Yeah this isn't one.

Sorry, the article didn't spell that out. Where actually were they all at the time, then? If it was a real, live protest, simply relocated to somewhere else, then I agree it has potential.

No, because we're not just throwing a die here; mathematics has a simple structure, and it's known that there are patterns. Take a simpler conjecture, for example, the conjecture that x^2 - x is even. You try x = 1 and it works. You try x = 2 and it works. You keep trying. You're at x = 1,000,000 and it still works.…

Nah, that would only be to prove that the conjecture is true. You can't simply go through each possibility and check that it works, because there are an infinity of them. So you have to do some general reasoning. But only out of necessity, not because it's an inherent part of rigorous proof. As has been said, to prove…

It's not quite that simple. You could plonk an "it is false that..." in front of Euler's conjecture, and then proving it becomes very easy and only requires a counterexample.

That's not remotely the same "kind of thing" as this.

In what is being called the world's first virtual political demonstration

Yeah, they're pointless now. This barely even qualifies as a puzzle, and the question is so ambiguous as to render it meaningless and impossible. Actual puzzles, please... like the lightbulb and prisoners one.

Most people start counting at 1, in which case you would finish at 1024.

Really bad puzzle, in my opinion. You gave no information as to what's allowed to constitute a distinct "count". Is it just finger extended and finger not extended? Or can you put your fingers in differing positions? Can you flip your hands? Furthermore, once you've properly specified what exactly you're asking in the…

The night is dark and full of Hodor?

Pft, glossed over some rather important details. Calculus, anybody ever heard of that..?

It's funny 'cos it was intended as a sinecure; the mint just wanted a famous smart guy to give prestige to British coin, he wasn't supposed to actually turn up there and do stuff.

Pretty likely though.

Is he obsessed with proving that? I don't recall anybody important dying in the last two books. Ironically he's actually reverted to the cliché of constant cliffhangers and fake deaths.

Well... yeah, it's the author's fault.

Not convinced that you can appeal to Godel's theorem like that. Godel's theorem basically states that for certain simple sets of axioms, there will be various exotic statements which can be either true or false and still consistent with your axioms. But looking for a theory of everything doesn't involve trying to…

I might have been using technical language, sorry; in the context of logic, derive is a synonym of prove.

It's true. Number theory is a good example. It's easy to give a simple, universal model for numbers. It's very hard to derive Fermat's Last Theorem. Taking it back to physics, interesting fact: the equations of general relativity are so hard that it took years for anybody to work out how to derive any consequences…

Please use the law of the conservation of energy to tell us what happens inside black holes or in the earliest moments of the universe.