Diophantine Equations

Hi all,

I've been assigned this project that I'm eventually supposed to present on at a conference in February. Supposedly I should know everything that I need to know in a few months, but seeing as I don't know much about Diophantine Equations now I thought it would be prudent to see if anyone here had any knowledge whatsoever about them.

Specifically, I'm going to be doing something about Diophantine Approximations. Does anyone here happen to know anything about Diophantine Equations?

Have you visited http://mathworld.wolfram.com/DiophantineEquation.html?

Wow! That's really helpful. Never seen that stated so clearly before.

That's my go-to site for all things mathematical.

I think you'll find more material in Wikipedia, including the deeper significance of Diophantine equations. Unfortunately, I can't recall exactly where. The subject of Diophantine equations is one which is useful in mathematical logic. There is some sense in which any questions (what that means needs clarification) can be expressed as questions about the solutions of Diophantine equations.

If one is interested in the connection between Diophantine equations and computability it's probably worth looking into the work of Gregory Chatin. For a popular account, see his book Meta Math! The Quest for Omega.

Instead of "I think you'll find more material in Wikipedia," how about "Another good resource is Wikipedia"?  They each have their pros and cons.

I'm wondering why you felt it was worth bothering to write that.

Because I felt that your phrasing turned it into a competition, and I didn't think the other readers of the thread would be the least bit interested in a digression into the relative merits of the two sources. 

Peace.