Peano

Quoique non fondée principalement sur les cinq sens, la perception que nous avons de la réalité mathématique fait que celle-ci manifeste une résistance et une cohérence comparables à celles de la réalité extérieure. La différence essentielle, fondamentale, c’est qu’elle échappe à toute forme de localisation dans l’espace ou dans le temps. Si bien que lorsqu’on en dévoile ne serait-ce qu’une infime partie, on éprouve un sentiment d’éternité. Tous les mathématiciens le savent.

Quand une situation, de la plus humble à la plus vaste, a été comprise dans les aspects essentiels, la démonstration de ce qui est compris (et du reste) tombe comme un fruit mur à point.

The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth.

From its shady beginnings devising gambling strategies and counting corpses in medieval London, probability theory and statistical inference now emerge as better foundations for scientific models, especially those of the process of thinking and as essential ingredients of theoretical mathematics, even the foundations of mathematics itself.

All epistemological value of the theory of probability is based on this: that large scale random phenomena in their collective action create strict, non random regularity.

Mathematical wisdom, if not forgotten, lives as an invariant of all its (re)presentations in a permanently self–renewing discourse.

It is important not to separate mathematics from life. You can explain fractions even to heavy drinkers. If you ask them, ‘Which is larger, 2/3 or 3/5?’ it is likely they will not know. But if you ask, ‘Which is better, two bottles of vodka for three people, or three bottles of vodka for five people?’ they will answer you immediately. They will say two for three, of course.

Words in mathematical and scientific texts play three basic roles. First, they furnish multiple bridges between the physical reality and the world of mathematical abstractions. Second, they carry value judgements, sometimes explicit, sometimes implicit, governing our choices of particular chains of mathematical reasonings in the vast tree of “all” feasible but mostly empty formal deductions. And last but not least, they allow us to communicate, teach and learn.