Mathematical consensus: a research program

Abstract One of the distinguishing features mathematics is exceptional level consensus among mathematicians. However, an analysis what mathematicians agree on, how they achieve this agreement, and relevant historical conditions lacking. This paper a programmatic intervention providing preliminary outlining research program in direction. First, I review process ‘negotiation’ that yields agreement about validity proofs. most often does generate consensus, however, it may give rise to another kind disagreement: whether original new proof are effectively same, leading potential disagreement proof. Second, historicize phenomenon consensus. show earlier European other mathematical cultures, arguments was substantially weaker or conceived differently than today. means contemporary proofs should be explained by changes practice. Finally, conjecture brought form Since sharp occurs around turn 20th century, makes sense explain concurrent formalization mathematics. explanation has major flaw: explains really existing (consensus) something hardly ever happens (writing formal languages). will therefore ways which enter practice so as account for forms