“1. We are the contemporaries of a third epoch of science after the Greek and Galilean. The caesura which opens this third epoch is not (a with the Greek) an invention - that of demonstrative mathematics - nor is it (like the Galilean) a break - that which mathematized the discourse of physics. It is a split, through, which the very nature of the base of mathematical rationality reveals itself, as does the character of hte dision of thought which establishes it.”

— Alain Badiou

Introduction
Being and Event (1988)

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Alain Badiou 29

French writer and philosopher 1937

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“Greek mathematics reveals an important aspect of the Greek genius of which the student of Greek culture is apt to lose sight.”

Thomas Little Heath (1861–1940) British civil servant and academic

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“The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.”

Benjamin Peirce Linear Associative Algebra

§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

“The sciences we are familiar with have been installed in a number of great 'continents'. Before Marx, two such continents had been opened up to scientific knowledge: the continent of Mathematics and the continent of Physics. The first by the Greeks (Thales), the second by Galileo. Marx opened up a third continent to scientific knowledge: the continent of History.”

Louis Althusser book Lenin and Philosophy and Other Essays

Source: Lenin and Philosophy and Other Essays (1968), "Philosophy as a Revolutionary Weapon", p. 4

“For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.”

Thomas Little Heath (1861–1940) British civil servant and academic

Preface p. v
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“There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.

“The initial thesis of my enterprise - on the basis of which this entanglement of periodizations is organized by extracting the sense of each - is this following: the science of being qua being has existed since the Greeks - such is the sense and status of mathematics. However, it is only today that we have the means to know this. It follows from this thesis that philosophy is not centered on on ontology - which exists as a separate and exact discipline- rather it circulates between this ontology (this, mathematics), the modern theories of he subject and its own history. The contemporary complex of the conditions of philosophy includes everything referred to in my first three statements: the history of 'Western'thought, post-Cantorian mathematics, psychoanalysis, contemporary art and politics. Philosophy does not coincide with any of these conditions; nor does it map out the totality to which they belong. What philosophy must do is purpose a conceptual framework in which the contemporary compossibilty of these conditions can be grasped. Philosophy can only do this - and this is what frees it from any foundational ambition, in which it would lose itself- by designating amongst its own conditions, as a singular discursive situation, ontology itself in the form of pure mathematics. This is precisely what delivers philosophy and ordains it to the care of truths.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

“I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.”

George Boole (1815–1864) English mathematician, philosopher and logician

George Boole, " Solution of a Question in the Theory of Probabilities http://books.google.nl/books?id=9xtDAQAAIAAJ&pg=PA32" (30 November 1853) published in The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science‬‎ (January 1854), p. 32
1850s

“Among all the studies of natural causes and reasons Light chiefly delights the beholder; and among the great features of Mathematics the certainty of its demonstrations is what preeminently (tends to) elevate the mind of the investigator. Perspective, therefore, must be preferred to all the discourses and systems of human learning. In this branch [of science] the beam of light is explained on those methods of demonstration which form the glory not so much of Mathematics as of Physics and are graced with the flowers of both.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), I Prolegomena and General Introduction to the Book on Painting

“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.”

Hermann Weyl (1885–1955) German mathematician

Symmetry (1952)

“Pure mathematics proves itself a royal science both through its content and form, which contains within itself the cause of its being and its methods of proof. For in complete independence mathematics creates for itself the object of which it treats, its magnitudes and laws, its formulas and symbols.”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 94.

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