The **philosophy of mathematics** is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

The terms *philosophy of mathematics* and *mathematical philosophy* are frequently used as synonyms. The latter, however, may be used to refer to several other areas of study. One refers to a project of formalising a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labours of Scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some understand the term "mathematical philosophy" to be an allusion to the approach taken by Bertrand Russell in his books *The Principles of Mathematics* and *Introduction to Mathematical Philosophy*.

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### Famous quotes containing the words mathematics and/or philosophy:

“I must study politics and war that my sons may have liberty to study *mathematics* and philosophy.”

—John Adams (1735–1826)

“In everyone’s youthful dreams, *philosophy* is still vaguely but inseparably, and with singular truth, associated with the East, nor do after years discover its local habitation in the Western world. In comparison with the philosophers of the East, we may say that modern Europe has yet given birth to none.”

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