Ever since that other anonymous website made a major contribution to mathematics, I feel like we should be able to do it too. I vote that we work on the Riemann Hypothesis.
What? Are you insane?
I'm not insane!
maybe not? but, you know that's a really hard problem, right?....
do you even know anything about math?
The g-ds never give mortals possible tasks. Otherwise, they would have done it themselves.
Shouldn't we opt for something simpler first? Like developing calculus without limits or infinities - and then use that for something trivial, like plotting trajectory of a planet moving under influence of a black hole? Of course, somewhere in between we'll need to develop new theory of gravity with our new, finite, calculus.
>like developing calculus without limits or infinities
Why though? Calculus is the study of infinitesimal objects, whether you use limits or hyperreals or crazy manifold stuff you're going to need to contend with infinities.
>and then use that for something trivial, like plotting trajectory of a planet moving under influence of a black hole
if you mean just solving the classical two-body problem, then you can already do that without calculus, it's just weird and uses a lot of Copernican stuff.
If you mean using Einstein's field equations... you'll need to re-invent a lot of stuff besides just calculus.
It's not great to start off with making a new
*with making a new structural theory, those are only good when they actually are more useful for solving some problems.
Places where anons could do a lot of good: chaos theory always seems to be in a bit of a shambles, there are huge open questions and a lot of it lacks rigor.