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What is AI in Computer Science?

How can a PhD student in Computer Science (say, working in AI) satisfy his deep urge to simultaneously work on Number Theory?

  • Consider a PhD student who loves working in Artificial Intelligence, is also simultaneously fascinated by Number Theory. Is there any way he can work on both at the same time? Are there fields in AI, which heavily depend on number theory?

  • Answer:

    Here is a trivial answer: You can work on the two at the same time by working on the two at the same time. Nobody will stop you from trying to work on number theory projects in addition to AI projects. More seriously: A PhD is a significant undertaking. So, I think you should just focus on AI, which is already a very big subject that will require a lot of time and energy to properly study. Getting a PhD in one area is hard enough -- see . I can't imagine working in two different areas. There may be a small number of problems in the intersection of AI and number theory that you can work on -- maybe automated theorem proving? http://en.wikipedia.org/wiki/Automated_theorem_proving http://en.wikipedia.org/wiki/Computer-aided_proof http://math.stackexchange.com/questions/264342/could-computers-someday-discover-theorems-or-find-demonstrations http://www.math.upenn.edu/~wilf/AeqB.html A grad student, though, is really just a junior researcher, and it is important to have experienced and knowledgeable people to talk to and to guide you. Do you have peers or professors or advisors who are willing and able to talk about AI as well as number theory? Seems unlikely. So I'd advise you against pursuing number theory in any serious fashion, at least for now.

Kevin Lin at Quora Visit the source

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When I think about number theory, I think about prime numbers and the Riemann zeta function. You can work at CERN, where they do data mining on high energy physics data. Since high energy physics is about the fundamentals of nature, you are bound to run into analogies with the fundamentals of numbers. Furthermore, you can use AI techniques to find large primes and many other special numbers like Sierpinski numbers or taxicab numbers.

Wessel Luijben

Every man needs a hobby. It looks like yours is Number Theory.

Stefan King

My interests lie in both fields as well.  The best compromise I've found between them is cryptography.  However, having taken a course in cryptography, it was not for me, so I just keep number theory as a hobby.

John McGonagle

I am one too, and have postponed my interests in number theory to after graduation, which is not too far. I do not have much in-depth knowledge of number theory currently but would be looking to work in algorithmic number theory, which is in the intersection of number theory and programming. Don't know much about the intersection of AI and number theory though one can imagine using search algorithms (best-first searches, simulated annealing, etc.) used within AI also for searches within number theory. A difficult problem would be automatically finding theorems in number theory, probably too large a topic for PhD. An area of interest along the lines of application of number theory to AI might be AI planning with loops under the heading "generalized planning".

Anonymous

I second Kevin Lin's answer, EXCEPT if you have a strong math background from undergrad and would be competitive with other math PhD's, in which case I'd say follow your heart and change fields if you would find working on NT more stimulating. Ed Witten is one of a few very successful examples of someone who became serious about math after starting his PhD (John Tate is another), though both were interested in math in undergrad. See e.g.

Dmitry Vaintrob

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