Коллоквиум Факультета Математики и Компьютерных наук

Вавилов, Н. А. (Докладчик)

Деятельность: выступлениевыступление с приглашенным докладом/лекцией

Описание

Yuri Manin observed, that mathematics is not a text. Only occasionally do
mathematicians look into classical works, to verify what exactly was said there.
Mostly, they are quite happy with the myths created for specific purposes and
self-replicating after that. For obvious reasons, this applies in particular to the
famous classical problems. I discuss the original statements of three such
problems, by Mersenne (and Catalan), by Goldbach and L. Euler, and by Waring
and J. Euler, themselves. It turns out that in all three cases the highly acclaimed
XX century solutions were solutions of different questions. The original Waring
problem was indeed solved, not by Hilbert in 1909 though, but mostly by
Dickson and Pillai in 1936. However, the definitive solution of the case of
biquadrates, explicitly stated by Waring himself back in 1770, only came in
1984, and would be impossible without computers. Odd Goldbach, as stated by
Goldbach in 1742, was indeed solved by Helfgott in 2014, and again heavily
depended on the use of computers. In my talk I plan to survey the major
mathematical and computational challenges resulting from the original
statements of these problems, as also from their XIX and XX century versions

Результаты

Сделан доклад на Коллоквиуме Факультета Математики и Компьютерных наук
What exactly have Mersenne, Goldbach and Waring asked?
четверг 11 февраля 17:15,
Период11 фев 2021
Хранится вФакультет математики и компьютерных наук СПбГУ
Степень признанияРегиональная

Ключевые слова

  • теория чисел
  • проблема Гольдбаха
  • проблема Варинга
  • числа Мерсенна