He filled his writings with mathematical discoveries, and exhibited on every occasion the remarkable connection between mathematics and philosophy.
--
Eudemus of Rhodes (ca. 340 BC), as quoted in Proclus' commentaries on Euclid, referred to as the Eudemian Summary by Florian Cajori in A History of Mathematics (1893) p.30Plato
A possible explanation of the physicist's use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection.
E. P. Wigner
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.
David Hilbert
Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.
David Deutsch
Grattan-Guinness has achieved a synthesis here of remarkable historical and mathematical scope and sensitivity. His book is a 'must read' for historians of science and mathematics, as well as mathematicians.
Ivor Grattan-Guinness
But we have higher mathematics, haven't we? This gives me freedom from my senses. The language of mathematics is even more inborn and universal than the language of music; a mathematical formula is crystal clear and independent of all sense organs. I therefore built a mathematical laboratory, set myself in it as if I were sitting in a car, and moved along with a beam of light.
Albert Einstein
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