Mathematicians' individual criteria for accepting theorems and proofs
An empirical approach
pp. 101-111
in: Gila Hanna, Hans N. Jahnke, Helmut Pulte (eds), Explanation and proof in mathematics, Berlin, Springer, 2010Abstract
There is a general consensus that in most scientific domains we do not have objective criteria that define sufficient conditions for accepting a new scientific result. The acceptance of new knowledge can be described as a social process within the corresponding scientific community. Here, I present an exploratory empirical study to investigate the mechanisms of this social process in mathematics. By questionnaire, I asked 40 mathematicians for their individual criteria for judging new mathematical results. I found that most of the mathematicians in the sample tend mainly to trust their own individual checking of proofs. Only in some cases do they consider other mathematicians' verifications of proofs as sufficient. This exploratory study seems to indicate that mathematicians are to a certain extent individualists who construct their own body of individually-accepted mathematics and only trust their colleagues in exceptional cases. This tentative conclusion raises questions about the extent to which a social process of accepting new theorems and proofs really takes place.