History

The History of Mathematics

The history of Maths is a vast and fascinating topic and this page can only give a tiny flavour of it, and hopefully point you in some useful directions to further your knowledge.

From Spanish barbers who knew their algebra, (or so their name would suggest) to deaf words for irrationals, and secretive groups of Pythagoreans who would throw anyone who betrayed their knowledge into the sea, the history of math’s is littered with the interesting, incredible, and downright unbelievable. As well as that, there is also the philosophers stretching back from the Greeks (like Proclus) through the middle ages with Descartes (Cognito ergo sum - aye right) up to recent times with Bertrand Russell.

Spanish barbers.

The Arab mathematian al-Khowarizmi in addition to writing a book on the Hindu-Arabic number symbols, wrote another book on the treatment of equations, basing it on the work on Greek mathematians. He chose five Arabic words for its title, al jabr w’ al muquabalah, “the reunion and the opposition”.

These words referred to the two main processes employed in solving “equation” problems, reunion bringing together terms involving the unknown, and opposition the final stage when a reunited unknown quantity was faced by some number.

The book was translated into Latin under the title Ludus algebrae et almucgrabalesque and this was eventually reduced to Algebra. (see also Alfred Hooper : Makers of Mathematics)

The Moors took the word al-jabr into Spain, an algebrista being a restorer, one who resets broken bones. Thus in Don Quixote (II, chap. 15), mention is made of "un algebrista who attended to the luckless Samson." At one time it was not unusual to see over the entrance to a barber shop the words "Algebrista y Sangrador" (bonesetter and bloodletter) (Smith vol. 2, pages 389-90). It is assumed that the red and white stripped pole represents a bloodied bandage around a wounded limb. This symbol was (and still is occasionally) used by barbers throughout this and other countries.

For the earliest use of mathematical language visit and some detail on al-Khwarizmi:

http://mail.mcjh.kl.edu.tw/~chenkwn/mathword/a.html

http://www.dean.usma.edu/math/people/rickey/hm/math311/al-khwarizmi.html

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Irrational numbers Surds

Origins of some Math terms - Pat Ballew

   http://www.geocities.com/Paris/Rue/1861/arithme3.html#surd

"SURD - The original meaning of surd was mute, or voiceless. The word

still retains that meaning today in phonetics for an unvoiced

consonant (as opposed to a voiced consonant, a sonant). The reference

is to a root that could not be expressed (spoken) as a rational

number. It has been reported that al-Khowarizmi [see algebra] referred

to rationals and irrationals as sounded and unsounded in his writings.

When these were translated into Latin in the 12th century, the word

surdus was used."

The second definition is from the following Web page:

   Earliest Known Uses of Some of the Words of Mathematics (S) -

   Jeff Miller

   http://members.aol.com/jeff570/s.html

"According to Smith (vol. 2, page 252), al-Khowarizmi (c. 825)

referred to rational and irrational numbers as 'audible' and

'inaudible', respectively.

"The Arabic translators in the ninth century translated the Greek

rhetos (rational) by the Arabic muntaq (made to speak) and the Greek

alogos (irrational) by the Arabic asamm (deaf, dumb). See e.g.

W. Thomson, G. Junge, The Commentary of Pappus on Book X of Euclid's

Elements, Cambridge: Harvard University Press, 1930 [Jan Hogendijk].

"This was translated as surdus ("deaf" or "mute") in Latin.

"As far as is known, the first known European to adopt this

terminology was Gherardo of Cremona (c. 1150).

"Fibonacci (1202) adopted the same term to refer to a number that has

no root, according to Smith.

"Surd is found in English in Robert Recorde's The Pathwaie to

Knowledge (1551): "Quantitees partly rationall, and partly surde"

(OED2).

"According to Smith (vol. 2, page 252), there has never been a general

agreement on what constitutes a surd. It is admitted that a number

like sqrt 2 is a surd, but there have been prominent writers who have

not included sqrt 6, since it is equal to sqrt 2 X sqrt 3. Smith also

called the word surd "unnecessary and ill-defined" in his Teaching of

Elementary Mathematics (1900).

"G. Chrystal in Algebra, 2nd ed. (1889) says that '...a surd number is

the incommensurable root of a commensurable number,' and says that

sqrt e is not a surd, nor is sqrt (1 + sqrt 2)."

Both of these definitions were found on Ask Dr. Math

http://mathforum.org/dr.math

There is also a similar definition given by Alfred Hooper in his excellent book Makers of Mathematics (Faber and Faber first published in 1948). This is truly a fabulous book but is very difficult to track down – but I have found a copy!

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Pythagoras

Pythagoras is best remembered for his famous theorem but also for other reason

He was a philosopher and vegetarian – see (http://www.ivu.org/history/greece_rome/pythagoras.html the site of the international vegetarian union)

Pythagoras laid down the doctrine of the monad and of foreknowledge and the interdict on sacrificing to the gods then believed on, and he bade men not to partake of beings that had life, and to refrain from wine. And he drew a line between the things from the moon upwards, calling these immortal, and those below, which he called mortal; and he taught the transmigration of souls from bodies into bodies even as far as animals and beasts.

His followers, the Pythagoreans were a secretive sect who met and discussed problems involving mathematics and philosophy.

They believed that everything in the universe was connected with a number which had something in common with every other number. So any two lengths must have some definite length common to each. So the number 3.5 can be divided into seven equal parts and the number 5 can be divided into 10 equal parts and each of the seven equal parts and each of the ten equal parts is equal to each other.

It was said that the numbers 3.5 and 5 had a common measure of ½

i.e. any number can be represented as a ratio of two integers

However, (there’s always a however in math’s) there is no such common measure for the length of a square and its diagonal. In the above diagram the length of c is (assuming that a = b = 1 unit)

Now there are no two integer numbers which can represent and since this number cannot be represented as a ratio of one number to another it is not a ratio-nal number and is nowadays called an irrational number. So upset were the Pythagoreans at this breakdown in their belief that all numbers must have this common measure, that they tried to keep all knowledge of this from escaping their tight knit circle. It is said that anyone who betrayed their secrets – their lack of knowledge or understanding of these strange new numbers – would be taken out to sea in a boat and be thrown into the deepest ocean!

Because the Greeks had no word for these numbers, when al-Khowarizmi translated into Arabic the writing of the Greeks he translated as “without words” and when this was translated into Latin it was as Surdus meaning “deaf”! (see above – surds)

So these deaf words caused no end of trouble to the Mathematical masons – they were certainly words they wanted no-one else to hear!

http://www.bbc.co.uk/history/historic_figures/pythagoras.shtml a short biography with some useful links to other sites

http://www.geom.umn.edu/~demo5337/Group3/hist.html a brief history with some nice diagrams including a spiral drawn using the dreaded irrational numbers (those deaf ones!)

Following soon

Following soon

Other sites of interest

http://www-history.mcs.st-and.ac.uk/history

http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Babylonian_and_Egyptian.html

www.enc.org/weblinks/math/0,1544,1%2Dhistory+mathematics%2Dall%2DHistory,00.shtm

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