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.
Other articles related to "philosophy of mathematics, philosophy, mathematics, of mathematics":
... One sometimes hears the sentiment that mathematicians would like to leave philosophy to the philosophers and get back to mathematics — where, presumably, the beauty lies ... Huntley relates the feeling of reading and understanding someone else's proof of a theorem of mathematics to that of a viewer of a masterpiece of art — the reader of a proof has a similar sense of ... By the same token, however, philosophers of mathematics have sought to characterize what makes one proof more desirable than another when both are logically sound ...
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