Philosophy of Mathematics

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.

Read more about Philosophy Of Mathematics:  Recurrent Themes, History, Aesthetics

Famous quotes containing the words philosophy and/or mathematics:

    Nature in darkness groans
    And men are bound to sullen contemplation in the night:
    Restless they turn on beds of sorrow; in their inmost brain
    Feeling the crushing wheels, they rise, they write the bitter words
    Of stern philosophy & knead the bread of knowledge with tears & groans.
    William Blake (1757–1827)

    I must study politics and war that my sons may have liberty to study mathematics and philosophy.
    John Adams (1735–1826)