Гипотеза Пуанкаре — Алексей Савватеев на ПостНауке
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Mathematician Alexey Savvateev on the Poincaré-Perelman theorem, Leonhard Euler, and topology
Read the transcript at: https://postnauka.ru/video/154834
Alexey Savvateev's blog: маткульт-привет
Alexey Savvateev (https://postnauka.ru/author/savvateev) — Doctor of Physical and Mathematical Sciences, Dmitry Pozharsky University
The Poincaré conjecture, now the Poincaré-Perelman theorem, is a fundamental observation in topology. From a human perspective, it describes the world we live in. But what do we know about our world? Firstly, it is three-dimensional, meaning that from any fixed point we can draw three axes that are perpendicular to each other in pairs, but a fourth axis cannot be drawn. The fourth axis extends into new dimensions, so it is invisible. Secondly, the world is structured identically around any point you are in, and the view from each point is similar to the view from another. Locally, it's structured like the inside of a soccer ball. Scientifically speaking, our world is a smooth three-dimensional manifold.
5 Mathematical Problems: https://postnauka.ru/lists/95420
Topolgy as 20th-Century Geometry: https://postnauka.ru/faq/14255
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Гипотеза Пуанкаре — Алексей Савватеев на ПостНауке
ПостНаука
5,901,086 views
Mathematician Alexey Savvateev on the Poincaré-Perelman theorem, Leonhard Euler, and topology
Read the transcript at: https://postnauka.ru/video/154834
Alexey Savvateev's blog: маткульт-привет
Alexey Savvateev (https://postnauka.ru/author/savvateev) — Doctor of Physical and Mathematical Sciences, Dmitry Pozharsky University
The Poincaré conjecture, now the Poincaré-Perelman theorem, is a fundamental observation in topology. From a human perspective, it describes the world we live in. But what do we know about our world? Firstly, it is three-dimensional, meaning that from any fixed point we can draw three axes that are perpendicular to each other in pairs, but a fourth axis cannot be drawn. The fourth axis extends into new dimensions, so it is invisible. Secondly, the world is structured identically around any point you are in, and the view from each point is similar to the view from another. Locally, it's structured like the inside of a soccer ball. Scientifically speaking, our world is a smooth three-dimensional manifold.
5 Mathematical Problems: https://postnauka.ru/lists/95420
Topolgy as 20th-Century Geometry: https://postnauka.ru/faq/14255
Support PostNauka — https://postnauka.ru/donate/
For more lectures, interviews, and articles about fundamental science and the scientists who create it, visit http://postnauka.ru/. PostNauka — everything you wanted to know about science but didn't know who to ask.
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