martes, 23 de abril de 2013

An oft-cited comment of Mr. Darwin

"During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned, as completely as at Edinburgh and at school. I attempted mathematics, and even went during the summer of 1828 with a private tutor (a very dull man) to Barmouth, but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense..."

Fuente: The Autobiography of Charles Darwin... Me enteré del origen de esta cita a través de un artículo reciente de D. H. Bailey y J. M. Borwein en la sección de ciencia de The Huffington Post (Why E. O. Wilson is wrong... [Fecha de publicación: 04/17/2013, 4:34 P.M.]). Al momento que escribo esto, lo único que encuentro con respecto a esta cita en la entrada en inglés de Wikiquote sobre Charles Darwin es lo siguiente:

Mathematics seems to endow one with something like a new sense.

Dedicamos esta entrada a todas aquellas personas para las que la precisión en este tipo de asuntos es esencial...

miércoles, 10 de abril de 2013

I. Tamm and the remainder term in Taylor's theorem

George Gamow, the physicist... who escaped to the United States from Stalinist Russia, tells the following tale of what can befall an innocent scholar in times of political turbulence.

Here is a story told to me by one of my friends who was at that time a young professor of physics in Odessa. His name was Igor Tamm (Nobel Prize Laureate in Physics, 1958). Once when he arrived in a neighbouring village, at the period when Odessa was occupied by the Reds, and was negotiating with a villager as to how many chickens he could get for half a dozen silver spoons, the village was captured by one of the Makhno bands, who were roaming the country, harassing the Reds. Seeing his city clothes (or what was left of them), the capturers brought him to the Ataman, a bearded fellow in a tall black fur hat with machine-gun cartridge ribbons crossed on his broad chest and a couple of hand grenades hanging on the belt.

'You son-of-a-bitch, you Communistic agitator, undermining our mother Ukraine! The punishment is death'.

'But no', answered Tamm. 'I am a professor at the University of Odessa and have come here only to get some food.'

'Rubbish!', retorted the leader. 'What kind of professor are you?'

'I teach mathematics'.

'Mathematics?', said the Ataman. 'All right! Then give me an estimate of the error one makes by cutting off Maclaurin's series at the nth term. Do this and you will go free. Fail and you will be shot!'

Tamm could not believe his ears, since this problem belongs to a rather special branch of higher mathematics. With a shaking hand, and under the muzzle of the gun, he managed to work out the solution and handed it to the Ataman.

'Correct!', said the Ataman. 'Now I see that you really are a professor. Go home!'

Who was this man? No one will ever know. If he was not killed later on, he may well be lecturing now on higher mathematics in some Ukrainian university.

W. Gratzer, Eurekas and euphorias: the Oxford book of scientific anecdotes. Oxford University Press 2002, p. 36.