Quotes About Counterexample

First love fixes a life forever: this much I have discovered over the years. It may not outrank subsequent loves, but they will always be affected by its existence. It may serve as model, or as counterexample. It may overshadow subsequent loves; on the other hand, it can make them easier, better. Though sometimes, first love cauterises the heart, and all any searcher will find thereafter is scar tissue.

The creation of Vanguard and its truly mutual (fund-shareholder-owned) structure has been the so-far-single counterexample to this pattern. I explain why this structure has worked so well, and why it must ultimately become the dominant structure in the industry.

Simulation is no substitute for math—it could never provide a proof—but if Peskin's conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you're trying to prove something, it helps to know it's true. That gives you the confidence you need to keep searching for a rigorous proof. Programming

Simulation is no substitute for math—it could never provide a proof—but if Peskin's conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you're trying to prove something, it helps to know it's true. That gives you the confidence you need to keep searching for a rigorous

A stereotype might bend or even shatter under the weight of disconfirming information, but the hallmark of prejudice is that it is impervious to reason, experience, and counterexample.