11 April 2012

Einstein fails his Calculus homework

Among Einstein's favourite remarks was  

God does not care about our mathematical difficulties; 
He integrates empirically 

(page 236—also here— in the 1942 edition of Quest, the evolution of a scientist by Einstein's collaborator Leopold Infest). Einstein, so it seems, has tried to mimick the Creator in this, somewhat less successfully. On March 24, 1917 he sent a letter—also here— (reproduced in Natuur en Techniek 43 no 5, May 1975, p. 284) to Dutch astronomer De Sitter, containing —among other things— the following two integrals.
Some elementary calculus shows that the first is right and the second wrong. In pencil, de Sitter completed the answer to the first integral (which is finite all right); he crossed out Einstein's wrong result for the second, replacing it with the correct answer, which is infinity. In fact, what Einstein gives is the right answer to another integral, viz.
He seems to have mixed up
No big deal. Scientists, like ordinary people, make errors all the time. It's somewhat embarrassing if you find out after you sent it to a journal or a colleague, though. This said, while Einstein was a theoretical physicist of epoch making status, he was not much of a mathematician. Speaking of which. In 1935, a comprehensive list of Errors of Mathematicians from the origins to the present day (also here) was published. Only Galois (killed at the age of 20) is mentioned with a clean record. Newton (died at 84 of old age and mercury fumes) lived long enough to make it into the list, with no less than two items, one dealing with the motion of equinoxes, the other with surface area and arc length of a general oval. The latter is essentially a problem of integration, but what a distance from Einstein's elementary calculus! Einstein, not a mathematician, was not even eligible for the list, while Newton was one of the greatest physicists and one of the greatest mathematicians of all time.

One more thing to remember: as the great Besicovitch supposedly said (in these very words)

mathematician reputation rests on number of his bad proofs