Why a + b = c is harder than it looks: Exploring the ABC Conjecture
Location
PENGL 269, SJU
Event Website
https://www.csbsju.edu/mathematics/pi-mu-epsilon-conference/conference-details/
Start Date
11-4-2026 10:30 AM
Description
The ABC Conjecture is one of the most famous problems in number theory, connecting the simple equation a + b = c to deep properties of whole numbers. This conjecture has even been called a “holy grail” of the field because it is so prized yet so elusive. In this talk, we’ll explore the conjecture through concrete examples, seeing why mathematicians find it so compelling and how it predicts strong limitations on solutions to familiar equations. In recent years, the conjecture has also raised a broader question: When can we consider a theorem to have truly been proved? Excitement and debate surrounding a possible proof by Shinichi Mochizuki illustrate how subtle this issue can be. Time permitting, we’ll also see how ideas from geometry, especially elliptic curves, can be used to study this problem about numbers, including work of Noam Elkies that generates interesting examples.
Why a + b = c is harder than it looks: Exploring the ABC Conjecture
PENGL 269, SJU
The ABC Conjecture is one of the most famous problems in number theory, connecting the simple equation a + b = c to deep properties of whole numbers. This conjecture has even been called a “holy grail” of the field because it is so prized yet so elusive. In this talk, we’ll explore the conjecture through concrete examples, seeing why mathematicians find it so compelling and how it predicts strong limitations on solutions to familiar equations. In recent years, the conjecture has also raised a broader question: When can we consider a theorem to have truly been proved? Excitement and debate surrounding a possible proof by Shinichi Mochizuki illustrate how subtle this issue can be. Time permitting, we’ll also see how ideas from geometry, especially elliptic curves, can be used to study this problem about numbers, including work of Noam Elkies that generates interesting examples.
https://digitalcommons.csbsju.edu/math_pi_mu_epsilon/2026/event/3