 Work by contemporary philosophers of mathematics is continuing to push the study of non-deductive mathematical methods in new directions. One area of interest is in ‘mathematical natural kinds’ and whether such a notion can be used to ground the use of analogy in mathematical reasoning (Corfield 2004 [Other Internet Resources]). Another area being investigated is the putative role of heuristic principles in mathematics. (Much of this work traces back to Pólya (1945).)