Victorian Political Correctness, Math Terminology, and Urban Legends

 The year 1913 seems to have had a strange effect on educational language, and as yet, I haven't figured out exactly what happened.

A few days ago, Dave Renfro, an internet associate who does more research into journals than anyone I have ever heard of, sent me a note that had an aside that said, "Also, ...,I've seen the terms "promiscuous exercises" and "promiscuous problems".

I did a little follow-up and found literally dozens of books that use the phrase "promiscuous problems". My Google Book search on the exact phrase produced 71 books and journals, mostly referring to mathematics, but not exclusively. In glancing at the dates, I noticed that almost all were before 1900. So I set the same search with a cut-off of before 1900. The result?... There were still 25, but only five of them were after 1910. Of these five, one was about sexual disorders of bulimic patients and had nothing to do with problem sets of the educational sort, one was a catalog of antiquarian objects and was referencing a phrase in an older object, two were reproductions of very old texts. That leaves the one final object after 1910 that referred to Promiscuous exercises in regard to problem sets, with a date of 1911, John Henry Diebel's  Arithmetic by Analysis. For some reason, the usage to describe a set of problems or exercises seems to have disappeared after that date almost completely.

So what do they mean, "promiscuous" problems. One of the definitions leads back to the old Latin root. Here is the way they gave the etymology in the Online Etymology Dictionary:

"consisting of a disorderly mixture of people or things," from L. promiscuus "mixed, indiscriminate," from pro- "forward" + miscere "to mix" (see mix). Meaning "indiscriminate in sexual relations" first recorded 1900, from promiscuity (1849, "indiscriminate mixture;" sexual sense 1865), from Fr. promiscuité, from L. promiscuus.

So the term was essentially used for a general mixture, thus promiscuous exercises were a mixed review; but then in 1900 the phrase became associated with "indiscriminate in sexual relations" and apparently that usage became so common, that the use of promiscuous exercises was no longer classroom acceptable.

Makes me think of a story that John H Conway, told (I believe) about the word hexagon. If you search the word "sexagon" you will see that it was very common in old math texts, then during the Victorian era, it became too suggestive for classroom use, and so hexagon, which also has a long history of use, became the preferred term. The earliest use of Sexagon in English , according to the OED, was by A. Rathborne in Surveyor, written in 1616. The term in English probably came from the use of Latin as the language of choice in science.  Sex was the prefix for six ans still remains in words like sextant, sexagenarian, and sextet.  Its demise may have been due to the hybrid nature of the word, sex from Latin and gon from the Greek for knee.  Hexagon was a union of two 

After I wrote this I got a comment:

r.r. vlorbik said...

i've heard, though never verified, that Victorian prudery also caused certain teachers to begin referring to the "arms" rather than the "legs" of a right triangle (the non-hypotenuse sides).
this is to say nothing of "parent function".i've *always* thought of the higher node
of a link in a tree as the "parent' of the lower... so this terminology (in discussion of
function transformations; x^2 is the "parent" for 3(x-2)^2 +1... you know the drill...) seems perfectly natural to me.

but somebody with some public-school experience told me,what may even be true, that up to a point,
one had called these things *mother* functions. which had to be made to stop.... latus rectum. (wrecked 'em, hell... it killed 'em).

So I was off on another search:

I have a pretty extensive collection of old textbooks, including many British texts, and I didn't remember ever seeing anyone use "arms" in that fashion, so my first thought was that, if it were true, it was only a very minor usage. Since the good lady Victoria, ruled from 1819 to 1901, I thought I would search before and after her reign.

I pulled out my 1804 edition of Playfair's "Elements of Geometry", published in Edinburgh. He referred to the right triangles sides as..."sides"... His Book VI, prop. XXXI reads exactly like the Thomas Heath Translation. No help there, so I skipped forward 99 years to the other end of the Victorian period, 1903 and looked in "A Junior Geometry" by Noel S Lyndon, published in London, only to find he also used only the terms hypotenuse and "other two sides" in his statement of the Pythagorean Thm.

Perhaps neither term was common in the Victorian period, and these stories were a bit of urban legend. I went on to Google Books to see if I could find any examples of geometric usage such as Vlorbik had described..... I entered a search for "arms 'right triangle' geometry"

....Yikes", there they were. The first listing was "Plane Geometry" by Arthur Schultze, Frank Louis Sevenoak, Limond C. Stone, from 1901. It contained, "The sum of the squares of the arms of a right triangle is equal to ..." along with 388 other listings, some dated as late as 2008. "In a right triangle whose arms have lengths a and 6, find the length of the .." appears on page 451 of the fourth edition of Schaum's Outline of Geometry from that year.

 Ok, but that still did not mean it was the influence of the dreaded Victorian stuffed-shirts... I switched the cut-off to 1850... and there were NO results prior to that year... only one last check. Would there be examples with the use of "legs" prior to that year? There were indeed, including several by the famous American Mathematician, Benjamin Pierce. Another from 1734 was from the British Benjamin Martin.

So it appears that there was some pressure to use "arms of a right triangle" suggested by these dates; but there is still no smoking gun. One observation that suggests that if such a suppression existed, it may have been much more influential in the US than in England. One is that the OED gives no reference to the use of arm as a mathematical or geometrical term.  The other is that most of the books  found using "arm" seemed to be of US origin. Does anyone out there know of a document or statement of any kind in the math education literature that makes a clear suggestion to teachers? If you know of such a document, please share whatever level of information you have and I will pursue it.

Functions, Parents, and Parent Functions

From what I have been able to discover in a short period of research, the use of terms like "parent function" seems to have worked its way into mathematics from statistics, which seems to have gotten it from the anthropologists/sociologists.

Across America and Asia: Notes of a Five Years' Journey Around the World ...‎ - Page 250 by Raphael Pumpelly - Voyages around the world - 1870
"if it should bear the same relation to the parent population that.."

Prior to 1900 there are almost no listings of "parent function" in a mathematical usage. Around the end of the 19th century, statisticians began to talk about the distribution from which a sample was taken as the "parent distribution" of the sampling distribution (population of all samples of some size n). Some of these may be related to the study of eugenics in which the study was about the relations of some characteristic of the offspring to the actual parents, but the usage grew.

Data reduction and error analysis for the physical sciences , by Philip R. Bevington - 1969 10-2 the F TEST As discussed in the previous section, the x^2(chi square) test is somewhat ambiguous unless the form of the parent function is known because the statistic
x^2 (chi-sq)... "

Occasionally I find the term "parent function" applied in this way when the distribution of the original sample was a normal distribution.
The Annals of mathematical statistics‎ - Page 179
by American Statistical Association, Institute of Mathematical Statistics, JSTOR (Organization) - 1948" Usually the parent function is the Type A or normal curve, as discussed by Gram "

There are also some early uses of the "parent function" in association with the use of inverses and derivatives in calculus and analysis texts back to about 1925. By 1970 the term had become commonly understood, but not abundantly used.

The teaching of secondary mathematics‎ - Page 521
by Charles Henry Butler, Frank Lynwood Wren - Education - 1965 - 613 pages
".. of an inverse function and its relation to the parent function or else in failure to attach clear meanings to the terminology and notation employed. ..."

It was the 1980's and the introduction of computers and graphing calculators into modern classrooms that seemed to make the term "parent function" ubiquitous. Any function that appeared on the calculator was a parent function, and the translations, rotations, shears, etc became the "children".
I think this use also led to the introduction of "mother function" rather than the other way around. I can only find a few examples of "mother function" and there does not seem to be any pattern to the frequency as one might expect if a term had arisen to replace this one as an "off-color" predecessor. In fact, it seems "mother function" is more commonly used by continental writers, often in conjunction with "daughter functions"; but admittedly the sample size I have to draw on was small. Perhaps these were early pioneers for language equality.

If you are one of those people with access to old journals, or a collection of old texts, I would appreciate any references to the use of any of these terms and a source earlier than 1900; and if you have a way to make a digital copy and send it by email, I will have my students name their children after you.  

On This Day in Math - May 3

We by art gain mastery over things which we are conquered by Nature

quotation from Antiphon which on the title page of John Wilkins' Mathematical Magick

The 123rd day of this year; The number formed by the concatenation of odd numbers from 123 down to 1 is prime. (ie 123121119...531 is Prime) *Prime Curios (Who figures stuff like this out???)

Japan Airlines Flight 123, was the world's deadliest single-aircraft accident in history

and 123 might remind you that ln(1) + ln(2) + ln(3) = ln (1 + 2 + 3 )

And here is an interesting curiosity from the archimedes-lab.org/numbers file:
Write down any number (excluding the digit 0):
64861287124425928
Now, count up the number of even and odd digits, and the total number of digits it contains, as follows:
12 | 5 | 17
Then, string those 3 numbers together to make a new number, and perform the same operation on that:
12517
1 | 4 | 5
Keep iterating:
145
1 | 2 | 3
You will always arrive at 123.   
Maybe not always !  A comment pointed out that if all the digits are odd, or all even, it doesn't work

And 123 is the difference of two squares in two different ways, 62² - 61² and 22² - 19².  The pattern of both these are explained in Day 111.  at Math Day of the Year Facts: Number Facts for Every Year Day (91-120) (mathdaypballew.blogspot.com)

---

EVENTS

1375 BC, the oldest recorded eclipse occurred, according to one plausible interpretation of a date inscribed on a clay tablet retrieved from the ancient city of Ugarit, Syria (as it is now). This date is one of two plausible dates usually cited from the record, though 5 Mar 1223 is the more favoured date by most recent authors on the subject. Certainly by the 8th century BC, the Babylonians were keeping a systematic record of solar eclipses, and possibly by this time they may have been able to apply numerological rules to make fairly accurate predictions of the occurrence of solar eclipses. The first total solar eclipse reliably recorded by the Chinese occurred on 4 Jun 180 *TIS
(A new historical dating of the tablet, and mention in the text of the visibility of the planet Mars during the eclipse as well as the month in which it occurred enables us to show that the recorded eclipse in fact occurred on 5 March 1223 BC. This new date implies that the secular deceleration of the Earth's rotation has changed very little during the past 3,000 years. *nature.com) With thanks to Bill Thayer ‏@LacusCurtius

---

1661 Equipment used by Hevelius with a telescope to project an astronomical image onto a sheet of paper. This arrangement was used in his historic observation of the transit of Mercury on May 3, 1661. His surviving books are filled with great images by himself and his second wife, Elisabeth Koopman whom he would marry two years after this transit. * Maria Popova at brainpickings.org
This was the first observation of a transit of Mercury in the Month of May. The two previous transits had both been in November in 1631 and 1651. This observation was visible in London and occurred on the day of the Coronation of King Charles II . It was observed by Christiaan Huygens in London. *Wik

---

1715 May 3 A total solar eclipse was observed in England from Cornwall in the south-west to Lincolnshire and Norfolk in the east. This eclipse is known as Halley's Eclipse, after Edmund Halley (1656–1742) who predicted this eclipse to within 4 minutes accuracy. Halley observed the eclipse from London where the city of London enjoyed 3 minutes 33 seconds of totality. He also drew a predictive map showing the path of totality across England. The original map was about 30 km off the observed eclipse path. After the eclipse, he corrected the eclipse path, and added the path and description of the 1724 total solar eclipse.Note: Great Britain didn't adopt the Gregorian calendar until 1752, so the date was considered 22 April 1715. *Wik… The Royal Society reports: Edmund Halley, a Fellow of the Royal Society, is most famous for his work on the orbits of comets, predicting when the one that now bears his name would be seen; however, his interests were more widespread. In 1715 the first total solar eclipse for 500 years took place over England and Wales. Halley, a talented mathematician, realized that such an event would generate a general curiosity and requested that the ‘curious’ across the country should observe ‘what they could’ and make a record of the time and duration of the eclipse. At the time, there were only two universities in England and their astronomy professors did not have much luck in observing the event: ‘the Reverend Mr Cotes at Cambridge had the misfortune to be oppressed by too much company’ and ‘Dr John Keill by reason of clouds, saw nothing distinctly at Oxford but the end’. The event did indeed capture the imagination of the nation and the timings collected allowed Halley to work out the shape of the eclipse shadow and the speed at which it passed over the Earth (29 miles per minute).

---

1834 In response to a letter from William Whewell at Cambridge suggesting the names "anode" and "cathode"; Faraday says ,"All your names I and my friend approve of or nearly all as to sense & expression, but I am frightened by their length & sound when compounded. As you will see I have taken deoxide and skaiode because they agree best with my natural standard East and West. I like Anode & Cathode better as to sound, but all to whom I have shewn them have supposed at first that by Anode I meant No way." (within a few weeks he would change his mind about using the two terms, see 15 may, 1834)

---

1841 L. G. J. Jacobi, who made a lengthy study of Euler’s and d’Alembert’s works, wrote “It is worth noting that it is impossible today to choke down a single line of d’Alembert’s mathematics, while most of Euler’s works can be read with delight, and they died in the same year [1783]. D’Alembert seems to have been entirely absorbed in belles-lettres.” [Hawkins, Jean D’Alembert, p 63]. *VFR

---

1849 Arthur Cayley called to the Bar. He abandoned his fellowship at Cambridge and took up law as he didn’t want to take Holy Orders. During his 14 years at the bar he wrote nearly 300 mathematical papers. *VFR
1902 The San Francisco Section of the AMS was founded at a gathering of twenty mathematicians at the Academy of Sciences, San Francisco, CA. [AMS Semicentennial Publications, vol 1, p 8].

---

1934 Henri-Leon Lebesgue elected foreign member of the Royal Society. From 1899 until 1903 he taught at the Lyc´ee at Nancy, France, where he wrote his famous doctoral thesis “Int´egrale, longueur, aire,” which proposed a now standard extension of the Riemann integral. See The Mathematical Intelligencer, 6(1984), no. 2, p. 8. *VFR

---

1997 Garry Kasparov beat IBM's Deep Blue in the first match of what many considered a test of artificial intelligence. The world's best chess player, Kasparov eventually lost the match and $1.1 million purse to the IBM supercomputer, which he had claimed could never surpass human chess ability. After losing the sixth and final game of the match, Kasparov accused IBM of building a machine specifically to beat him. Observers said he was frustrated by Deep Blue's quickness although they expected him to win with unconventional moves. *CHM On February 10, 1996, Deep Blue became the first machine to win a chess game against a reigning world champion (Garry Kasparov) under regular time controls. However, Kasparov won three and drew two of the following five games, beating Deep Blue by a score of 4–2 (wins count 1 point, draws count ½ point). The match concluded on February 17, 1996.
Deep Blue was then heavily upgraded (unofficially nicknamed "Deeper Blue")[11] and played Kasparov again in May 1997, winning the six-game rematch 3½–2½, ending on May 11. *Wik

---

2016 Three computer scientists have announced the largest-ever mathematics proof: a file that comes in at a whopping 200 terabytes1, roughly equivalent to all the digitized text held by the US Library of Congress. The researchers have created a 68-gigabyte compressed version of their solution — which would allow anyone with about 30,000 hours of spare processor time to download, reconstruct and verify it — but a human could never hope to read through it.
Computer-assisted proofs too large to be directly verifiable by humans have become commonplace, and mathematicians are familiar with computers that solve problems in combinatorics — the study of finite discrete structures — by checking through umpteen individual cases. Still, “200 terabytes is unbelievable”, says Ronald Graham, a mathematician at the University of California, San Diego. The previous record-holder is thought to be a 13-gigabyte proof2, published in 2014.
The puzzle that required the 200-terabyte proof, called the Boolean Pythagorean triples problem, has eluded mathematicians for decades. In the 1980s, Graham offered a prize of US$100 for anyone who could solve it. (He duly presented the cheque to one of the three computer scientists, Marijn Heule of the University of Texas at Austin, earlier this month.) The problem asks whether it is possible to colour each positive integer either red or blue, so that no trio of integers a, b and c that satisfy Pythagoras’ famous equation a2 + b2 = c2 are all the same colour. For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were coloured blue, 4 would have to be red.
In a paper posted on the arXiv server on 3 May, Heule, Oliver Kullmann of Swansea University, UK, and Victor Marek of the University of Kentucky in Lexington have now shown that there are many allowable ways to colour the integers up to 7,824 — but when you reach 7,825, it is impossible for every Pythagorean triple to be multicoloured1. There are more than 102,300 ways to colour the integers up to 7,825, but the researchers took advantage of symmetries and several techniques from number theory to reduce the total number of possibilities that the computer had to check to just under 1 trillion. It took the team about 2 days running 800 processors in parallel on the University of Texas’s Stampede supercomputer to zip through all the possibilities. The researchers then verified the proof using another computer program. *Evelyn Lamb, nature.com

---

BIRTHS

1695 Henri Pitot (3 May 1695; 27 Dec 1771 at age 76) French hydraulic engineer who invented the Pitot tube (1732), an instrument to measure flow velocity either in liquids or gases. With subsequent improvements by Henri Darcy, its modern form is used to determine the airspeed of aircraft. Although originally a trained mathematician and astronomer, he became involved with an investigation of the velocity of flowing water at different depths, for which purpose he first created the Pitot tube. He disproved the prevailing belief that the velocity of flowing water increased with depth. Pitot became an engineer in charge of maintenance and construction of canals, bridges, drainage projects, and is particularly remembered for his kilometer-long Roman-arched Saint-Clément Aqueduct (1772) at Montpellier, France.*TIS

---

1860 Vito Volterra (3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations.In 1922, he joined the opposition to the Fascist regime of Benito Mussolini and in 1931 he was one of only 12 out of 1,250 professors who refused to take a mandatory oath of loyalty. His political philosophy can be seen from a postcard he sent in the 1930s, on which he wrote what can be seen as an epitaph for Mussolini’s Italy: Empires die, but Euclid’s theorems keep their youth forever. However, Volterra was no radical firebrand; he might have been equally appalled if the leftist opposition to Mussolini had come to power, since he was a lifelong royalist and nationalist. As a result of his refusal to sign the oath of allegiance to the fascist government he was compelled to resign his university post and his membership of scientific academies, and, during the following years, he lived largely abroad, returning to Rome just before his death.*Wik
André WEIL spent 1925-1926 studying with Volterra. Volterra was President of the the ACCADEMIA DEI LINCEI (or Lyncei). This was the first modern learned society. It was founded in Rome by Prince Federigo Cesi in 1603. The word 'lincei' means 'lynx-eyed', but actually derives from the Greek argonaut Linkeus, the eponym of the animal. Lynxes are on the crest of the Accademia

---

1874 V(agn) Walfrid Ekman (3 May 1874, 9 Mar 1954 at age 79) Swedish physical oceanographer and mathematical physicist whose research into the dynamics of ocean currents led to his name remaining associated with terms for particular phenomena of the ocean or atmosphere, including Ekman spiral, Ekman transport and Ekman layer. Fridtjof Nansen pointed out to Ekman that he had noticed that icebergs drift at an angle of 20°-40° to the prevailing wind, rather than directly with the wind. In 1902, Ekman published an explanation, known now as the Ekman spiral, describing movement of ocean currents influenced by the Earth's rotation. He also developed experimental techniques and instruments such as the Ekman current meter and Ekman water bottle.*TIS

---

1892 Sir George Paget Thomson (3 May 1892; 10 Sep 1975 at age 83) English physicist who shared (with Clinton J. Davisson of the U.S.) the Nobel Prize for Physics in 1937 for demonstrating that electrons undergo diffraction, a behaviour peculiar to waves that is widely exploited in determining the atomic structure of solids and liquids. He was the son of Sir J.J. Thomson who discovered the electron as a particle. *TIS

---

1902 Alfred Kastler (3 May 1902; 7 Jan 1984 at age 81) French physicist who won the Nobel Prize for Physics in 1966 for his discovery and development of methods for observing Hertzian resonances within atoms. This research facilitated the greater understanding of the structure of the atom by studying the radiations that atoms emit when excited by light and radio waves. He developed a method called "optical pumping" which caused atoms in a sample substance to enter higher energy states. This idea was an important predecessor to the development of masers and the lasers which utilized the light energy that was re-emitted when excited atoms released the extra energy obtained from optical pumping. *TIS

---

1924 Isadore Manuel Singer (April 24, 1924), Detroit Michigan. "Singer is justifiably famous among mathematicians for his deep and spectacular work in geometry, analysis, and topology, culminating in the Atiyah-Singer Index theorem and its many ramifications in modern mathematics and quantum physics." *SAU

---

1933 Steven Weinberg (3 May 1933, )American nuclear physicist who shared the 1979 Nobel Prize for Physics (with Sheldon Lee Glashow and Abdus Salam) for work in formulating the electroweak theory, which explains the unity of electromagnetism with the weak nuclear force. *TIS

---

DEATHS

1657 Johann Baptist Cysat (1586, 3 May 1657), Latinized as Cysatus was a Swiss astronomer who entered the Jesuit order (1604), and by 1611 was studying at the Jesuit college in Ingolstadt, Bavaria, under Christoph Scheiner, whom he assisted in the observation of sunspots. From 1618, he taught mathematics there. As an early user of a telescope, he was the first to make substantial telescopic observation of a comet (1 Dec 1618 to 22 Jan 1619), Although he discovered the Orion Nebula independently (1619), it had been first noted by Peiresc in 1610. Cysat wrote to Kepler describing a lunar eclipse (1620) and observed the transit of Mercury (1631). It is the comet study for which Cysat is noted. His measurements of its position were made using a 6-foot radius wooden sextant. He published his data and analysis in an 80-page booklet, Mathemata astronomica de locu...cometae... (1619). *TIS

---

1764 Francesco Algarotti (11 Dec 1712, 3 May 1764 at age 51) Italian scholar of the arts and sciences, recognized for his wide knowledge and elegant presentation of advanced ideas. At age 21, he wrote Il Newtonianismo per le dame (1737; "Newtonianism for Ladies"), a popular exposition of Newtonian optics. He also wrote about architecture, opera and painting. *TIS

---

1779 John Winthrop (December 19, 1714 – May 3, 1779) was the 2nd Hollis Professor of Mathematics and Natural Philosophy in Harvard College. He was a distinguished mathematician, physicist and astronomer, born in Boston, Mass. His great-great-grandfather, also named John Winthrop, was founder of the Massachusetts Bay Colony. He graduated in 1732 from Harvard, where, from 1738 until his death he served as professor of mathematics and natural philosophy. Professor Winthrop was one of the foremost men of science in America during the 18th century, and his impact on its early advance in New England was particularly significant. Both Benjamin Franklin and Benjamin Thompson (Count Rumford) probably owed much of their early interest in scientific research to his influence. He also had a decisive influence in the early philosophical education of John Adams, during the latter's time at Harvard. He corresponded regularly with the Royal Society in London—as such, one of the first American intellectuals of his time to be taken seriously in Europe. He was noted for attempting to explain the great Lisbon earthquake of 1755 as a scientific—rather than religious—phenomenon, and his application of mathematical computations to earthquake activity following the great quake has formed the basis of the claim made on his behalf as the founder of the science of seismology. Additionally, he observed the transits of Mercury in 1740 and 1761 and journeyed to Newfoundland to observe a transit of Venus. He traveled in a ship provided by the Province of Massachusetts - probably the first scientific expedition ever sent out by any incipient American state. *Wik

---

1880 Jonathan Homer Lane (August 9, 1819, Geneseo, New York – May 3, 1880, Washington D.C.) U.S. astrophysicist who was the first to investigate mathematically the Sun as a gaseous body. His work demonstrated the interrelationships of pressure, temperature, and density inside the Sun and was fundamental to the emergence of modern theories of stellar evolution. *TIS Simon Newcomb, in his memoirs, describes Lane as "an odd-looking and odd-mannered little man, rather intellectual in appearance, who listened attentively to what others said, but who, so far as I noticed, never said a word himself." Newcomb recounts his own role in bringing Lane's work, in 1876, to the attention of William Thomson who further popularized the work. Newcomb notes, "it is very singular that a man of such acuteness never achieved anything else of significance." *Wik

---

1885 Ernst Ferdinand Adolf Minding (23 Jan 1806 in Kalisz,Russian Empire (now Poland) - 3 May 1885 in Dorpat, Russia (now Tartu, Estonia))His work, which continued Gauss's study of 1828 on the differential geometry of surfaces, greatly influenced Peterson. In

---

1830 Minding published on the problem of the shortest closed curve on a given surface enclosing a given area. He introduced the geodesic curvature although he did not use the term which was due to Bonnet who discovered it independently in 1848. In fact Gauss had proved these results, before either Minding of Bonnet, in 1825 but he had not published them.
Minding also studied the bending of surfaces proving what is today called Minding's theorem in 1839. The following year he published in Crelle's Journal a paper giving results about trigonometric formulae on surfaces of constant curvature. Lobachevsky had published, also in Crelle's Journal, related results three years earlier and these results by Lobachevsky and Minding formed the basis of Beltrami's interpretation of hyperbolic geometry in 1868.
Minding also worked on differential equations, algebraic functions, continued fractions and analytic mechanics. In differential equations he used integrating factor methods. This work won Minding the Demidov prize of the St Petersburg Academy in 1861. It was further developed by A N Korkin. Darboux and Émile Picard pushed these results still further in 1878. *SAU

---

1988 Lev Semenovich Pontryagin (3 September 1908 – 3 May 1988) One of the 23 problems posed by Hilbert in 1900 was to prove his conjecture that any locally Euclidean topological group can be given the structure of an analytic manifold so as to become a Lie group. This became known as Hilbert's Fifth Problem. In 1929 von Neumann, using integration on general compact groups which he had introduced, was able to solve Hilbert's Fifth Problem for compact groups. In 1934 Pontryagin was able to prove Hilbert's Fifth Problem for abelian groups using the theory of characters on locally compact abelian groups which he had introduced. *SAU [He was buried at the Novodevichie Memorial Cemetery in Moscow.

---

1988 Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician. He was known for his research to commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several important papers.*Wik

---

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

 

On This Day in Math - May 2

 

We call a thing big or little

with reference to what it is wont to be, 

as we speak of a small elephant

or a big rat.

D'Arcy Thompson, "On Growth and Form"

The 122nd day of the year; there are 122 different ways to partition the number 24 into distinct parts.  Euler showed that this is the same as the number of ways to partition a number into odd parts.

122 ends in the digit two when written in base 3, 4, 5, 6, 8, 10, 12, 15, and 20.  How unusual is that?

122 squared minus each of its prime factors squared is also prime
and 122 is the smallest sum of two non-consecutive factorials of distinct primes (2! + 5!) *Prime Curios

---

EVENTS

1775 Benjamin Franklin completed the first scientific study of the Gulf Stream. His observations began in 1769 when as deputy postmaster of the British Colonies he found ships took two weeks longer to bring mail from England than was required in the opposite direction. Thus, Franklin became the first to chart the Gulf Stream.He described the Gulf Stream as a river of warm water and mapped it as flowing north from the West Indies, along the East Coast of North America and east across the Atlantic Ocean to Europe. *TIS

---

In 1800, English chemist William Nicholson was the first to produce a chemical reaction by electricity. He had been working with Anthony Carlisle, a London surgeon, experimenting with Allesandro Volta's voltaic pile. The new effect was discovered when wires from the poles of the battery being used came into contact with water and bubbles of gas were released as current flowed through the water. Closer examination of the electrolysis showed oxygen was released at the (positive) anode, and hydrogen appeared at the cathode. Electricity had separated the molecules of water. Further, the effect of the amount of hydrogen and oxygen set free by the current was proportional to the amount of current used.*TIS

---

1880 The first commercial order of an Edison Lighting system was installed on the newly launched Steamship Columbia. The dynamo and lights were installed by Edison Engineers and first lighting was on May 2, 1880. The event was featured in the May issue of Scientific American. John Roach and Sons had built the ship in their Chester, Pennsylvania ship works and launched it on Feb 24, 1880. *The History of the American Bureau of Shipping.

---

1983 Microsoft Introduces 2-button Mouse:
Microsoft Corp. announced the two-button Microsoft Mouse, which it introduced to go along with its new Microsoft Word processor. Microsoft built about 100,000 of these fairly primitive units for use with IBM and IBM-compatible personal computers but sold only 5,000 before finding success in a 1985 version that featured, among other improvements, near-silent operation on all surfaces.*CHM
In ensuing years, as mice made their way to personal computers, there was something of a battle waged between proponents of 2-button and 3-button mice, with Logitech favoring the 3-button variety

---

BIRTHS

1588 Etienne Pascal (Clermont, May 2, 1588 - Paris, September 24, 1651), for whom the limacon of Pascal was named. He was the father of Blaise Pascal. The limacon was named by another Frenchman Gilles-Personne Roberval in 1650 when he used it as an example of his methods of drawing tangents
i.e. differentiation.
The name "limacon" comes from the Latin limax meaning 'a snail'. Étienne Pascal corresponded with Mersenne whose house was a meeting place for famous geometers including Roberval.
Dürer should really be given the credit for discovering the curve since he gave a method for drawing the limacon, although he did not call it a limacon, in Underweysung der Messungpublished in 1525. *SAU [Etienne Pascal was one of the "nine lovers of literature established a regular meeting. In 1635, Richelieu organized them into an Académie Libre or ACADÉMIE FRANÇAISE." This was the forerunner of the ACADÉMIE DES SCIENCES. pb]

---

1601 Athanasius Kircher (2 May 1601; 28 Nov 1680 at age 79) German Jesuit priest and scholar, sometimes called the last Renaissance man. Kircher's prodigious research activity spanned a variety of disciplines including geography, astronomy, physics, mathematics, language, medicine, and music. He made an early, though unsuccessful attempt to decipher hieroglyphics of the Coptic language. During the pursuit of experimental knowledge, he once had himself lowered into the crater of Vesuvius to observe its features soon after an eruption. He made one of the first natural history collections. Kircher studied animal luminescence, writing two chapters of his book Ars Magna Lucis et Umbrae to bioluminescence, and debunked the idea that that an extract made from fireflies could be used to light houses.*TIS

---

1773 Henrik Steffens (2 May 1773–13 February 1845), was a Norwegian-born Danish philosopher, scientist, and poet. He was one of the so-called "Philosophers of Nature", a friend and adherent of Schelling and of Schleiermacher. More than either of these two thinkers he was acquainted with the discoveries of modern science, and was thus able to correct or modify the highly imaginative speculations of Schelling. He held that, throughout the scheme of nature and intellectual life, the main principle is Individualisation. As organisms rise higher in the scale of development, the sharper and more distinct become their outlines, the more definite their individualities. This principle he endeavoured to deduce from his knowledge of geology, in contrast to Lorenz Oken, who developed the same theory on biological grounds. His influence was considerable, and both Schelling and Schleiermacher modified their theories in deference to his scientific deductions.*Wik

---

1860 Sir D'Arcy Wentworth Thompson (2 May 1860; 21 Jun 1948 at age 88)
Scottish zoologist and classical scholar, who is noted for his influential work On Growth and Form (1917, new ed. 1942). It is a profound consideration of the shapes of living things, starting from the simple premise that “everything is the way it is because it got that way.” Hence one must study not only finished forms, but also the forces that moulded them: “the form of an object is a ‘diagram of forces’, in this sense, at least, that from it we can judge of or deduce the forces that are acting or have acted upon it.”' One of his great themes is the tremendous light cast on living things by using mathematics to describe their shapes and fairly simple physics and chemistry to explain them..*TIS
He graduated from Cambridge University in Zoology and was appointed Professor of Biology at Dundee and later Professor of Natural History at St Andrews. He combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. He became an honorary member of the EMS in 1933.*SAU [The University of Dundee and the University of St Andrews joined to host a celebration of Thompson's sesquicentennial birth year (2010) with a series of events. They have a photo gallery still available at the time of this writing. ]

---

1868 Robert W. Wood (2 May 1868; 11 Aug 1955 at age 87) was an American physicist who photographed the reflection of sound waves in air, and investigated the physiological effects of high-frequency sound waves. The zone plate he devised could replace the objective lens of a telescope. He invented an improved diffraction grating, did research in spectroscopy, and extended the technique of Raman spectroscopy (a method to study matter using the light scattered by it.) He made photographs showing both infrared and ultraviolet radiation and was the first to photograph ultraviolet fluorescence. Wood was the first to observe the phenomenon of field emission in which charged particles are emitted from conductors in an electric field. *TIS
According to a post at Greg Ross' Futility Closet:

"How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:
The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.
This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”

---

1901 Edouard Zeckendorf (2 May 1901 - 16 May 1983) was a Belgian doctor, army officer and mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem. Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.
Zeckendorf was born in Liège in 1901. He was the son of a Dutch dentist. In 1925, Zeckendorf graduated as a medical doctor from the University of Liège and joined the Belgian Army medical corps. When Germany invaded Belgium in 1940, Zeckendorf was taken prisoner and remained a prisoner of war until 1945. During this period, he provided medical care to other allied POWs. *Wik

---

1928 Jacques-Louis Lions (2 May 1928 in Grasse, Alpes-Maritimes, France - 17 May 2001 in Paris, France) French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John Von Neumann prize in 1986. *Wik

---

Sumio Iijima (May 2, 1939, )is a Japanese physicist, often cited as the discoverer of carbon nanotubes. Although carbon nanotubes had been observed prior to his "discovery"1, Iijima's 1991 paper generated unprecedented interest in the carbon nanostructures and has since fueled intense research in the area of nanotechnology. For this and other work Sumio Iijima was awarded, together with Louis Brus, the inaugural Kavli Prize for Nanoscience in 2008. *Wik (Quotes of Sumio Iijma by Arjen Dijksman)

---

DEATHS

1519 Leonardo da Vinci (15 Apr 1452, 2 May 1519 at age 67) Italian painter, draftsman, sculptor, architect, and engineer. Da Vinci was a great engineer and inventor who designed buildings, bridges, canals, forts and war machines. He kept huge notebooks sketching his ideas. Among these, he was fascinated by birds and flying and his sketches include such fantastic designs as flying machines. These drawings demonstrate a genius for mechanical invention and insight into scientific inquiry, truly centuries ahead of their time. His greater fame lies in being one of the greatest painters of all times, best known for such paintings as the Mona Lisa and The Last Supper.*TIS

---

1925 Johann Palisa (6 Dec 1848, 2 May 1925 at age 76)Austrian astronomer who was a prolific discoverer of asteroids, 122 in all, beginning with Asteroid 136 Austria (on 18 Mar 1874, using a 6" refractor) to Asteroid 1073 Gellivara in 1923 - all by visual observation, without the aid of photography. In 1883, he joined the expedition of the French academy to observe the total solar eclipse on May 6 of that year. During the eclipse, he searched for the putative planet Vulcan, which was supposed to circle the sun within the orbit of Mercury. In addition to observing the eclipse, Palisa collected insects for the Natural History Museum in Vienna. He also prepared two catalogs containing the positions of almost 4,700 stars. He remains the most successful visual discoverer in the history of minor planet research.*TIS

---

1967 Robert Daniel Carmichael (1 March 1879 in Goodwater, Coosa County, Alabama, USA - 2 May 1967 in Merriam, Northeast Johnson County, Kansas, USA) Carmichael is known for his mathematical research in what are now called the Carmichael numbers (numbers satisfying properties of primes described by Fermat's Little Theorem although they are not primes- see below), Carmichael's theorem, and the Carmichael function, all significant in number theory and in the study of the prime numbers. Carmichael might have been the first to describe the Steiner system S(5,8,24), a structure often attributed to Ernst Witt. While at Indiana University Carmichael was involved with special theory of relativity. *Wik Fermat had proved that if n is prime then xn-1 = 1 mod n for every x coprime to n. A 'Carmichael number' is a non-prime n satisfying this condition for any x coprime to n. It was given this name since Carmichael discovered the first such number, 561, in 1910 (there are several base ten Carmichael numbers below 561 for the interested student to search for). For many years it was an open problem as to whether there were infinitely many Carmichael numbers, but this was settled in 1994 by W R Alford, A Granville, and C Pomerance in their paper There are infinitely many Carmichael numbers. *SAU

---

1981 David Wechsler (12 Jan 1896, 2 May 1981 at age 85) U.S. psychologist and inventor of several widely used intelligence tests for adults and children. During WW I, while assisting Edwin Garrigues Boring (1886-1968) in testing army recruits, Wechsler realized the inadequacies of the Army Alpha Tests (designed to measure abilities of conscripts and match them to suitable military jobs). He concluded that academically defined "intelligence" did not apply to "real life" situations. After leaving the military and more years of research, he developed the Wechsler Adult Intelligence Scale, and introduced deviation scores in intelligence tests. He developed the Wechsler Memory Scale in 1945, Wechsler Intelligence Scale for Children (1949), and Wechsler Preschool and Primary Scale of Intelligence (1967). *TIS

---

1982 Salomon Bochner (20 Aug 1899, 2 May 1982 at age 82) Galician-born American mathematician and educator responsible for the development of the Bochner theorem of positive-definite functions and the Bochner integral.*TIS
In 1925 he started work in the area of almost periodic functions, simplifying the approach of Harald Bohr by use of compactness and approximate identity arguments. In 1933 he defined the Bochner integral, as it is now called, for vector-valued functions. Bochner's theorem on Fourier transforms appeared in a 1932 book. His techniques came into their own as Pontryagin duality and then the representation theory of locally compact groups developed in the following years.
Subsequently he worked on multiple Fourier series, posing the question of the Bochner–Riesz means. This led to results on how the Fourier transform on Euclidean space behaves under rotations.
In differential geometry, Bochner's formula on curvature from 1946 was most influential. Joint work with Kentaro Yano (1912–1993) led to the 1953 book Curvature and Betti Numbers. It had broad consequences, for the Kodaira vanishing theory, representation theory, and spin manifolds.*WIK

---

2004 John Hammersley (21 March 1920-2 May 2004) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. *Wik when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)
During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, `On the enfeeblement of mathematical skills by `Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. (from his Independent obituary)

---

2010 Clive W. Kilmister (1924 – May 2, 2010) was a British Mathematician who specialized in the mathematical foundations of Physics, especially Quantum Mechanics and Relativity and published widely in these fields (see References). He was one of the discoverers of the Combinatorial Hierarchy, along with A. F. Parker-Rhodes, E. W. Bastin, and J.C.Amson. He was strongly influenced by astrophysicist Arthur Eddington and was well known for his elaboration and elucidation of Eddington’s fundamental theory.
Kilmister attended Queen Mary College London for both his under- and postgraduate degrees. His PhD was supervised by cosmologist George McVittie (himself a student of Eddington), and his dissertation was entitled ‘’The Use of Quaternions in Wave-Tensor Calculus’’ which related to Eddington’s work. Kilmister received his doctoral degree in 1950. His own students included Brian Tupper (1959, King's College London, now professor emeritus of general relativity and cosmology at University of New Brunswick Fredericton [2]), Samuel Edgar (1977, University of London), and Tony Crilly (reader in mathematical sciences at Middlesex University and author of The Big Questions: Mathematics (1981).
Kilmister was elected as a member of the London Mathematical Society during his doctoral studies (March 17, 1949). Upon graduation, he began his career as an Assistant Lecturer in the Mathematics Department of King’s College in 1950. The entirety of his academic career was spent at King’s. In 1954, Kilmister founded the King’s Gravitational Theory Group, in concert with Hermann Bondi and Felix Pirani, which focused on Einstein’s theory of general relativity. At retirement, Kilmister was both a Professor of Mathematics and Head of the King’s College Mathematics Department.
He was Gresham Professor of Geometry, 1972-88. *Wik

---

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

On This Day in Math - May 1

The only way to learn a new programming language

is by writing programs in it.

- B. Kernighan & D. Ritchie

The 121st day of the year; 121 will be the largest year day of the form n!+1 which is a square number. Brocard conjectured in 1904 that the only solutions of n! + 1 = m² are n = 4, 5, and 7. There are no other solutions with \(n \lt 10^ 9\). 121 is also the only square of the form 1 + n + n²+ n³ + n⁴. *What's So Special About This Number

121 is also a Smith Number, a composite number for which the sum of its digits is equal to the sum of the digits in its prime factorization. Smith numbers were named by Albert Wilansky of Lehigh University. He noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:
4937775 = 3 × 5 × 5 × 65837, while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42.
There are 49 Smith numbers below 1000, collect the whole set.

121 is a palindrome in base ten, and also in base 3 (11111), base 7 (232) and base 8(171). No other year day is a base ten palindrome  and also palindrome in as many other (2-9) bases.

---

EVENTS

1006 Supernova is observed in the constellation Lupus, the Wolf. *VFR
[SN 1006 was a supernova, widely seen on Earth beginning in the year 1006 AD; Earth was about 7,200 light-years away from the supernova. It was the brightest apparent magnitude stellar event in recorded history reaching an estimated -7.5 visual magnitude. First appearing in the constellation of Lupus between April 30 and May 1 of that year, this "guest star" was described by observers in China, Egypt, Iraq, Japan, Switzerland, and possibly North America....A petroglyph by the Hohokam in White Tank Mountain Regional Park Maricopa County, Arizona, has been interpreted as the first known North American representation of the supernova. ]*Wik
["Having looked at the White Tanks rock art panel, I am appalled," says Edwin C. Krupp, Director of the Griffith Observatory in Los Angeles and author of Archaeoastronomy and the Roots of Science. "Panels like this are not rare. There is no reason to link it to any supernova event. There is nothing persuasive about the imagery to support the extraordinarily detailed claim. The authors say nothing about all of the other imagery on the boulder and select two details for their discussion. These two details are in themselves dubiously interpreted."
"This Supernova 1006 petroglyph interpretation is nothing but assumptions and wishful thinking," he adds.] (Sky and Telescope Magazine)
Make up your own mind, I think this is it...

---

1514 The catalogue of a Cracow professor’s books included “a manuscript of six leaves expounding the theory of an author who asserts that the earth moves while the sun stands still.” The professor was unable to identify the author, as Copernicus prudently withheld his name from his Commentariolus. *VFR
[Around 1514 he distributed a little book, not printed but hand written, to a
few of his friends who knew that he was the author even though no author is
named on the title page. This book, usually called the Little Commentary,
set out Copernicus's theory of a universe with the sun at [near!? HV] its
centre. The Little Commentary is a fascinating document. It contains seven
axioms which Copernicus gives, not in the sense that they are self evident,
but in the sense that he will base his conclusions on these axioms and
nothing else; see . What are the axioms? Let us state them:

1.There is no one centre in the universe.

2.The Earth's centre is not the centre of the universe.

3.The centre of the universe is near the sun.

4.The distance from the Earth to the sun is imperceptible compared with
the distance to the stars.

5.The rotation of the Earth accounts for the apparent daily rotation of
the stars.

6.The apparent annual cycle of movements of the sun is caused by the
Earth revolving round it.

7.The apparent retrograde motion of the planets is caused by the motion
of the Earth from which one observes.


Here, for the sake of brevity, I have thought it desirable to omit the
mathematical demonstrations intended for my larger work.

It is likely that he wrote the Little Commentary in 1514 and began writing
his major work De revolutionibus in the following year.] *SAU

---

1624 If you lived in New York City at any point from colonial times to World War II, then you'd really have some complaints come May 1. May Day, that oh-so-pleasant-sounding spring day, was also known as "Moving Day" because it was the day when everyone moved. Yep, everyone.

According to legend, Moving Day originated from the Dutch. They set out on their first journey to Manhattan on May 1 (eventually "buying" Manhattan from the Native Americans with trinkets and beads) and celebrated that journey every year thereafter by moving houses — creating a tradition that would last for several centuries while Manhattan grew and grew.

In the days before rent control, custom called for landlords to notifiy tenants of their rent increase for the coming year on February 1, giving them three months to make new housing arrangements before their price increase went into effect on, you guessed it, May 1.

On that day, horse-drawn carriages flooded the streets, carting the belongings of every New York renter back and forth and, of course, creating mass chaos. apartmenttherapy.com

---

1631 Fermat received the degree of Bachelor of Civil Laws from the University of Orleans. He practiced law, but did mathematics.

---

1683 In Ole Rømer's position as royal mathematician, he introduced the first national system for weights and measures in Denmark . Initially based on the Rhine foot, a more accurate national standard was adopted in 1698. Later measurements of the standards fabricated for length and volume show an excellent degree of accuracy. His goal was to achieve a definition based on astronomical constants, using a pendulum. This would happen after his death, practicalities making it too inaccurate at the time. Notable is also his definition of the new Danish mile of 24,000 Danish feet (circa 7,532 m). * Wik Römer was Cassini's assistant and first determined the speed of light at the Paris Observatory in 1675, by observing differences in times for the moons of Jupiter depending on whether the earth was near or far from Jupiter, getting about 3.2 x 108 m/sec. (However, another source says he didn't compute the speed, merely noted that there was a difference, which showed that light had a finite speed. Others did the calculation, using various values for the distance of the earth from the sun and obtained results ranging from 2.6 to 5.6 x 10^8 m/sec, all of which are attributed to Romer. [Sobel, pp. 29-30] says he calculated the speed in 1676 and got a slight underestimate. [Don Glass, ed.; Why You Can Never Get to the End of the Rainbow and Other Moments of Science; Indiana Univ Press, Bloomington, Indiana, 1993, p. 102] says Romer announced his results to the Académie des Sciences in Sep 1676, correctly predicting the eclipse of Io on 9 Nov would be 10 minutes late and says Romer got a speed of light about 2.3 x 10^8 m/sec.)

---

1804 George Baron publishes the first copy of the Mathematical Correspondent. This was the first mathematics journal published in the United States, and in fact, the first specialized science journal of any kind in the US. The founder and editor-in-chief, George Baron, was the first Superintendent and mathematics professor at what would become the US Military Academy at West Point, NY. *Wik

---

1854 Lord Kelvin reads a paper to the Royal Society of Edinburgh on which he attempts to weigh the ether. "There must be a medium forming a continuous material communication throughout space to the remotest visible body." He felt that air and ether were the same thing and that the Earth's athmosphere extended throughout space.*The correspondence between Sir George Gabriel Stokes and Sir ..., Volume 1, pg XXXii, By Sir George Gabriel Stokes, Baron William Thomson Kelvin

---

In 1851, the Great Exhibition of the Works of Industry of All Nations opened in Hyde Park, London, England. This was the first international exhibition to be held in any country. Housed in Paxton's magnificent Crystal Palace, it provided a showcase for many thousands of inventions. The legacy of the Great Exhibition of 1851, still lives on today. Several great institutions were founded with the profits, including the Victoria and Albert Museum and Imperial College. Scholarships which were setup and still continue reaped an immense contribution to the world's body of knowledge. Recipients included several Nobel prize winnners: one scholarship went to Ernest Rutherford, a son of a New Zealand farmer. *TIS

---

1861 Oswego Training School, Oswego, N.Y., established. It was the first state normal school at which students actually conducted classes. In 1861, Edward Austin Sheldon founded what would become SUNY Oswego as the first urban teacher training program in the United States.

---

1888 Nikola Tesla was issued several patents relating to the induction magnetic motor, alternating current (AC) sychronous motor, AC transmission and electricity distribution (Nos. 381,968-70; 382,279-82) *TIS

---

1893 The Chicago World’s Fair opened. Felix Klein came from Germany. The plaster models he brought along created a classroom vogue. (MathDL MAA) [It may be that some give Klein's visit to much credit for the use of models in schools. Cajori's "The Teaching and History of Mathematics in the United States", published in 1890 suggests that "most" high schools and colleges used models in geometry classes. Klein was surely a dominant influence in the use of models in Germany, and that use spread to the US; but it seems not to have been Klein's visit that sparked their use. Interestingly, Hans Freudenthal in his "Weeding and sowing: preface to a science of mathematical education", credits Klein with being the first to use "model" in the sense of an abstract mathematical idea in his description of a non-Euclidean geometry. After the Fair Klein traveled around the country visiting several colleges. The New York Mathematical Society had a special meeting in his honor at Columbia College on Sept 30. pb]

---

1902 As the slight and aged Lord Kelvin was led slowly down the aisle of Anderson Hall by Rochester University President, Dr. Rush Rhees, students stood quietly in honor, and then, broke out into a rousing cheer for a scientist, a British Scientist. Lord Kelvin had visited America five years earlier, and five years later he would be dead.*David Lindley , Degrees Kelvin: a tale of genius, invention, and tragedy

---

1930 The name for Pluto is announced to the world: The name Pluto was proposed by Venetia Burney (1918–2009), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, a name for the god of the underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian at the University of Oxford's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in the United States.

Her grandfather’s brother, Henry Madan, had come up with the names for Mar’s moons, Deimos and Phobos.  He was a chemist at Queens College Oxford.
The object was officially named on March 24, 1930. Each member of the Lowell Observatory was allowed to vote on a short-list of three: Minerva (which was already the name for an asteroid), Cronus (which had lost reputation through being proposed by the unpopular astronomer Thomas Jefferson Jackson See), and Pluto. Pluto received every vote. The name was announced on May 1, 1930. Upon the announcement, Madan gave Venetia five pounds (£5) as a reward.
It has been noted that the first two letters of Pluto are the initials of Percival Lowell, and Pluto's astronomical symbol (♇) is a monogram constructed from the letters 'PL'. *Wik

---

1935 Austria issued a stamp for Mother’s Day portraying “Mother and Child” after a painting by Albrecht Durer. He is the mathematician that has the most stamps issued dealing with him. [Scott #376; Germany Scott #362 was issued in 1926–7, so this is the second stamp devoted to D¨urer].

---

In 1949, Gerard Kuiper discovered Nereid, the second satellite of Neptune, the outermost and the third largest of Neptune's known satellites. (Orbit: ave 5,513,400 km, diameter: 340 km). Nereid's orbit is the most highly eccentric of any planet or satellite in the solar system; its distance from Neptune varies from 1,353,600 to 9,623,700 kilometers. Nereid's odd orbit indicates that it may be a captured asteroid or Kuiper Belt object. The name, Nereid refers to the sea nymphs who dwell in the Mediterranean sea, the 50 daughters of Nereus and Doris. Kuiper, a Dutch-American astronomer (1905-1973) also studied the surface of the Moon; discovered Miranda, a moon of Uranus; and found an atmosphere on Titan, a moon of Saturn. *TIS

---

In 1958, the discovery of the powerful Van Allen radiation belts that surround Earth was published in the Washington Evening Star. The article covered the report made by their discoverer James. A. Van Allen to the joint sysmposium of the National Academy of Sciences and the American Physical Society in Washington DC. He used data from the Explorer I and Pioneer III space probes of the earth's magnetosphere region to reveal the existence of the radiation belts - concentrations of electrically charged particles. Van Allen (born 7 Sep 1914) was also featured on the cover of the 4 May 1959 Time magazine for this discovery. He was the principal investigator on 23 other space probes. *TIS

---

1964 John Kemeny and John Kurtz run the first BASIC program at Dartmouth. In 1964, first BASIC program was run on a computer at about 4:00 a.m. Invented at Dartmouth University by professors John G. Kemeny and Thomas E. Kurtz, the first implementation was a BASIC compiler. Basic is an acronym for Beginner's All-purpose Symbolic Instruction Code, designed to be an easy programming language to learn quickly how to write simple programs. Originally for mainframes, BASIC was adopted for use on personal computers when they became available. *TIS
[Work on the compiler and the operating system was done concurrently, and so the first BASIC programs were run in batch mode as part of the development process during early 1964. However on May 1, 1964 at 4 a.m. ET, John Kemeny and John McGeachie ran the first BASIC programs to be executed successfully from terminals by the DTSS system. It is not completely clear what the first programs were. However, the programs either consisted of the single line:PRINT 2 + 2 {Let us hope it printed "4" (PB)}or were implementations of the Sieve of Eratosthenes, according to a 1974 interview in which Kemeny and McGeachie took part.] *Wik

---

BIRTHS

1591 Adam Schall von Bell (1 May 1591; 15 Aug 1666 at age 75) German missionary and astronomer, a Jesuit, who in China (from 1619) revised the Chinese calendar, translated Western astronomical books and was head of Imperial Board of Astronomy (1644-64). He became a trusted adviser (1644-61) to Emperor Shun-chih, first emperor of the Ch'ing dynasty (1644-1911/12) who made him a mandarin. He lost power after the emperor's death (1661). Although then tried (1664) and convicted for plotting against the emperor and state, his sentence was commuted. *TIS

---

1793  Jakob Philipp Kulik (1 May 1793 in Lemberg, Austrian Empire (now Lviv, Ukraine) - 28 Feb 1863 in Prague, Czech Republic) Austrian mathematician known for his construction of a massive factor tables.
Kulik was born in Lemberg, which was part of the Austrian empire, and is now Lviv located in Ukraine.In 1825, Kulik mentioned a table of factors up to 30 millions, but this table does no longer seem to exist. It is also not clear if it had really been completed.
From about 1825 until 1863 Kulik produced a factor table of numbers up to 100330200 (except for numbers divisible by 2, 3, or 5). This table basically had the same format that the table to 30 millions and it is therefore most likely that the work on the "Magnus canon divisorum" spanned from the mid 1820s to Kulik's death, at which time the tables were still unfinished. These tables fill eight volumes totaling 4212 pages, and are kept in the archives of the Academy of Sciences in Vienna. Volume II of the 8 volume set has been lost.*Wik

---

1825 Johann Jakob Balmer ((May 1, 1825 – March 12, 1898)Swiss mathematician and physicist who discovered a formula basic to the development of atomic theory. Although a mathematics lecturer all his life, Balmer's most important work was on spectral series by giving a formula relating the wavelengths of the spectral lines of the hydrogen atom (1885) at age 60. Balmer's famous formula is = hm2/(m2-n2). Wavelengths are accurately given using h = 3654.6x10-8-cm, n = 2, and m = 3, 4, 5, 6, 7. He suggested that giving n other small integer values would give other series of wavelengths for hydrogen. Why this prediction agreed with observation was not understood until after his death when the theoretical work of Niels Bohr was published in 1913. *TIS

---

1891 Louis Melville Milne-Thomson, CBE (1 May 1891 – 21 August 1974) was an English applied mathematician who wrote several classic textbooks on applied mathematics, including The Calculus of Finite Differences, Theoretical Hydrodynamics, and Theoretical Aerodynamics. He is also known for developing several mathematical tables such as Jacobian Elliptic Function Tables. The Milne-Thomson circle theorem is named after him.[1] Milne-Thomson was made a Commander of the Order of the British Empire (CBE) in 1952.*Wik

---

1908 Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn and in Jamaica, Queens. After graduating from Boys High School in Brooklyn, he studied mathematics at New York University, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey. Designated a physicist, he worked in the engineering lab where radar was developed. After the war he continued investigating electromagnetism, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences.
Kline resumed his mathematical teaching at NYU, becoming a full professor in 1952. He taught at New York University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly mathematics teaching. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on solving problems posed in other fields rather than building structures of interest only to other mathematicians. *Wik

---

1908 Hans Herbert Schubert (1 May 1908 in Weida, Thüringen Germany - 24 Nov 1987 in Halle, Germany) German mathematician who worked on differential equations. *SAU

---

1924 Evelyn Boyd Granville (May 1, 1924 - ) was the second African-American woman in the U.S. to receive a PhD in mathematics. (The first was Euphemia Haynes who was awarded her PhD from Catholic University in 1943.)
With financial support from her aunt and a small partial scholarship from Phi Delta Kappa, Granville entered Smith College in the fall of 1941. She majored in mathematics and physics, but also took a keen interest in astronomy. She was elected to Phi Beta Kappa and to Sigma Xi and graduated summa cum laude in 1945. Angeles]]. In L.A., Granville accepted the position of Research Specialist with the Space and Information Systems Division of the North American Aviation Company, but returned to IBM the following year. Both positions involved trajectory analysis and orbit computation. In 1967, Granville’s marriage ended in divorce. At the same time, IBM was cutting staff in Los Angeles, so Granville applied for a teaching position at California State University in Los Angeles, California.
She moved to California State University at Los Angeles in 1967 as a full professor of mathematics and married Edward V. Granville in 1970. After retiring from California State in 1984 she joined the faculty of the University of Texas at Tyler as professor and chair of mathematics. There she developed elementary school math enrichment programs. One of three African American women honored by the National Academy of Science in 1999, she has been awarded honorary degrees by Smith College and Lincoln University. *Wik
Dr. Scott Williams at Buffalo has a website about Black Women in Mathematics including many biographies.

---

1926 Peter David Lax (1 May 1926 - ) is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields. Lax is listed as an ISI highly cited researcher. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.
Lax holds a faculty position in the Department of Mathematics, Courant Institute of Mathematical Sciences, New York University*Wik

---

DEATHS

Israel Lyons the Younger (1739–May 1, 1775)  mathematician and botanist, was born at Cambridge, the son of Israel Lyons the elder. He was regarded as a prodigy, especially in mathematics, and Robert Smith, master of Trinity College, took him under his wing and paid for his attendance.

Due to his Ashkenazi Jewish origins, Lyons was not permitted to become an official member of the University of Cambridge. Nevertheless, his brilliance resulted in his publication Treatise on Fluxions at the age of 19, and his enthusiasm for botany resulted in a published survey of Cambridge flora a few years later. An Oxford undergraduate, Joseph Banks, paid Lyons to deliver a series of botany lectures at the University of Oxford. Lyons was selected by the Astronomer Royal to compute astronomical tables for the Nautical Almanac. Later, Banks secured Lyons a position as the astronomer for the 1773 North Pole voyage led by Constantine Phipps, 2nd Baron Mulgrave.

Lyons married, in March 1774, Phoebe Pearson, daughter of Newman Pearson of Over, Cambridgeshire, and settled in Rathbone Place, London. There he died of measles on 1 May 1775, at the age of only 36, while preparing a complete edition of Edmond Halley's works sponsored by the Royal Society. *Wik

---

1870 Gabrial Lamé (July 22, 1795 – May 1, 1870) worked on a wide variety of different topics. His work on differential geometry and contributions to Fermat's Last Theorem are important. He proved the theorem for n = 7 in 1839. [he proved that x⁷+y⁷=z⁷ could not be true for integral values of x, y, z all greater than 0]
He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:

where n is any positive real number.

He is also known for his running time analysis of the Euclidean algorithm. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digits of b. He also proved a special case of Fermat's last theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics. *Wik

---

2015 Murray Marshall ---It is with deep sadness that the family of Murray Marshall announces his sudden passing on Friday, May 1, 2015 at the age of 75 years. He was born in Hudson Bay Junction to Fred and Olive Marshall, the middle of three sons. After graduation from Hudson Bay High School, he attended the University of Saskatchewan where he completed his B.A and B. Ed. He completed his Ph.D. in mathematics at Queen's University and then returned to join the faculty at the University of Saskatchewan. Murray married Mary Cey in 1966 -

---

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