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

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.