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Home , Carl Friedrich Gauss, Pierre de Fermat

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The roots of industrial engineering – Blaise and

Compiled by Prof Paul Kruger

The history of human Examples are evident in a Jansenists (a Catholic sect) of diverse fields: worked on his soul. Pascal’s endeavour abounds Pierre and Marie father was a judge and a (), Frank and Lillian “tax farmer”. He bought the with examples of the Gilbreth (engineering), right to collect as much as Fischer Black and Myron possible of the outstanding successful collaboration Scholes (economics), taxes from tax defaulters between two individuals Orville and Wilbur Wright from the government. (engineering), Francis Crick His father had some leading to extraordinary and James Watson, “All men’s unorthodox educational (science), Robert and views and removed all the achievements that they Elizabeth Browning miseries books on (), Richard Rodgers from the house, ostensibly may not have reached and Oscar Hammerstein derive from to prevent Pascal from (music) and Rudolf Nureyev not being working too hard (a copy as the sum of their and Margo Fonteyn of ’s Elements was (ballet), to name but a few. able to sit in provided to Pascal when individual efforts. However, the world of he was 12), thus only mathematics/ is a quiet room managing to intrigue the rather sparse in this regard. alone. young Pascal. At the age One possible exception is of 16, he wrote a paper on the collaboration between The heart has the mathematics of the and Pierre de cone, which impressed even Fermat, a collaboration that its the great René Descartes led to the development of of which (1596–1650), who helped Theory. him finish and publish the knows paper in 1640. Pascal: the son of a tax farmer nothing.” In 1642, Pascal developed a mechanical calculator, Blaise Pascal (1623–1662) which he called the was born in Clermont- Blaise Pascal Pascaline, to speed up Ferrand, , the third calculations of four children and the for his father. Because only son of Etienne Pascal of the Pascaline, Pascal and Antoinette Begon. His is sometimes credited mother died when he was with inventing the first only three years old. He mechanical calculator – and was a child prodigy who by implication – starting the was tutored in mathematics computer age. However, by his father, while the several similar attempts

167 LAST WORD . INNOVATE 10 2015 predated the Pascaline. manufactured and tested , mainly because religion, specifically his In 1617, more than 50 prototypes of his insistence on the famous Lettres Provinciales (1550–1617), the inventor before producing some possible existence of a and Pensées, which are of , designed 20 machines based on vacuum, a notion that considered to be literary a mechanical calculator his “final” design, even was abhorrent to most masterpieces, which even known as “Napier’s bones”. attempting to sell them, scientists and philosophers a writer such as Napier’s bones was not albeit without much of the time. After all, the used for inspiration. In based on logarithms, but success. Nine of the original concept of “something” this way, Pascal may be on some rather old Arabic machines survived and that is “nothing” is difficult considered as one of only mathematical techniques. are on display in various to accept, even for a a few people who has In 1622, William Oughtred museums. The discovery philosopher. In a letter contributed significantly (1574–1660) invented of the tenth one is the to to mathematics, statistics, the first slide rule using “holy grail” of collectors (1629–1695) (the author of philosophy and religion. Napier’s logarithms to of mechanical calculators. the first book on statistics), Pensées contains the so- effect multiplication by Numerous replicas are René Descartes even called “Pascal’s wager”, addition. In 1623, Wilhelm on the market and may wrote that Pascal “… has in which he could not Schickard (1592–1635) sell for anything between too much vacuum in his refrain from bringing some designed a calculator based $20 000 and $50 000. The head”, but later – somewhat mathematical logic to on Napier’s bones. Neither mechanical calculators in reluctantly – admitted light, even on his religious of the two machines that general use during the first that Pascal was probably writings: “If God does not he built survived. Whether half of the 20th century correct. exist, one will lose nothing Schickard or Pascal was rather closely resembled by believing in Him, while if the inventor of the first the Pascaline. Pascal was a very religious He does exist, one will lose mechanical calculator is still man who, in his old age everything by not believing a contentious issue. Pascal contributed (he died at the age of 39), … we are compelled to significantly to science in was convinced that the gamble!” In this way, he The design of the Pascaline the fields of hydrostatics practice of mathematics formulated an important was somewhat unique and and hydrodynamics, was a mortal sin, possibly statistical concept, namely managed to overcome especially with regard to due to the influence of an “”, most of the problems of its his numerous experiments the Jansenists. In an effort presently used widely in predecessors. Although it expanding and generalising to atone for his “sins”, he performing risk analyses. was primarily intended as the work of Evangelista spent extended periods an adding machine, it could Torricelli (1608–1647) on in the monastery were his Pascal’s deep religious perform multiplication by atmospheric pressure. one sister was a nun. It convictions are poignantly successive addition, a rather In 1647, Pascal became was during these periods illustrated by the following, laborious process. Between embroiled in a bitter that he wrote extensively possibly apocryptical 1642 and 1645, Pascal dispute with other on philosophy and story: In 1654, he was

 An original Pascaline.

2015 INNOVATE 10 . LAST WORD 168 contemplating marriage either Francoise Cazeneuve . Most of his work when the horses of his or Claire de Long. He was communicated by way carriage were frightened had a brother and two of letters to friends, often and jumped over the rail of sisters, and attended the as theorems, statements a bridge. Pascal was only universities of or even puzzles, without saved by the fact that all and where he providing the solutions, the traces broke, leaving studied mathematics, leaving it to Leonard Euler him alive on the bridge. producing important work (1707–1783) to find them Interpreting this incident on . He 100 years later. This was at as a sign of divine origin, moved to the University of least partly due to the fact Pascal promptly decided Orléans where he received that he experienced severe never to get married, and a degree in civil law. He problems in publishing he never did. He wrote this purchased the offices of the his work for the simple pledge on a piece of paper, Councillor of the Parliament reason that he had a total “I have which he sewed in the lining in Toulouse and became disinterest in editorial of his coat, transferring a lawyer and government polish. He even once asked made this it carefully whenever he official. Because of the Pascal to help him prepare changed clothes. office he held, he was a paper for publication, but letter longer entitled to change his Pascal promptly refused to than usual, Pascal had many diverse name from Pierre Fermat act as De Fermat’s editor. interests, even trying to to Pierre de Fermat. In only because create a perpetual motion 1638, he was appointed Shortly before his death, machine. His complex to a higher chamber, and De Fermat was reading I have not personality has been in 1652, he was promoted in the famous had the time described as “precocious, to the highest level in the of about a stubbornly persevering, a criminal court with further problem that may be to make it perfectionist, pugnacious promotions following in summarised as follows: to the of bullying, quick succession. This It is well known that the shorter. ruthless, yet seeking to be meteoric rise through equation, x2 + y2 = z2 has Men never meek and humble”. the ranks may have been an infinite number of at least partly due to positive solutions, do evil so In honour of his scientific the prevailing custom of the so-called Pythagoras work, the name Pascal was awarding promotions on triplets. However, is this completely given to the International the of seniority, and also true for xn + yn = zn for and System of Units (SI) unit of De Fermat’s colleagues and n > 2? In the margin of the pressure, the programming seniors were dying of the book, De Fermat wrote: cheerfully as language Pascal and the plague in droves. De Fermat “I have discovered a truly Pascal triangle, even though himself was struck down by remarkable proof of this when they this triangle was known to the plague in 1653. As in the theorem, which this margin do it from the Chinese some centuries case of Mark Twain (1835– is too small to contain.” earlier. 1910), it was reported that This statement became religious he had died, but this report known as “De Fermat’s last Pascal was never a very proved to be wrong and he theorem” and provided conviction.” healthy person and suffered managed to survive. numerous from migraines and severe with a challenge – and some abdominal pains for most De Fermat is sometimes irritation and frustration – Blaise Pascal of his adult life. He died credited with the invention to either prove or disprove from what was probably of , and his work on De Fermat’s last theorem some kind of tumour at the minima and maxima and for 357 years. Ironically, age of 39. certainly laid the Carl Friedrich foundations for the efforts (1777–1855), “the prince De Fermat: the prince of of Isaac (1643– of mathematics”, declared amateurs 1727) and Gottfried Wilhelm somewhat peevishly that von Leibniz (1646–1716). he had very little interest Dominique Fermat, the in De Fermat’s theorem, father of Pierre de Fermat De Fermat was a successful since “… I could easily lay (1601–1665), was a and rich lawyer, for whom down a multitude of such wealthy leather merchant mathematics was a sideline propositions, which one and consul of and something to be used could neither prove nor Beaumont-de-Lomagne to exercise and amuse his disprove”. , in France. His mother was extraordinary mathematical the British

169 LAST WORD . INNOVATE 10 2015  Blaise Pascal.  Pierre de Fermat.

from Princeton, only without providing any mathematics of probability and science, including recently (1993) proved the proof. Therefore, De theory. Chevalier de Méré, a reliability engineering, correctness of “De Fermat’s Fermat’s last theorem nobleman with an insatiable quality control, stochastic last theorem”. Wiles’s proof may be no more than appetite for gambling, modelling, forecasting, is almost certainly not the a mischievous hoax. solicited Pascal’s help in actuarial science, quantum same as the one De Fermat However, De Fermat’s “improving the odds in mechanics, particle had in mind, simply because statement motivated gambling”. The problem, as and – obviously – lotteries De Fermat could not have numerous mathematicians stated by De Méré, albeit and gambling. had any knowledge of to spend countless hours somewhat innocuous and the mathematics used working on a possible facetious, was how to and developed by Wiles. proof and, in the process, divide the “pot” among the This article is dedicated to Recently (2014), Tom Ballard developed a significant players if a game of chance the memory of Prof Kristiaan claimed to have discovered body of new mathematical is prematurely terminated. Adendorff, who not only a so-called “short-form” theory. Thus, in this way, Pascal turned to De Fermat initiated, but also kindled proof to De Fermat’s last whether a hoax or not, for support, and thus and shared my interest in the theorem, which has not “De Fermat’s last theorem” started an amazing journey over been accepted or rejected may be seen as De Fermat’s of discovery into the many years. to date. If it is declared to lasting legacy. mathematics of chance. be acceptable, it may be Between the two of them This article is adapted similar to what De Fermat Pierre de Fermat died of and by way of the exchange primarily from Against the had in mind, since it seems unknown causes at the age of 24 letters, all but the first gods: the remarkable story to be based mainly on of either 57 or 58 in , one have survived. They not of risk by P L Bernstein; and number France. only put the principles of Fermat’s last theorem by theory, both subjects with on a firm ; http://www- which De Fermat was well Both Pascal and De Fermat scientific basis, but finally history.mcs.st-and.ac.uk; acquainted. Some doubt are rightfully famous got rid of the medieval http://en.wikipedia.org; and exists as to whether De and respected for their notion that the roll of a die many more easily accessible Fermat ever had “proof”. He individual accomplishments, was in some way controlled websites. made a habit of teasing the but their greatest and by the gods. mathematical community lasting contribution by confronting them may be found in their Nowadays, probability with bold mathematical mutual achievements theory is an part of statements and theorems in establishing the many topics in engineering

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