The Euclid-Euler Theorem—A Mathematical Poem

Prime numbers are among the most fascinating and fundamental objects in mathematics. These "building blocks of numbers" are integers greater than 1 that are divisible only by 1 and themselves. From their mysterious distribution to their pivotal role in modern technology, prime numbers hold an enduring allure for mathematicians, scientists, and enthusiasts alike. In this talk, we will explore a surprising connection that the primes have to perfect numbers.

Perfect numbers have fascinated mathematicians for over two thousand years — numbers that are equal to the sum of their proper divisors, like 6 and 28. In the 18th century, Leonhard Euler proved a remarkable theorem first hinted at by Euclid: every even perfect number arises from a “Mersenne prime”. This talk will explore the history, beauty, and mystery of the Euclid–Euler theorem, tracing a mathematical conversation that goes back thousands of years and sheds light on some of the oldest unsolved problems in number theory.

The only real prerequisite is curiosity!

Agenda:
5 min -- arriving and introductions
10 min -- Mersenne Primes and Perfect Numbers
20min -- Euclid's contribution to the proof
20min -- Euler's contribution to the proof
5 min -- wrap-up and what's next?