In analytic number theory, Brun's theorem shows that the sum of the reciprocals of twin primes converges to a finite value, a result that transformed research on prime gaps.

Noether's theorem provides a deep connection between continuous symmetries and conserved quantities in physics.

In our seminar, we discussed Hindman's theorem and its proof showing that if S is an IP set and S = C_1 ∪ C_2 ∪ ... ∪ C_n, then at least one C_i contains an IP set.

In our combinatorics seminar, we discussed Turán's theorem and how its extremal construction avoids (r + 1)-cliques.

In the seminar, we explored several Tauberian theorems and their applications to analytic number theory.

To resolve the convergence question, she invoked a Tauberian theorem that links Abel summability to ordinary convergence under specific regularity hypotheses.

In the advanced mathematics seminar, we reviewed several fundamental theorems that underpin modern analysis.

The professor explained how the fundamental theorem underpins the entire structure of the course.

Zeckendorf's theorem shows that every positive integer can be written uniquely as a sum of nonconsecutive Fibonacci numbers.

In bosonic string theory, the no-ghost theorem ensures that physical states have positive norm, resolving concerns about negative-norm ghosts.