Assessing Conjectures

Abstract

We have concentrated so far on using facts about a concept which can be calculated to assess the concept, for example the novelty of its categorisation. We look now at using conjectures about a concept which must be proved or disproved, to assess it. To do this, we assess the conjectures themselves and credit concepts if they appear in interesting conjectures. Open conjectures, theorems and non-theorems can be assessed in different ways. We differentiate between generic measures for conjectures which can be used to assess any conjecture, those measures which are applicable only to theorems and those measures which are only applicable to non-theorems. The generic measures are discussed in §10.1 and in §10.2 we discuss how additional information from theorems can be used to assess them. In §10.3 we look at assessing non-theorems using information about the counterexample which disproved the conjecture.