudly in my dining room.  It is the work of Dan Durda, Senior Research Scientist, Department of Space Studies, Southwest Research Institute, and a former high school student of mine.   Dan may have learned a little about math from me, but surely none of his art.

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2005 Astronomy Picture of Day gives visual evidence of water on Mars. (Please remember the day. No Hate mail please)

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2006  In 2006, Math Horizons challenged its readers to pose a problem in such a way that it contained its own answer. Rheta Rubenstein of the University of Michigan-Dearborn offered a pair of questions that answer one another:

What fraction of the letters in three-eighths are vowels?

What fraction of the letters in one-third are vowels?

*Greg Ross, Futility Closet

Can you create more?  Send them to me.

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BIRTHS

Seth Ward (1 April, 1617* – 6 January 1689)   (It seems clear he was born in 1617, and baptized on 5 April of that year.  I have seen both Jan 1 and April 1, and even April 5, but that seems very unlikely)  He was an English mathematician, astronomer, and bishop, born in Hertfordshire, and educated at Sidney Sussex College, Cambridge, where he graduated B.A. in 1636 and M.A. in 1640, becoming a Fellow in that year. In 1643 he was chosen university mathematical lecturer, but he was deprived of his fellowship next year for opposing the Solemn League and Covenant (with Isaac Barrow, John Barwick and Peter Gunning).
In the 1640s, he took instruction in mathematics from William Oughtred, and stayed with relations of Samuel Ward.
In 1649, he became Savilian professor of astronomy at Oxford University, and gained a high reputation by his theory of planetary motion. It was propounded in the works entitled In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (Oxford, 1653), against the cosmology of Ismael Boulliau, and Astronomia geometrica (London, 1656) on the system of Kepler. About this time he was engaged in a philosophical controversy with Thomas Hobbes, in fact a small part of the debate with John Webster launched by the Vindiciae academiarum he wrote with John Wilkins which also incorporated an attack on William Dell.
He was one of the original members of the Royal Society of London. In 1643 he was chosen university mathematical lecturer, but he was deprived of his fellowship next year for opposing the Solemn League and Covenant (with Isaac Barrow, John Barwick and Peter Gunning).

In 1659, he was appointed President of Trinity College, Oxford, but not having the statutory qualifications he resigned in 1660.*Wik

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1640 Georg Mohr (also Jorgen)(April 1, 1640 – January 26, 1697)
His only original contribution to geometry was the proof that any geometric construction which can be done with compass and straightedge can also be done with compasses alone, a result now known as the Mohr–Mascheroni theorem. He published his proof in the book Euclides Danicus, Amsterdam, 1672.
In Denmark the Georg Mohr Competition is a mathematics competition aimed at mathematics students interested in secondary education. The purpose of Georg Mohr contest is to stimulate interest in mathematics by challenging the brightest students with assignments in severity beyond that they encounter in their daily education. The contest also functions as a step in the selection of participants to the IMO, the International Mathematics Olympiad. *Wik

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1644 Otto Mencke (22 March (OS) April 1, 1644 – 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

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1776 Sophie Germain (1 Apr 1776; died 27 Jun 1831 at age 55) French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc,{"In describing the honourable mission I charged him with, M. Pernety informed me that he made my name known to you. This leads me to confess that I am not as completely unknown to you as you might believe, but that fearing the ridicule attached to a female scientist, I have previously taken the name of M. LeBlanc in communicating to you those notes that, no doubt, do not deserve the indulgence with which you have responded." Letter to Gauss (1807)} She corresponded with Lagrange who recognized her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer.*TIS She worked in several areas of mathematics and science, including number theory. She proved Fermat's Last Theorem for exponents less than 100. In 1816 she won the Prix Bordin for her work on vibrations of elastic plates. Naturally, she was the first woman to win this prize. The competition question had be first set in 1811, and Germain was the only entry. In the reopened competitions of 1813 she was again the only entry, and she received an honorable mention. In the 1815 competition she was deemed worthy of the prize. *WM

Grave of Sophie Germain in Père Lachaise Cemetery

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1801 Henry Perigal, Jr. FRAS MRI (1 April 1801 – 6 June 1898) was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.
In his booklet Geometric Dissections and Transpositions (London: Bell & Sons, 1891) Perigal provided a proof of the Pythagorean theorem based on the idea of dissecting two smaller squares into a larger square. The five-piece dissection that he found may be generated by overlaying a regular square tiling whose prototile is the larger square with a Pythagorean tiling generated by the
two smaller squares. Perigal had the same dissection printed on his business cards, and it also appears on his tombstone.

As well as being interested in mathematics, Perigal was an accomplished lathe worker, and made models of mathematical curves for Augustus De Morgan. He believed (falsely) that the moon does not rotate with respect to the fixed stars, and used his knowledge of curvilinear motion in an attempt to demonstrate this belief to others. *Wik

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1874 Ernest William Barnes (1 April 1874 in Birmingham, England - 29 Nov 1953 in Sussex, England) English mathematician and theologian
In all, Barnes wrote 29 mathematical papers during the years 1897-1910. His early work was concerned with various aspects of the gamma function, including generalisations of this function given by the so-called Barnes G-function, which satisfies the equation

G(z+1)=G(z)Γ(z)

and to the double gamma function. Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure. He also considered second-order linear difference equations connected with the hypergeometric functions. In the last five of his papers dealing with the hypergeometric functions, Barnes made extensive use of the integrals studied by Mellin in which the integral involves gamma functions of the variable of integration. It was in these papers that he brought to the attention of British mathematicians the power and simplicity associated with these integrals, and which now bear the name Mellin-Barnes integrals. His last mathematical paper, published in 1910, was a short and elegant demonstration of a previously known result of Thomae concerning a transformation of a generalised hypergeometric function of unit argument into a more rapidly convergent function of the same kind. *SAU
He was educated at King Edward's School, Birmingham and Trinity College, Cambridge. He was Master of the Temple from 1915 to 1919. He was made Bishop of Birmingham in 1924. Barnes was perhaps the best known liberal bishop of his time, identified with the modernist or broad church movement. His episcopate was marked by continual controversy. His book The Rise of Christianity (1947) attacked many Christian claims, including the Virgin Birth and the bodily Resurrection of Christ. This led to calls that he should resign as a bishop. This Barnes refused to do. Earlier he had written "Should Such a Faith Offend?" (1927) and "Scientific Theory and Religion" (1933), and he was a contributor to 18 other books. His "Gorilla sermons", in which he promoted a Darwinian integration into theology, were famous throughout the country. *Wik

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1895 Alexander Craig Aitken (1 April 1895 in Dunedin, New Zealand - 3 Nov 1967 in Edinburgh, Scotland) He was asked to turn 4/47 into a decimal. After four seconds he answered, giving one digit every three-quarters of a second: `Point 08510638297872340425531914.' He stopped there|after 24 seconds, discussed the matter for a minute, and then started up again. `Yes, 191489. I can get that.' Five-second pause. `361702127659574468. Now that's the repeating point. It starts again at 085. So, if that's 46 places, I'm right.' " Exercise: Check this calculation on your hand calculator. Quoted from The Body by Anthony Smith, NY: Walker & amp; Co., 1968, p. 320. *VFR [Most hand calculators won't show all of the decimal places.. a nice property of repeating fractions can help uncover the rest.]

Aitken was one of New Zealand's most eminent mathematicians.  In a 1935 paper he introduced the concept of generalized least squares, along with now standard vector/matrix notation for the linear regression model. Another influential paper co-authored with his student Harold Silverstone established the lower bound on the variance of an estimator,  now known as Cramér–Rao bound. He was elected to the Royal Society of Literature for his World War I memoir, Gallipoli to the Somme.

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1898 – William James Sidis (April 1, 1898 – July 17, 1944) an American child prodigy with exceptional mathematical and linguistic abilities. He became famous first for his precocity, and later for his eccentricity and withdrawal from the public eye. He avoided mathematics entirely in later life, writing on other subjects under a number of pseudonyms. The difficulties Sidis encountered in dealing with the social structure of a collegiate setting may have shaped opinion against allowing such children to rapidly advance through higher education in his day.*Wik

He entered Harvard University at age 11 and, as an adult, was claimed by family members to have an IQ between 250 and 300, and to be conversant in about 25 languages and dialects. Some of these statements have not been verified, but many of his contemporaries, including Norbert Wiener, Daniel Frost Comstock, and William James, agreed that he was extremely intelligent.

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1932 Norman Abramson (April 1, 1932 – December 1, 2020 ) American computer scientist who created ALOHANET, the first modern data network, which formed the basis of the protocols essential in the Ethernet now in wide use. It opened in 1970, operating at 9600 bits per second, using radio to provide a wireless packet-switched data network between several Hawaii islands. Its innovations included the first packet radio sensors, the first packet radio repeaters, the first satellite packet network and the first radio access to the Internet. Abramson's U.S. patents include the first patent for CRC redundancy checks to provide data error control technique (No. 3,114,130), and the first patent issued for the design of burst errors in digital systems (No. 3,163,848).*TIS

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1947 Alain Connes (1 Apr 1947, )French mathematician won the 1982 Fields Medal (awarded in 1983) for his work in operator theory. His most remarkable contributions are general classification and a structure theorem for factors of type III, obtained in his thesis (1973);  classification of automorphisms of the hyperfinite factor, which served as a preparation for the next contribution;  classification of injective factors; and  application of the theory of C*-algebras to foliations and differential geometry in general. Connes' recent work has been on noncommutative geometry and he has studied applications to theoretical physics *TIS

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DEATHS

1820 Rev. Isaac Milner FRS (11 January 1750 – 1 April 1820) was a mathematician, an inventor, the President of Queens' College, Cambridge and Lucasian Professor of Mathematics.
He began his education at a grammar school in Leeds in 1756, but this ended in 1760 with the death of his father. He was apprenticed as a weaver, reading the classics when time permitted, until his elder brother, Joseph Milner, provided him with an opportunity. Joseph was offered the mastership at Hull's grammar school and invited Isaac to become the institution's usher.
Through the patronage of his brother, Milner was subsequently freed from his duties in Hull and entered Queens' College, Cambridge, as a sizar in 1770. He graduated BA as senior wrangler in 1774, winning the Smith's first prize.
In 1776 Nevil Maskelyne hired him as a computer for the board of longitude, and two of his mathematical papers were presented to the Royal Society, of which he was elected fellow in 1780. In these papers Milner displayed three things: proficiency in mathematics, suspicion of French philosophy, and adherence to English Newtonian mechanics.
In 1782 the Jacksonian professorship of natural philosophy was established and the syndicate selected Milner as the inaugural professor, a position he retained until 1792.
Milner also developed an important process to fabricate nitrous acid, a key ingredient in the production of gunpowder. His paper describing this process was published in the Royal Society's Philosophical Transactions in 1789 alongside an article of Joseph Priestley's, and the two corresponded on the subject. In later years Milner transferred his elaborate collection of chemical apparatus into the president's lodge at Queens' and performed experiments with E. D. Clarke, William Whewell, and the Wollaston brothers; he also collaborated with Humphry Davy and Joseph Banks in an attempt to cure gout.
He was instrumental in the 1785 religious conversion of William Wilberforce and a great supporter of the abolitionists' campaign against the slave trade, steeling Wilberforce with his assurance before the 1789 Parliamentary debate: "If you carry this point in your whole life, that life will be better spent than in being prime minister of many years."
*Wik

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1863 Jakob Steiner (18 Mar 1796; 1 Apr 1863 at age 67) Swiss mathematician who was one of the greatest, contributors to projective geometry. He discovered the Steiner surface which has a double infinity of conic sections on it. The Steiner theorem states that the two pencils by which a conic is projected from two of its points are projectively related. He is also known for the Poncelet-Steiner theorem which shows that only one given circle and a straight edge are required for Euclidean constructions. His work included conic sections and surfaces, the theory of second-degree surfaces and centre-of-gravity problems. He developed the principle of symmetrization (1840-41). In 1848 he ws the first to define various polar curves with respect to a given curve, and introduced the “Steiner Curves.” *TIS

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1872 Martin Ohm (6 May 1792 in Erlangen, Bavaria (now Germany)- 1 April 1872 in Berlin, Prussia, German Empire) was a German mathematician and a younger brother of physicist Georg Ohm. He earned his doctorate in 1811 at Friedrich-Alexander-University, Erlangen-Nuremberg where his advisor was Karl Christian von Langsdorf. Ohm was the first to fully develop the theory of the exponential a^b when both a and b are complex numbers in 1823. He is also often credited with introducing the name "golden section" (goldener Schnitt).
Ohm's students included Friedrich August, Friedrich Bachmann, Paul Bachmann, Joseph Brutkowski, Heinrich Eduard Heine, Rudolf Lipschitz, Leo Pochhammer, Friedrich Prym, Wilhelm Wagner, Hermann Waldaestel, Wilhelm Wernicke, Elena Gerz, Valentien Gerz, and Johanna Gerz. *Wik
Martin Ohm made a distinction between writing for mathematicians and writing for students, a distinction that many of his contemporaries, including Hermann Grassmann, did not consider appropriate. His colleagues Steiner and Kummer also ridiculed him for not following Alexander von Humboldt's firm belief in the unity of teaching and research. It is quite difficult to assess the importance of Ohm's mathematical contributions. The first thing to say is that they certainly weren't as important as he himself thought. He had a very high opinion of himself as the following quotation indicates. Niels Abel wrote to Christopher Hansteen, the professor of astronomy at the University of Christiania, while he was on a visit to Berlin in 1826

There is at [August Crelle's] house some kind of meeting where music is mainly discussed, of which unfortunately I do not understand much. I enjoy it all the same since I always meet there some young mathematicians with whom I talk. At Crelle's house, there used to be a meeting of mathematicians, but he had to suspend it because of a certain Martin Ohm with whom nobody could get along due to his terrible arrogance.

*SAU

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1912 Pyotr Nikolayevich Lebedev (8 Mar 1866; 1 Apr 1912 at age 46) Russian physicist who, in experiments with William Crookes' radiometer, proved (1910) that light exerts a minute pressure on bodies (as predicted by James Clerk Maxwell's theory of electromagnetism), and furthermore that this effect is twice as great for reflecting surfaces than for absorbent surfaces. He had proposed that light pressure on small particles of cosmic dust could be greater than gravitational attraction, thus explaining why a comet's tail points away from the Sun (though it is now understood the solar wind has a greater influence). He built an extremely small vibrator source capable of generating 4-6 mm waves, which he used to demonstrate the first observation of double refraction of electromagnetic waves in crystals of rhombic sulphur.*TIS

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1921 Carl Johannes Thomae (11 December 1840, Laucha an der Unstrut – 1 April 1921, Jena) (sometimes called "Johannes Thomae", "Karl Johannes Thomae", or "Johannes Karl Thomae") was a German mathematician. Carl Johannes Thomae's research was concerned with function theory and with what German-speaking mathematicians often call "Epsilontik", the precise development of analysis, differential geometry, and topology using epsilon-neighborhoods in the style of Weierstrass. The Thomae function, the Thomae transformation formula (aka, Thomae's transformation and Thomae's theorem), the Thomae formula for hyperelliptic curves, and the Sears–Thomae transformation formula are named after him. He called himself Riemann's student, although he never attended a lecture by Riemann. *TIS

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1908 Lev Davidovich Landau (22 Jan 1908; 1 Apr 1968) Soviet physicist who worked in such fields as low-temperature physics, atomic and nuclear physics, and solid-state, stellar-energy, and plasma physics. Several physics terms bear his name. He was awarded the 1962 Nobel Prize for Physics for his theory to explain the peculiar superfluid behaviour of liquid helium at very low temperature (2.18 K). Landau's further contributions are partly reflected in such terms as Landau diamagnetism and Landau levels in solid-state physics, Landau damping in plasma physics, the Landau energy spectrum in low-temperature physics, or Landau cuts in high-energy physics. *TIS

Offer Pade' added that The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938–1939. (Wikipedia)

I have used several of the book in the series and found them excellent.

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1971 Dame Kathleen Lonsdale (28 Jan 1903; 1 Apr 1971) British crystallographer (née Yardley) who developed several X-ray techniques for the study of crystal structure. Her experimental determination of the structure of the benzene ring by x-ray diffraction, which showed that all the ring C-C bonds were of the same length and all the internal C-C-C bond angles were 120 degrees, had an enormous impact on organic chemistry. She was the first woman to be elected (1945) to the Royal Society of London. *TIS

She received the highest score in 10 years during her university education, Seeing this, W.H. Bragg for his research team, gave her an invitation. The carbon allotrope, Lonsdaleite, was recognized by bearing her name.

In the abstract for a paper on Dame Lonsdale, 'WHERE ARE YOUR INTELLIGENT MOTHERS TO COME FROM?': MARRIAGE AND FAMILY IN THE SCIENTIFIC CAREER OF DAME

KATHLEEN LONSDALE FRS (1903-71) by Melinda Baldwin, Baldwin writes " Although she was one of the most successful female scientists in twentieth-century, the X-ray crystallographer Kathleen Yardley Lonsdale (1903-71) has received relatively little attention from historians of science. This paper, ... argues that Lonsdale' s scientific career was shaped in particular ways by her identity not just as a woman, but as a married woman and a mother.When interacting with her scientific colleagues, Lonsdale frequently had to confront the assumption that married women should not pursue scientific careers, an attitude shaped by

British concerns about reasserting traditional gender roles after the World Wars I and II.

Furthermore, although Lonsdale' s husband, Thomas, was an ardent supporter of her carrer, in the early 1930s Lonsdale left research temporarily to care for her small children. Her desire to work from home during this period led her to pursue one of her most significant scientific projects: the creation of crystallographic reference tables. Lonsdale's own experiences, and those of her female students, led her to focus on issues of marriage and family when she began speaking and writing about women in science during the late 1960's."

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And for a final teaser..here is an April Fools video about complex numbers.. enjoy





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 & Campbel