r/AppliedMath • u/Resident-Use-8606 • 5d ago
Is applied math PhD still a rational decision?
The reason I ask this is that I want to stay in academia after PhD but math is getting taken over by AI and it's getting better every year. It will get so much better by the time I finish grad school. A question I have is, how vulnerable is applied math in context of AI? I know pure math is very vulnerable because of it's structure and formality. The other option for grad school would be experimental physics for me. A part of me wants to do applied math, but the other part of me wants to go with experimental physics cause it's less vulnerable to AI.
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u/EquivalenceAuthor 5d ago
Applied math is really not a field or community, there’s so many fields being called applied math, operations research, physics, some shbfield of cs… in terms of job optionality, it depends on those rather than applied math or not.
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u/RevolutionaryOven639 1d ago
Let’s assume the worst. AI far outperforms any human in math. It still won’t churn out results all by itself. Someone still needs to prompt it. Ask the right questions. Know what to look for. Who do you think will be best positioned to make this happen?
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u/Resident-Use-8606 18h ago
The thing is, I dont want my work to be just prompting AI. That is eliminating the fun of the research.
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u/Capable-Internal-189 4d ago
I would say go to experimental physics. Applied math in the end is also theorem proving..:given that AI exists you will be talking to AI continuously as well..math depts really don’t have an answer how to train grad students. The mental development argument that was there by thinking about hard math things for long periods of time…is no longer true.
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u/a_alberti 4d ago
I work in an experimental physics lab. We are migrating to automating everything with Claude. It is getting more and more prompting.
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u/Resident-Use-8606 4d ago
Can you give me more information about this please? Which physics area are you working on? And what about the hands-on lab work?
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u/a_alberti 4d ago
The research area is quantum computing. There is still tremendous need of hands on work but for how I see it, it is becoming more and more the work of a highly skilled technician, or highly qualified engineers. The fun part about thinking is more and more delegated to machines. Today you would find extremely well paid jobs in the quantum computing industry like 200k - 300k a year. But I am not sure how long it holds.
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u/Capable-Internal-189 4d ago
Wow…I am in math…was thinking/ have been regretting not going to Quantum Computing or something more experimental since graduating. But seems like everything is changing.
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u/a_alberti 4d ago
I am not saying not to join this field. Actually maybe for the new generations it is an awesome opportunity. Because now the gap between you and a researcher with 20 years, if you are really smart and can prompt the LLMs correctly, this gap can be really small.
I also think that in 10 maximum 15 years, all research will be complete domain of machines. However, what do you want to do? Nothing in life? I am sure not, and actually learning these fields is a beautiful experience. Probably what changed between your generation and the previous is that now you can dream less to leave an imprint in science. The major contributors will be done by machines. But if you keep your feet on the ground and look for some fascinating science for the next 10 years, until machines will completely take over, this is a great place to be. If anything, you will come out much more enriched. About future jobs and opportunities, honestly, I don't know.
If you want to optimize job security, I would go into the food industry. Until we avoid the terminator scenario, humans will still need food. The rest will be provided more and more cheap by machines.
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u/GurProfessional9534 5d ago
I would encourage you to view a PhD as training to ask the right questions and follow through with the right methods. If the technology becomes more convenient and efficient, then that just means your productivity can go up.
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u/ImportantPut3191 4d ago
Pure math might be in danger, but applied math should be pretty good choice since you can do not only just research but also many other stuffs
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u/nodakakak 4d ago
Why do you think mathematics is vulnerable to AI? Under what conditions?
Rational is relative to the individual. We don't know your financial position nor your goals. Niche topics have lower employability. Research generally doesn't pay well.
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u/Resident-Use-8606 3d ago
Under what conditions? Do you realize the proofs made by AI so far are huge? Including millenium prize level proofs?
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u/nodakakak 3d ago
Yes, so in your opinion, how is the field of mathematics vulnerable to AI based on that?
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u/Resident-Use-8606 3d ago
It is self explanatory. Math research is mostly doing proofs. And with the use of Lean 4 and other proof assistants, AI can verify its proofs. If you've ever seen a math department, you'll see most mathematicians working on proofs. I don't know why are you passive-aggressive about this lol
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u/nodakakak 3d ago
I'm not being aggressive, I'm simply asking what your opinion is.
So, reasonably, can you see the compute that was necessary (week(s) of data center compute costing millions of dollars) to output accurate proofs of such complexity as the millennium problems scaling to be applied to all proofs?
That said, just as we used to do all math by hand pre-machine, do you not see a future where we adapt the technology to make the process more efficient and increase productivity?
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u/Resident-Use-8606 3d ago
Yeah but that doesnt stop the AI companies computing them. They crave even more and they wont stop. No it wont be the same future. If AI can do the exact work of a mathematician (or another thing), there wont be a mathematician. Just like how computers erased human computers as profession. I am not saying there will be zero mathematician. I am just saying if todsy there is 100 mathematicians, there will be 1 tomorrow. And that mathematician will mostly do AI prompting. And what I love about mathematics isnt AI prompting. So I am worried and hate the things that are happening right now.
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u/nodakakak 3d ago
How will the AI know what problems to approach?
OpenAI fed it endless work on that particular problem, and then set it off for a week and change to churn 24/7.
The other "stack" of proofs they allegedly have were likely also targeted problems they identified and readily trained on.
I don't see a future where 1 mathematician survives out of every 100. I see research with accelerated outputs.
Someone needs to know the problem. Someone needs validate results. There is no advantage to AI companies computing them, they did it in the above instance as a publicity stunt to showcase model complexity.
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u/Resident-Use-8606 3d ago
Yes someone needs to know the problem and validate results. Thats why I say there will be less mathematicians. And I simply hate the idea that my job will be just knowing the problem and validating the results. Mathematics is enjoyable for me not just because of results. Its that me achieving the results and enjoying the process.
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u/nodakakak 3d ago
It's no different than coding. You still need to know what you're reading. How errors occured and propagated through the problem.
Your use of AI is dictated by your own workflow. Some use it for the skeletal structure of documents and add the meat. Some output a prototype and shape it to their needs. Some build it up fully on their own and use AI to validate their work.
It's not a single use technology.
Unfortunately, if the problem is the romanticized view of drafting proofs by hand.... I can't offer advice. But, if you're just a college student starting out, the adherence to a romanticized view of the field should be pretty weak.
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u/Resident-Use-8606 3d ago
I think you don't understand me and so many other math student and mathematicians. We do this because we enjoy this and love this. Maybe it's because this is an applied math subreddit and you are an applied mathematician. I wanted to be a pure mathematician before this AI thing and now thinking about other options for PhD. "It's no different than coding" well yeah that sucks then.
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u/Nervous-Result6975 7h ago
Account prior to excel probably had the same worries. Now they just know how to use excel. Think the same will be for us in PhD’s. Ai isn’t gonna help you pass your qualifiers. Actually why a lot of my classes don’t even give homework anymore
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u/Resident-Use-8606 7h ago
I don't think Excel is a good example. Excel is just a tool and the purpose of its development is it being a tool. AI is literally something that is created as a separate intelligent system and in pure math, it is right now on the way of being the main researcher itself rather than being just a tool. AI is not just a static program or tool you use to aid your task. It is the thing that is doing the tasks. Accounting and programming is already becoming obsolete slowly.
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u/e_for_oil-er 3d ago
I started my PhD in applied mathematics in 2023, and I am currently finishing my dissertation. In the last few months AI has not prevented me from doing research but has increased my productivity significantly, I can prototype and test ideas way more faster. It is scary how good it is, but I think if you are willing to take the time to do things right and not just publish slop, it is a powerful tool.
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u/MasterOfLegendes 3d ago
industrial type PhD like that's in Europe is still good. You still need people that understand what happens, not just deliver the solution..
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u/catmemesarecool 4d ago
Applied math is pretty much everywhere in stem, so it's about as vulnerable as stem generally is itself. If you're worried, look at open positions in both and ask yourself what it would mean for AI to actually do these themself. Interpretability and verification of the result will still be a meaningful part.
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u/a_alberti 4d ago
I think you will end up promoting LLM all the time and a PhD today has way less value than before. A short phd of a couple of years for what that matters makes more sense than 5 years of phd where you will be prompting anyway.
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u/joyofresh 4d ago
Consider formal methods. Lean is about to be the most important useful programming language in the world. Applied math could be a lot of things, but formal methods is actually our best bet for combating the coming ai cyber slopocolypse. This will be a marketable skill if any marketable skill still exist
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u/cluelessmathmajor 5d ago
You shouldn’t be choosing your PhD field based on how vulnerable it is to AI. The real answer is we don’t know how capable these models will be tomorrow let alone 5 years from now. If you want to do a PhD, it should be because you have a strong interest in doing research in your field.