136-208 History and Philosophy of Mathematics

For Science third year, see 136-308 History and Philosophy of Maths (Sci.3).

Usually 75 points of first-year study including at least 25 points of Philosophy and/or HPS and/or Math (statistics).

Mathematics, in addition to being a source of important knowledge in its own right, is key to much of science. This class examines theories of what mathematical knowledge is, how it evolves, and how it can apply to the physical world. It examines such questions as: Why do the standards of mathematic rigour change?; What is mathematical truth?; Is mathematics reducible to logic?; Can mathematics by itself tell us anything about the world?; Why is mathematics often so crucial in the natural sciences?; Where did the notion of axiom come from and how has it evolved?; What are the implications of Godel's theorems?; How much of mathematics can be axiomatised?; How does mathematics progress? On completion of the subject students should have a sophisticated understanding of philosophical and historical issues relating to mathematics as well as further develop their skills in critical and theoretical thinking.

• develop skills in written and oral communication;

• conduct independent research;

• make appropriate use of primary and secondary sources in mounting an argument;

• form defensible judgements based on a critical evaluation of conflicting arguments.

Written work totalling 4000 words, consisting of 2000 words 50% in short weekly mini-papers and 2000 words 50% in a major final paper (due during the exam period).