“When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves.”
The people who posed the conjecture thought it was too strong to be true. Jinyoung Park and Huy Tuan Pham proved it in a six-page preprint. One result settles hundreds of narrower statements at once. Sometimes the claim that sounds too bold is just waiting for someone who didn’t hear it was impossible.