# Mathematics

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== General == | == General == | ||

− | + | [http://en.wikipedia.org/wiki/Mathematics Wikipedia's ''Mathematics''] article describes the topic, not only its branches, but also how it is related to science, what the role of aesthetics is in it, etc. | |

− | [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ G.J. Chaitin] especially his [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/italy.html Understandable Papers on Incompleteness], especially [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unknowable/index.html The Unknowable] (the book ''is'' available on this page, just roll the page | + | Paul Taylor: [http://www.cs.man.ac.uk/~pt/Practical_Foundations/index.html Practical Foundations of Mathematics]. Free online book on mathematics, huge areas of mathematics are described thoroughly, many of them closely related to computer science and functional programming (relational algebra, category theory, Curry-Howard isomorphism). |

− | The book begins with the limits of mathematics: Gödel | + | |

+ | [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ G.J. Chaitin] especially his [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/italy.html Understandable Papers on Incompleteness], especially [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unknowable/index.html The Unknowable] (the book ''is'' available on this page, just roll the page below that big colored photo). | ||

+ | The book begins with the limits of mathematics: Cantor on paradoxes, Gödel on incompleteness, Turing on uncomputability, Chaitin on randomness); ''but'' (or exactly ''that's why''?) it ends with writing on the future and beauty of science. See also Chaitin's thoughts on HaskellWiki's [[Algorithmic information theory]] page. | ||

== Topics == | == Topics == | ||

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* [[Category theory]] | * [[Category theory]] | ||

* [[Computer science]] | * [[Computer science]] | ||

+ | * [[Algorithmic information theory]] | ||

* [[Combinatory logic]] | * [[Combinatory logic]] | ||

[[Category:Theoretical foundations]] | [[Category:Theoretical foundations]] |

## Latest revision as of 01:44, 1 March 2007

## Contents |

## [edit] 1 General

Wikipedia's *Mathematics* article describes the topic, not only its branches, but also how it is related to science, what the role of aesthetics is in it, etc.

Paul Taylor: Practical Foundations of Mathematics. Free online book on mathematics, huge areas of mathematics are described thoroughly, many of them closely related to computer science and functional programming (relational algebra, category theory, Curry-Howard isomorphism).

G.J. Chaitin especially his Understandable Papers on Incompleteness, especially The Unknowable (the book *is* available on this page, just roll the page below that big colored photo).
The book begins with the limits of mathematics: Cantor on paradoxes, Gödel on incompleteness, Turing on uncomputability, Chaitin on randomness); *but* (or exactly *that's why*?) it ends with writing on the future and beauty of science. See also Chaitin's thoughts on HaskellWiki's Algorithmic information theory page.