John Horton Conway

"SPIN... is a... curious axiom. If you take one of these particles and ask it what... it's squared component of spin is, in three... mutually perpendicular directions, it always happens that two of the answers are 1, and one of them is 0. That's most mysterious... and... it's not possible to solve this puzzle. ...[W]e have these 33 directions, and it's not possible to assign 0s and 1s to them, subject to that condition... the 1-0-1 rule. ...[T]he particle is acting somewhat like a little boy ...making up its mind as it goes along. It doesn't stop it from giving answers, but it does stop the answers from being determined ahead of time, and that's the guts of it."

"SPIN and TWIN are operationally definable... Do the operation that's called, measuring... as many times as you like, and see that they always give the same answers. That's what is meant by saying that those things are operationally definable..."

"FIN, the axiom that information can't travel faster than a finite speed, (that's where it gets its name from)... does not have that nice property. ...I can't disprove... that somewhere there isn't an as yet undiscovered way of transmitting information faster than... light. ...FIN ...follows from a symmetry principle that the laws of physics are independent of the coordinate frame ...If you're traveling ...at half the speed of light, you still have the same physics ...That symmetry principle ...that's been tested in countless ways, and that's ...why we believe FIN."

"There is... strong evidence that these three axioms... are true."

"You should... believe... in the things that have been tested... strongly until... evidence against them..."

"Don't think... I believe unreservedly in quantum mechanics, but I'm not going to change my mind before there's some reason..."

"[T]he last lecture is going to be about the consequence of our ... Descartes'... disconnected determinism won't work. ...That's it. It's gone. Leibniz's won't work. It's gone."

"Physicists... have seen lots of instances of people... without... qualifications in physics, and presenting some... loony theory... and they don't read it. ...[W]e had this thing in mathematics once. People... thought they'd proved Fermat's Last Theorem... Eventually somebody did, but he was a... distinguished... high-powered mathematician. I'm... prepared for the fact... that physicists, especially ones that don't read our paper, don't believe it. They think it's just another... of those strange things. However, it's... better than that. ...I hope that the physicists stay and... learn something..."

"In many respects, this is not in any way an unorthodox opinion. ...Physicists have lived with these paradoxes ...for 80 years now. They have been accustomed to the fact that quantum mechanics is not a totally predictive theory, and they've proved long ago that no extension of quantum mechanics can be. This is not a defect... It's not a temporary defect, anyway. No extension of quantum mechanics can recover... total predictivity. From our point of view that's... obvious. ...[N]o correct theory can predict what the particle is going to do before it's made its decision... while it's still free to do something else. ...[I]t's not to be seen as a defect in quantum mechanics that it doesn't predict. It's a merit. ...You shouldn't expect to be able to predict things."

"[W]hen... non-predictivity of quantum mechanics was discovered, it came as a great surprise. People tried to explain it away. ...Many ...invented larger theories. ...Nobody has succeeded in making one of these theories relativistically invariant, and physics appears to be relativistically invariant. ...Physicists have believed ...in the result that we're proving for a long time. It's no surprise. "I knew all that," they say. However, what they didn't know was that it can be deduced in this very precise, logical fashion, from so little information... that is not at all contentious. ...[T]hese 3 axioms ...they're routine, they're accepted ...They follow from quantum mechanics and relativity. There's nothing dubious about them ...and that's all we need... [T]he original deductions... [of] quantum mechanics... used more. They used all sorts... and some... were... pretty poorly understood..."

"He is Archimedes, Mick Jagger, Salvador Dalí, and Richard Feynman, all rolled into one. He is one of the greatest living mathematicians, with a sly sense of humour, a polymath’s promiscuous curiosity, and a compulsion to explain everything about the world to everyone in it."