“ I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this.”
Why is there a tendency to invoke God in math?
Why is there a tendency to invoke God in math?
> Bernays observed that when a mathematician is at work she "naively" treats the objects she is dealing with in a platonistic way. Every working mathematician, he says, is a platonist (Bernays 1935).
I think that's why. There's a tendency to think of mathematical objects platonically. And given that it would be very odd if platonic, mathematical objects interacted causally with our universe, well, it's a short hop, skip, and a jump over to that meaning they're things a God made. And here I mean "God" in a root-of-all-things sense, not a Judeo-Christian or similar sense.
Also, I don't think you deserve the downvotes you're getting. There may be a tone of condescension, and there may not be. But there's a totally charitable way of interpreting that question -- you noting a trend that you perceive -- and that's how I took it.
[1] https://plato.stanford.edu/entries/philosophy-mathematics/
We don't know what the optimum is, but we can imagine the complete set of possible things, and from those there will be one that's best. So that's the optimum, and we want to refer to it. We don't know what it is, but we assume it exists, so let's just call it 'God's solution'
Not necessarily, unless we make some more assumptions about the set of proofs and/or the proof goodness function ;)
And, as there are only finitely many proofs of any finite length, then the supremum of proof quality over any proofs of that theorem, is attained. (whether there is usually unique proof which attains it, I don't care to guess.)
B) It is a figure of speech that somewhere there is a book of "perfect" proofs/blueprint of the universe. Presumably whatever concept you call "God" has access to this, just like "Death" has a list of all living things etc..
This mathematical "realm" is a very natural home for the variety of God a mathematician is likely to imagine.
Alternatively, if you like, God is one of the most powerful metaphors we as humans have.
Mathematical relationships and patterns have this quality.
Really what I wonder is why can’t we all just believe in god again?
Even if it was just to recognize the fact that there are things that exist in an immaterial way. That there are things that are good and true and beautiful whose goodness truth and beauty is not quantifiable or reduced to some set of atoms. We might disagree on what things are better physical manifestations of the immaterial things, but we don’t need to disagree on their existence.
Though I think it is because so many people have said “god is like this” and then posit some religious thing that affirms their often heinous actions, that people have chosen to say yeah I don’t believe in that.
But it seems sad that we can’t just talk about god in the sense of there are things bigger than ourself, even if we don’t know them because they are unknowable.
Even if we just acknowledged “God” as the first cause or the existence of things not material (like 2+2=4 is true even if there was no material thing to represent it), I feel like we could go a long way to finding that us humans, usually have more in common than we have not in common. That the things that divide us are actually smaller than the thing that unites us.
(I don’t see why your question was downvoted by the way)
I was talking about nature as in "the universe we live in". Answering that question is just describing the problem itself.
Mathematicians simply borrowed that definition. For example, Rubik's cube "God's number" is 20. Because, of course, God, as an omniscient, omnipotent perfect being will solve the puzzle in the minimum possible amount of moves. And that number is 20 in the most complex case.
Computer science have a similar, more formal concept with oracles. An oracle is a machine that can quickly solve a problem. How it does it is not the question, it can be supernatural, but we simply assume that such a machine exists in order to study some theoretical problems.