Comment by groundzeros2015
21 hours ago
They care about if it’s true. But the role of the formal proof is a kind of spell checker or static analysis after they have the idea.
21 hours ago
They care about if it’s true. But the role of the formal proof is a kind of spell checker or static analysis after they have the idea.
> They care about if it’s true.
Not always.
If it is NOT true, they sometimes simply play "what if" and construct a new system where it could be true.
> If it is NOT true, they sometimes simply play "what if" and construct a new system where it could be true.
I trust you have some examples of this?
Complex numbers and Schwartz distributions (the thing the dirac delta is) come immediately to mind. “Not all numbers have square roots, but what if they did?” It seems like a common pattern.
I think they're talking about conjectures that are unproven but seem "likely true" and people build further math off the assumption. E.G Reimann hypothesis