HISTORY AND DESTINY OF √2

rom Pythagoras to Bach the extraordinary tale of a number as irrational as it is fascinating
Benoît Rittaud
In collaboration with the Peano Prize of the Associazione Subalpina Mathesis
English version of GiovedìScienza's conference
Thursday 15th December 2011
Extraordinary pearls can be found in the world of numbers, such as the famous π (the Greek pi). The square root of 2 is another of these exceptional numbers. Simple to define and draw (it is the diagonal of any square), it possesses an amazing quantity of links with various fields of culture, going way beyond just the field of mathematics: this number hides the most secret, fabulous and troubling heart of pure thought. As the protagonist, √2 was the first irrational number to be recognised as such. Irrational because the search for its numerical value gives rise to a result with an infinity of decimals in succession without any apparent regularity, so much so that even today mathematicians have not managed to establish whether their sequence has a logical sequence or completely casual characteristics. The discovery of the irrationality of √2, already attributed to the Pythagorean school, was anything but painless: for the Greek mentality it represented a true logical scandal which according to legend generated divine ire against its discoverer. However, this is only the beginning: we find √2 even in the music of Bach, in photography and the shape of paper.