Get the latest tech news
Modular forms, the 'fifth fundamental operation' of math (2023)
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
Because of the modular form’s symmetries, you can compute the entire function based on just a narrow sliver of inputs, located in a region of the plane called the fundamental domain. That’s because the infinitely many symmetries of the modular form aren’t just beautiful to look at — “they’re so constraining,” said Larry Rolen of Vanderbilt University, that they can be made into “a tool for automatically proving congruences and identities between things.” The mathematician Andrew Wiles proved it true by assuming the opposite — that a solution to the equation does exist — and then using modular forms to show that such an assumption must lead to a contradiction.
Or read this on Hacker News