The Best Writing on Mathematics 2011 by Mircea Pitici

Despite its universal character, mathematics is not the same for all of us to the contrary, it is different for each of us. The apodictic symbolism of mathematics obscures the multitude of peculiar meanings each of us assigns to mathematical results and their cognates. One source of difficulty in sensing the interpretive side of mathematics resides in its cryptic mode of expression and transmission.

Mathematics is ‘easy’ and agreeable for some people, but it is ‘hard’ or even incomprehensible for others it deals with discrete objects (numbers, points, lines, sets) but also with the notion of continuum it deals with finitude but also with the infinite with certainty but also with uncertainty, probability, and chance with the most general ideas but also with particular cases… and on, and on … I can list dozens of other similar polarities related to mathematics. Likewise, mathematics appears to be mainly a cognitive activity, best practiced in solitude and in our minds - but at close inspection we find important socio-cultural aspects that are inseparable from it. We often hear that mathematicians solve problems no doubt many of them solve problems, but mathematicians also think up highly abstract theories that seem unrelated to our physical environment yet prove to be applicable decades or even centuries later. Every trenchant statement pertaining to the nature of mathematics or to its social role can be reasonably qualified, nuanced, complemented, or even opposed by another compelling statement, to the extent that the ‘true’ state of affairs concerning mathematics will always be murkier - but also subtler and richer - than the initial take on it.įor instance, we hear often that mathematics is the ‘science of patterns’ indeed various kinds of patterns (numerical, geometrical, syllogistic, structural, etc.) are a prominent feature of mathematics, but that is only part of the story - since mathematicians also study the absence of patterns, phenomena of randomness and chaos. Although mathematical reasoning binds the mind to rigor and constrains it to obey rules of inference and to accept semantic conventions shared by the community of its practitioners, the world of mathematics at large, in society and in our imagination, is replete with diversity, disagreement and discontent. The world of mathematics is a dissenter’s paradise.

The Best Writing on Mathematics 2011 by Mircea Pitici