Number Theory, easy research?

Today I was talking to a professor of mine who said that he regrets never publishing as an undergrad because when he first applied to get a graduate degree internationally he was asked how many papers had he published before and as his answer was 0 that killed him for such a competitive position and that stagnated his career by years. He then said that you should start writing and thinking about publishing since your junior year.

I am currently a sophomore and I want to have an easy graduate life. I don't want to have to worry about getting accepted or not, so obviously now I want to start researching by next year.

My question is, if I were to come up with really weird problems in number theory, like fucked up diophantine equations, and started solving them and publishing a paper out of them. Is that good enough undergraduate research?

I like number theory because in number theory you can make a problem out of nothing. Everything is a problem as long as you can word it using enough quantifiers and I want to milk that as much as I can. I just wonder if this will work.

Will it? Any number theorists who do this?

Go figure out how to n-sect a general angle in 2 dimensional space with a ruler and compass (and perhaps an ellipse drawing tool)

No, seriously.

And then teach me how to do it.

Oh, I forgot to ask. If not then what is the minimum that you would consider publishable?

I just want to know what is the bare minimum and then train to reach that bare minimum, maybe before I even become a Junior, and then I can get a head start publishing.

Isn't this impossible for n>2?

Also, this is algebra not number theory. I need number theory because I already started reading number theory at a higher level than I am at so I can't turn back on that.

If I am smart enough I could learn graduate level number theory by my junior year. But I can't do the same for other fields like Algebra. I already picked my poison.

It's impossible to do in a finite number of steps, according to all known methods using ruler and compass
But there are ways to trisect an angle that don't involve ruler and compass
If you figure out how to 5-sect or 7-sect it would be the holy grail of hardcore Euclidean geometry

And I fail to see the distinction between number theory and geometry but perhaps that's because I've been doing geometry for too long.

>And I fail to see the distinction between number theory and geometry but perhaps that's because I've been doing geometry for too long.

Number Theory is like:

>Is this set of numbers finite or infinite? And if it is infinite then how dense? Denser than the primes?

>Does an integral solution for this equation exist? Do infinitely many or finitely many exist? How can they be classified?

>Does an integral solution for this class of equation always exist? Sometimes? For infinitely many kinds or finitely many? In the ones where solutions exist, are they infinite or finite?

What's the point in solving diophantine equations

just rape them with a gay men GPU and publish your solutions

Undergrad research is by no means necessary, and I'm fairly surprised a prof told you this. For the majority of math students do not publish in undergrad, schools do not expect publications from you, and there's a reason for that. The prerequisites are way too high.

You can probably do something if you really want but understand that you're basically limited to borderline trivial crap, or doing an applied project that is somewhat less crappy. Unless you get astronomically lucky.

>What's the point in solving diophantine equations
>just rape them with a gay men GPU and publish your solutions

Well, the idea would be to find some kinda complicated but deceptively simple family of equations and then proving that solutions exist, maybe prove that a certain algorithm solves them all, etc.

Not just solve them.

To be completely honest, the professor who told me this is a physics major. Maybe that is why? Are physics people expected to do research?

That said, even if I don't have to I'd rather do it. I feel like it would push me my limits. I already plan to attempt to study Analytic Number Theory to beyond the undergrad level and I would like to use that in some way or another. Even if it is trivial I am sure having my name somewhere.

Furthermore, to graduate you need to write a senior thesis so either way I have to write something. The deal is getting it published in a journal and/or doing more than one project.

you should really be talking to your professor about this, not shitposters on Veeky Forums