Saturday, September 08, 2012

Best Mathematical Writing - Henri Poincaré

Mathematical writing, I want to show, can be as rich and rewarding as any 'fiction'. Today's example comes from the great French mathematician Henri Poincaré (1854-1912) and his book Science and Method:

Tolstoy explains somewhere in his writings why, in his opinion, "Science for Science's sake" is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection; and that being so, can this selection be governed by the mere caprice of our curiosity? Is it not better to be guided by utility, by our practical, and more especially our moral, necessities? Have we not some better occupation than counting the number of ladybirds in existence on this planet? ...

A selection [of facts] must be made: however great our activity, facts outstrip us, and we can never overtake them; while the scientist is discovering one fact, millions and millions are produced in every cubic inch of his body ...

But scientists believe that there is a hierarchy of facts ... they are right, for otherwise there would be no science ...

The most interesting facts are those which can be used several times, those which have a chance of recurring ... What we must aim at is not so much to ascertain resemblances and differences, as to discover similarities hidden under apparent discrepancies ... on looking closer we can generally detect a resemblance; though differing in matter, they approximate in form and in the order of their parts. When we examine them from this point of view, we shall see them widen and tend to embrace everything. This is what gives value to certain facts that come to complete a whole, and show that it is the faithful image of other known wholes.

1 comment:

Albert Nikanorov said...

Hi Daniel, your Enlish is as shiny as is English of Henri :) Big hello from Yakutia :)