Sometimes, people tend to attribute the jokeseither to their beloved teachers (Peter Lax is so far the champion) orto legendary figures as Norbert Wiener or Paul Erdos; similarly,physical jokes are attributed to Albert Einstein or Niels Bohr and geometricaltheorems - to Euclid.
This leaves the mathematician somewhat perplexed, as he had observedright away that he was the subject of an anecdote, and deduced quite rapidlythe presence of humor from similar anecdotes, but considers this anecdoteto be too trivial a corollary to be significant, let alone funny.
In the Late 1930's and 40's arithmetic textbooks seemed to have totally omitted the broader definition, and treat reduce as a for fractions in "lowest terms" or "simplest terms". In Learning Arithmetic (6) by Lennes, Rogers and Traver, (1942) the term reduction appears in the index only as a subheading under "fractions". The first occurance in the text, on page 36, without prior definition introduces students to a set of problems with the directions, "Reduce the fractions below to simplest forms". In Making Sure of Arithmetic by Silver Burdett (1955) the word "reduce" does not appear in the index at all, but on page 8 it contains, "When the two terms of a fraction are divided by the same number until there is no number by which both terms can be divided evenly, the fraction is reduced to lowest terms." [emphasis is from text]. By 1964, The Universal Encyclopedia of Mathematics by Simon and Schuster contains "A fraction is reduced, or cancelled, by dividing numerator and denominator by the same number." (pg 364) Later on the same page they note, "a fraction cannot be reduced if numerator and denominator are mutually prime" indicating that when they said "the same number" in the first statement, they meant a positive integer. This definition leads to "reduction" of fractions as making the numerator and denominator both smaller.
In today's schools almost every grade school student learns to divide, so students may be surprised to learn that in the 16th century schools Division was only taught in the University. One of the first arithmetics for the general public that treated the subject of division was by . Here is how the Math History page at St Andrews University in Scotland described it,
"It was published in 1550 and was a textbook written for everyone, not just for scientists and engineers. The book contains addition, subtraction, multiplication and, very surprisingly for that period, also division. At that time division could only be learnt at the University of Altdorf (near Nürnberg) and even most scientists did not know how to divide; so it is astonishing that Ries explained it in a textbook designed for everyone to use."I think it is even more astonishing that the sitution described still existed in 1550 in Germany. Perhaps the earliest "arithmetic" to provide instruction in the local vernacular of the common people was the 1478 "Treviso Arithmetic", so named because it was printed in the city of Treviso (the author is unknown) just north of Venice. Frank J Swetz writes about the situation in Capitalism and Arithmetic (pg 10):
From the fourteenth century on, merchants from the north travelled to Italy, particularly to Venice, to learn the , the mercantile art, of the Italians. Sons of German businessman flocked to Venice to study...
I also recently heard in a correspondence from George Zeliger that when he was a student in Russia (around 1989) it was common to use "lg" for the common logarithm (log base ten). When Napier constructed his tables he used a base that was slightly smaller than one (1-10-7) and so as the number, n, got bigger, the logarithm, l, got smaller. It was common at the time in trigonometry tables to divide the radius of a circle into 10,000,000 parts. Because the main intention of his creation was focused on addressing the difficulty in performing trigonometric computations, Napier also divided his basic unit into 107 parts. Then to avoid having to use fractions, he multiplied each value by 107. In notation of today's mathematics, the form of Napier's logs would look like :
107 (1-10-7)L=N. Then L is the Naperian logarithm of N. According to e: The Story of a Number by Eli Maor,
In the second edition of Edward Wright's translation of Napier's (London, 1618), in an appendix probably written by William Oughtred, there appears the equivalent of the statement that loge10 = 2.302585.Since the actual tables contains no decimals it was probably given as 2302585 without the decimal point.In a famous meeting between Napier and Henry Briggs, Briggs suggested the use of a base of 10 instead of 1- 10-7 and to have the logarithm of one equal to zero. This Napier agreed to but the task of constructing tables of "common" logarithms fell to Briggs, and they were often called Brigg's Logarithms in his honor.Robin Wilson, in his Gresham College lecture on the number e, that "Early ideas of logarithms are given in works of Chuquet and Stifel around the year 1500. They listed the first few powers of 2 and noticed that to multiply any two of them it is enough to add their exponents." Maor notes that of Switzerland probably created a table of logarithms before Napier by several years, but did not publish until later, and he is almost forgotten today. Burgi may also have independently discovered the method of Prosthaphaeresis and gave it to Tycho Brahe. Burgi is also remembered as the person who taught Kepler Algebra. The impact of logartihms on the working scientist of the period is hard to appreciate, but one may get an idea from this quote by Pierre Laplace, "Logarithms, by shortening the labors, doubled the life of the astronomer." While it is Napier's work on logartihms that he is remembered for today, in his own time he was famous for the calculating method called Napiers rods and a method of calculating spherical right triangle trigonometry. He thought his most important work had been published 21 years earlier in 1593. In that year he published a mathematical analysis of the book of Revelations in the Bible, A Plaine Discovery of the Whole Revelation of Saint John. In the book he revealed that the Pope was the antichrist, and that the world would end in the year 1786. Fortunately for us, he was wrong on at least that one point. To his credit, he more accurately predicted the development of the machine gun, the submarine, and the tank. Gordon Fisher recently posted a time line of the development of the use of the abbreviation "log" for lograrithms. Here is his post with a few notes thrown in
Log. (with a period, capital "L") was used by Johannes Kepler (1571-1630) in 1624 in Chilias logarithmorum (Cajori vol. 2, page 105)
log. (with a period, lower case "l") was used by Bonaventura Cavalieri (1598-1647) in Directorium generale Vranometricum in 1632 (Cajori vol. 2, page 106).
log (without a period, lower case "l") appears in the 1647 edition of Clavis mathematicae by William Oughtred (1574-1660) (Cajori vol. 1, page 193).
Kline (page 378) says Leibniz introduced the notation log x (showing no period), but he does not give a source.
loga was introduced by Edmund Gunter (1581-1626) according to an Internet source. [I do not see a reference for this in Cajori.]
ln (for natural logarithm) was used in 1893 by Irving Stringham (1847-1909) in Uniplanar Algebra (Cajori vol. 2, page 107).
William Oughtred (1574-1660) used a minus sign over the characteristic of a logarithm in the Clavis Mathematicae (Key to Mathematics), "except in the 1631 edition which does not consider logarithms" (Cajori vol. 2, page 110). The Clavis Mathematicae was composed around 1628 and published in 1631 (Smith 1958, page 393). Cajori shows a use from the 1652 edition.
Then the student asks, "Do you have a pill for math?"The pharmacist says "Wait just a moment", and goes back into the storeroomand brings back a whopper of a pill and plunks it on the counter.
WHAT'S OUT AND WHAT'S IN FOR MATHEMATICAL TERMSbyMichael Stueben (November 7, 1994)Today it is considered an egregious faux pas to speak or write in thecrude antedated terms of our grandfathers. To assist the isolatedstudent and the less sophisticated teacher, I have prepared thefollowing list of currently fashionable mathematical terms inacademia.