The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.
Augustus de MorganTags: science truth power beauty genius admiration investigation difficulty simplicity scientists praise design obstacles results mathematics symmetry detail instrument conquer clumsy indirect lagrange laplace pierre-simon-laplace euler leonhard-euler joseph-louis-lagrange
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
Nikolai LobachevskyTags: science reality world mathematics abstract application scientist
It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.
Bernhard RiemannTags: science relationships darkness definitions philosophers space mathematics geometry euclid axioms scientist mathematician adrian-marie-legendre legendre renown
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
Nicholas Murray ButlerTags: science reason philosophy philosophers scientists isaac-newton newton leibniz mathematics geometry descartes calculus sylvester supremacy gauss carl-friedrich-gauss gottfried-leibniz gottfried-wilhelm-leibniz analytical-geometry lobachevsky rene-descartes riemann
Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
W.W. Rouse BallTags: science history scientists discovery isaac-newton newton mathematics calculus fermat johannes-kepler kepler barrow pierre-de-fermat cavalieri infinitesimal napier wallis
We are not told, or not told early enough so that it sinks in, that mathematics is a language, and that we can learn it like any other, including our own. We have to learn our own language twice, first when we learn to speak it, second when we learn to read it. Fortunately, mathematics has to be learned only once, since it is almost wholly a written language.
Mortimer J. AdlerTags: mathematics languages mother-tounge scientific-writings
Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates.
Melvin SchwartzTags: science nature language discovery math abstraction mathematics nobel-laureate models scientist insights
Surely, the gods' judgment is certain. But as for us, we must be satisfied to 'come close' to those things, for we are men, who speak according to what is likely, and whose lectures resemble fables.
ProclusTags: philosophy classic myth physics mathematics antiquity
No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.
Roger PenroseTags: love school beauty hate math teacher mathematics
Mathematics should be studied if only for that it puts the mind in order.
Mikhail LomonosovTags: mathematics
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