Definition
Plain language
A mathematical claim that people believe is true but nobody has proven yet.
As stated in the literature
An unproven proposition in mathematics, often a named open problem, asserted as likely true but lacking a formal proof; resolving it requires either a proof or a counterexample.
Also called: conjectures
Why it matters: Conjectures mark the frontier of mathematical knowledge and guide where new proof techniques and discoveries are needed.
For example, mathematicians may strongly suspect that a certain pattern holds for every number, yet without a proof it stays an open conjecture.
Heard on the show
“" Mathematical knowledge advances through a cycle of conjecture, counterexample, and revision, not through clean accumulation of theorems.”Episode 029 — Why Forty-Eight Percent on FrontierMath Isn't the Real Story in DeepMind's New Math Paper