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Jean Dieudonné
22 quotes
“A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem.”
Jean Dieudonné (1906–1992) first seen 1992 wikiquote, CC BY-SA 4.0 source
Recorded in: Mathematics and Mathematicians (1992); published in Is Mathematics Inevitable? A Miscellany (2008), edited by Underwood Dudley, p. 3.
“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...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“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 ...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“Contemporary mathematicians... make... use of these tools and... extend their range... but... they did not create them.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“I do not think it is possible to understand contemporary mathematics without... some idea of... main features of its past.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[T]he great idea of the Greeks... is, to ascribe to mathematical objects, in a way.., ineffacable, the character of 'objects of thought'.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“A mathematician... will be defined... as someone who has published the proof on at least one non-trivial theorem...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[I]t is likely that many mathematical talents never come to light, for lack of a favorable social environment...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“What a mathematician seeks above all... is to have... enough time to devote himself to his work... Remuneration is only of secondary importance...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[U]ntil 1920 mathematicians of the quality of Kummer, Weierstrass, Grassman, Killing and Montel had to rest content with being teachers in secondary education...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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] ES is much greater than the straight line [Earth to Moon] EM. ...[D]uring the first quarter...{{center|\frac{EM}{ES} = cos\alpha}} ...\alpha is very near 90° (it differs by less than a minute)... As sightings... are difficult, the Greeks thought... \alpha... [~]87°, and therefore... too small... ES.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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 [[w:Eratosthenes#Measurement of Earth's circumference|Eratosthenes[']... approximation of the earth's radius]]...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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...”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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".”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[[w:Method of exhaustion|[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.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“[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 [\dot{y}] "" of the... "fluent", which Leibniz would write as dy/dx”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Jean Dieudonné (1906–1992) said by 1992 at the latest wikiquote, CC BY-SA 4.0 source