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I am in my first year phD in pure math but I am getting bored, I think a phD in computer science would be a better fit. How should I go about in order to switch the program?

Is it possible to do both in the same time? There might be a bit of overlap between the two.

I hear that there is a lot of work in the computer science side (publications, conferences, building things,…) and I like to be productive and compete with others.

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    My first question is: why do you want a PhD at all? Why not go work for a few years and figure out what you're interested in enough to do a PhD in? Aug 6, 2023 at 21:47
  • I was bored at work, I figured they do more interesting things in academia, turns out it is the same kind of boring.
    – metaUser
    Sep 3, 2023 at 3:15

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How to switch depends on where you are, but if it would be at a different institution, then it would probably entail going through the full application process again. Even at the same university, it is likely that CS is in a different department, but it is easy to ask them what you might do.

It is unlikely that you can (or should) try to do both at once. It will get much harder as you go on. In the US, you would need to pass two sets of qualifiers most likely.

Yes, there is a lot of work in any field. But it differs by field. In CS you probably want to attend as many conferences as you are able. Not so much in math.

There might be some overlap between fields, depending on your CS focus, but probably not a lot between pure math and CS. If you are bored, talk to a faculty member or two about how to get un-bored. There may be projects around that would interest you.

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I will attempt to answer your question based on my experience; well, not really my own experience but something similar as you read on.

I am a PhD in Computer Science (specializing in ML), and my wife is a Mathematician with a PhD in Pure Mathematics (primarily, Number Theory, Representation Theory, and such). Trust me when I say things are not as easy in our respective fields as they may seem. I can undoubtedly say that Pure Mathematics is no fun. I have seen her frustration when she sits on a single theorem or idea for months, and nothing comes out of it sometimes. So I do understand what you mean when you say, "I am getting bored." However, she always tells me that that is what keeps her going and keeps her love for mathematics. She also tells me, and I too know that Pure Mathematics is often called the "Recreational Mathematics". It is what these mathematicians do for fun sometimes. They do have beautiful applications in real life; but that remains least of their concern. So, I think you should be proud that you are getting to do this. Maybe, to get your motivation back in your field, you could read or watch some documentaries on the great mathematicians: Ramanujan, Hardy, Godel, Fermat, etc. Their lifes were worth reading about.

On the other side, that is, Computer Science, probably the closest (not too much!) to Pure Mathematics that you could do, is Theoretical Computer Science, that involves a lot of exciting research on Prime numbers, automata theory and computation, logic, compilers, etc. If you are interested in probability and statistics, you could try your hands on the theoretical aspects of machine learning. However, from your questions, I guess that you may not have been trained in computer science. That could make your life a bit difficult if you switch entirely. As other answers suggest, it will depend a lot on administrative factors too if you plan to switch anyway.

That said, you could see if you could work on an area that uses ideas from pure mathematics to solve (open) computer science problems.

Last, remember, it is okay to feel like "I don't belong here". But that is okay, and just hang in there; just try to do something every single day.

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  • I like your answer, thank you. It is the closest to my specific problem. I will tell you something, I only want to publish, apparently the publish or perish thing is the norm, my supervisor is always busy trying to get his name out there, he never shared anything about what he is working on, ...
    – metaUser
    Sep 3, 2023 at 3:25
  • ... I am left with free time so I spend it solving (or trying) Putnam problems. From what I understand it is not only his case, actually he is one of the best profs out there, it is the environment which is like that, all the profs are doing the same with their students, if you are pragmatic, why would anyone help you publish something if he can publish it himself? It is like a race...
    – metaUser
    Sep 3, 2023 at 3:25
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Contact suitable supervisors in the computer science field.

Talk to your existing supervisor - they would rather you move and eventually complete than fail or drop out.

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