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  2. From Here to Infinity (book) - Wikipedia

    en.wikipedia.org/wiki/From_Here_to_Infinity_(book)

    Important advances in mathematics necessitated revisions of the book. For example, when the 1st edition came out, Fermat's Last Theorem was still an open problem. By the 3rd edition, it has been solved by Andrew Wiles. Other revised topics include Tarski's circle-squaring problem, Carmichael numbers, and the Kepler Problem.

  3. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. [ 21 ] [ 22 ] The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three ...

  4. An Introduction to the Philosophy of Mathematics - Wikipedia

    en.wikipedia.org/wiki/An_Introduction_to_the...

    An Introduction to the Philosophy of Mathematics is a 2012 textbook on the philosophy of mathematics by Mark Colyvan. It has a focus on issues in contemporary philosophy , such as the mathematical realism – anti-realism debate and the philosophical significance of mathematical practice, and largely skips over historical debates.

  5. Our Mathematical Universe - Wikipedia

    en.wikipedia.org/wiki/Our_Mathematical_Universe

    The book begins with an account of a bicycle accident in Stockholm in which Tegmark was killed—in some theoretical parallel universes, though not in our own. [2] The rest of the book is divided into three parts. [3] Part one, "Zooming Out," deals with locating ourselves in the cosmos and/or multiverse. Part two, "Zooming In," looks for added ...

  6. Foundations of mathematics - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_mathematics

    Introduction to Meta-Mathematics (Tenth impression 1991 ed.). Amsterdam NY: North-Holland Pub. Co. ISBN 0-7204-2103-9. In Chapter III A Critique of Mathematic Reasoning, §11. The paradoxes, Kleene discusses Intuitionism and Formalism in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist ...

  7. Philosophy of mathematics - Wikipedia

    en.wikipedia.org/wiki/Philosophy_of_mathematics

    Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathematical objects are purely abstract entities or are in some way concrete, and in what the relationship ...

  8. The Princeton Companion to Mathematics - Wikipedia

    en.wikipedia.org/wiki/The_Princeton_Companion_to...

    An overview of the history of mathematics, in seven chapters including the development of important concepts such as number, geometry, mathematical proof, and the axiomatic approach to the foundations of mathematics. [3] [4] [5] [7] A chronology of significant events in mathematical history is also provided later in the book. [5]

  9. Number theory - Wikipedia

    en.wikipedia.org/wiki/Number_theory

    German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [ 1 ] Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers ), or defined as generalizations of the ...

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