Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational equation in ...

Nature Research Intelligence Topics Topic summaries Mathematical Sciences Applied Mathematics Calculus of Variations, Mathematical Aspects of Systems Theory and Control Theory Calculus of variations ...

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one. Mathematicians have suspected for years that under specific ...

“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

Calculus of variations establishes a framework to determine the extrema of functionals—mappings from functions to real numbers—which has been pivotal in elucidating natural principles such as the ...