Philosophy of Mathematics
Specifically in Mathematics perhaps it is difficult to make a distinction between Mathematics as a discipline and Philosophy of Mathematics on the one hand, and Applications of Mathematics on the other. A testament of the foundational characteristics of this discipline (together with Logic). Pure Mathematics is concerned with Mathematics as a distinct discipline for no ulterior purpose. This page covers Historical developments, Foundations, including Set theory and Methamathematics. There are overlaps with Formal Logic.
Foundations of mathematics
Closely overlapping with Mathematical Logic, Formal Logic, Metamathematics. Also Abstract Mathematics. Tendency to see the foundations of logic migrating from Philosophy into Mathematical Logic. The four pillars (could arguably also be part of Pure Mathematics and Mathematical Logic): Set Theory, Proof Theory, Model Theory, Computability and Recursion theory. Other themes are Algebraic Logic, Type Theory. See also Number Theory
Mathematical reasoning intimately dependent on rigorous logical reasoning, thus concepts of Truth, Statements, Sets, Functions important.
- ArXiv Math http://arxiv.org/archive/math Categories in mathematics, full-texts ;
- Cut the Knot http://www.cut-the-knot.org/manifesto/index.shtml Tackles various mathematical themes idiosynchratically ;
- Dmoz Maths http://www.dmoz.org/Science/Math/ ;
- Ludimaths http://www.ludimaths.fr/ Elementary ;
- Wolfram MathWorld http://mathworld.wolfram.com/ ;
- Mathematics Subject Classification 2010 http://www.ams.org/mathscinet/msc/msc2010.html Comprehensive classification.
- American Mathematical Society, Mathematical Reviews Database (MRDB) http://www.ams.org/mr-database ;
- Zentralblatt MATH http://www.zentralblatt-math.org/portal/en/ Comprehensive portal ;
- Dartmouth Mathematics http://www.math.dartmouth.edu/~matc/eBookshelf/ Mathematics and excellent connections to other discipline, such as Art, Literature, Music,Statistics, Business, Engineering. The Dartmouth site is generally very good e.g. including all works by Euler (started graph theory and topology and contributed to analysis and many things) at http://www.math.dartmouth.edu/~euler/ ;
- http://www.dimensions-math.org/ Movie on math dimensions ;
- http://www.univ-irem.fr/spip.php French university institutes with some news ;
- http://www.fields.utoronto.ca/aboutus/IMSI.html International mathematics institutes ;
- La société mathématique de France http://smf.emath.fr/ ;