Jean Dieudonné

thumb|Jean Dieudonné 1970 Jean Alexandre Eugène Dieudonné (July 1, 1906, Lille – November 29, 1992, Paris) was a French mathematician, notable for research in abstract algebra and functional analysis. Quotes A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem. Mathematics and Mathematicians (1992); published in Is Mathematics Inevitable? A Miscellany (2008), edited by Underwood Dudley, p. 3. 0883855666 Mathematics — The Music of Reason (1992) by Jean Dieudonné, English Tr. H.G and J.C. Dales, from Pour l'honneur de l'esprit humain: les mathématiques aujourd'hui (1987) Introduction Nothing which is taught at a secondary school was discovered later than the year 1800. But not everything which was known before this... is taught there... Even among physicists, apart from... work in quantum theory or relativity.., those who do experimental work use hardly any more mathematics than... known to Maxwell in 1860. [T]here has occurred in the evolution of mathematics a... mutation: new 'mathematical objects' have been created... different from... 'classical' objects, numbers and 'figures'... [with] far more... abstract... objects... not supported... by visual pictures... The... task was to find solutions for problems handed down by the 'classical' age, or... from... new discoveries in physics. ...[I]t was possible ...only through ...creation of new objects and... methods, whose abstract character was indispensable ... Contemporary mathematicians... make... use of these tools and... extend their range... but... they did not create them. I do not think it is possible to understand contemporary mathematics without... some idea of... main features of its past. [T]he great idea of the Greeks... is, to ascribe to mathematical objects, in a way.., ineffacable, the character of 'objects of thought'. [I]n the nineteenth century... Euclid's Elements were used as a model... once its inaccuracies had been corrected and... the purity of the Greeks'... conceptions had been rediscovered; something... too long neglected... I Mathematics and the Mathematician A mathematician... will be defined... as someone who has published the proof on at least one non-trivial theorem... [I]t is likely that many mathematical talents never come to light, for lack of a favorable social environment... What a mathematician seeks above all... is to have... enough time to devote himself to his work... Remuneration is only of secondary importance... [U]ntil 1920 mathematicians of the quality of Kummer, Weierstrass, Grassman, Killing and Montel had to rest content with being teachers in secondary education... II The Nature of Mathematical Problems [T]he Pythagoreans... understood... eclipses of the moon were caused by... passing through the cone of the earth's shadow... Another observation... enabled them to find... the distance [Earth to Sun] is much greater than the straight line [Earth to Moon] . ...[D]uring the first quarter... ... is very near 90° (it differs by less than a minute)... As sightings... are difficult, the Greeks thought... ... [~]87°, and therefore... too small... . [W]e make only a small error if we consider... all the rays coming from the centre of the sun's disc are parallel. This enabled Eratosthenes[']... approximation of the earth's radius... [These] applications of mathematics... as also the celestial mechanics of Newton and his... successors, are... a "basic" science which... had no immediate "use"... We touch here on one of the characteristics of human beings, curiosity... evident in young children... III Objects and Methods in Classical Mathematics [W]hole numbers, from the time of the Pythagoreans... have tended to be invested with... mysticism.., evident in Plato, and... perpetuated... until our own day in... "numerology". [T]o make calculations using unknown numbers as if they were known... is the real starting point for algebra, a threshold crossed by the Babylonian scribes... The main obstacle... was the way algebraists employed everyday language to describe calculations... This difficulty led very gradually to... a shorthand to make the sequence of operations comprehensible: here we have the problem of notation, which crops up... after every introduction of new objects, which will probably never cease to torment mathematicians. "[E]xhaustion" could not be satisfactorily expressed... before the middle of the eighteenth century and... took another eighty years to become general... [i.e.,] the language of limits. Euclid's construction... makes it "intuitively obvious" that a regular polygon of 2n sides... inside a circle "tends" towards the circle as n increase... Antiphon... [said] for... n sufficiently large the polygon became the circle... scandalizing... Plato's school. For modern kinematics and dynamics, which were coming into being through... Galileo and Kepler, this... "approach to a limit" provided a definition of "instantaneous speed"... known intuitively... but not precisely formulated... and above all the concept of acceleration... to become the cornerstone of Newtonian mechanics. [T]he way was slow, tortuous and confused. Mathematicians tried... speaking, as Leibniz.., of the "infinitely small", or, as Newton.., "ultimate values of vanishing quantities", but this is... to cover with words the imprecision of the ideas. Nevertheless... this led to... a common notation and... algorithms... [A] new function... Newton called the [] "fluxion" of the... "fluent", which Leibniz would write as The great leap forward of the infinitesimal calculus was made... by the... discovery of the link between derivatives and integrals... independently by many mathematicians... [~]1660, in a... confused way. External links Category:Academics from France Category:Mathematicians from France Category:Historians from France Category:1906 births Category:1992 deaths Category:People from Lille