Pure Math vs Applied Math for AI/ML

[member 757689]

TL;DR Summary: Wondering which of Pure Math or Applied Math would be better for AI/ML.

Hey everyone, I've been on this forum a while but never posted. I essentially have the choice to major in math or applied math, and was wondering which would be better for machine learning or AI as a career.

 

[berkeman]

What journals are the most papers published in for those subject areas? What authors are doing a lot of publishing? You can look at the degree backgrounds of those publishing actively in the field to start to get a better idea.

EDIT/ADD -- since a lot of this research may not be getting published (for proprietary company reasons), you can also look at the top researchers in the field who are working at the biggest companies in this work to see what their uni degrees are in.

 

[jack action]

Apparently, it is technically all applied math now:

 

[FactChecker]

TL;DR Summary: Wondering which of Pure Math or Applied Math would be better for AI/ML.

Hey everyone, I've been on this forum a while but never posted. I essentially have the choice to major in math or applied math, and was wondering which would be better for machine learning or AI as a career.

Here are my two cents. If you want to publish research about AI and ML, you should go into pure math. If you want to apply AI and ML, you should go into applied mathematics.
These are not hard and fast rules. Many people switch over.

 

[StatGuy2000]

To the OP:

I personally think you are making a false dichotomy between pure math and applied math, especially when you are thinking about what would be better specifically for AI/ML.

It is important to keep in mind that pure math is a discipline that primarily focuses on development of mathematical knowledge for its own sake, building on proofs and logical consequences from existing areas of math and building new knowledge based on these foundations. Applied math is essentially using the tools of math (in various fields) to apply to existing problems in the "real world", whether that is the physical world or the "digital world".

There are clearly areas within applied math that apply directly to AI/ML (e.g. optimization, differential equations/dynamical systems, statistics, control theory, etc.). At the same time, there have been much research in areas traditionally associated with pure math such as harmonic analysis, algebraic topology, random matrix theory, etc. that have found new applications in problems related to AI/ML.

I think the key is to build a solid mathematical foundation in your education, which you can then leverage to be able to apply to various intellectual areas.

 

[member 757689]

To the OP:

I personally think you are making a false dichotomy between pure math and applied math, especially when you are thinking about what would be better specifically for AI/ML.

It is important to keep in mind that pure math is a discipline that primarily focuses on development of mathematical knowledge for its own sake, building on proofs and logical consequences from existing areas of math and building new knowledge based on these foundations. Applied math is essentially using the tools of math (in various fields) to apply to existing problems in the "real world", whether that is the physical world or the "digital world".

There are clearly areas within applied math that applies directly to AI/ML (e.g. optimization, differential equations/dynamical systems, statistics, control theory, etc.). At the same time, there has been much research in areas traditionally associated with pure math such as harmonic analysis, algebraic topology, random matrix theory, etc. that have found new applications in problems related to AI/ML.

I think the key is to build a solid mathematical foundation in your education, which you can then leverage to be able to apply to various intellectual areas.

Thanks for the reply. My school's applied math dept. is pretty small, and offers general courses (like intro to optimization, intro to topology, continuous modeling for biology). The math department is larger, and offers separate courses like linear optimization, discrete optimization, 3-course topology series, etc. Do you think applied math major in my case would still apply to what you are saying?

 

[MidgetDwarf]

I do not know annything about this. But I did take a functional analysis course a while back, and a student asked whether they should be taking more applied or pure math, since they wanted to do data science/ml

The professor stated that applied math would be more applicable directly, but the rigors of pure math would prepare you to learn abstract concepts easier, and give you a framework in which to learn new things. They did suggest to take as much statistics/probability as possible.

Professor did have a background in machine learning…

 

[Hornbein]

I have a masters in applied mathematics and it seems to me to have nothing to do with machine learning. (Though that was just the name of the degree. It was really pure math. I never applied anything.) I also audited a course in machine learning way back in 1991 or so and didn't understand what they were doing at all. Though I imagine what is going on today is quite different.

I also have a masters in statistics and that seems relevant. Higher dimensional spaces, correlations, that sort of thing. But the thing to do is find someones who are in positions similar to where you want to go and ask them. It makes a big difference whether you want to be in academia or industry or start your own business.

 

[Hornbein]

Applied mathematics is numerical solutions to optimization problems and modeling of physical systems. Physics and engineering and astronomy. Lots of calculus. These are important in robotics but otherwise have nothing to do with AI.

 

[StatGuy2000]

Thanks for the reply. My school's applied math dept. is pretty small, and offers general courses (like intro to optimization, intro to topology, continuous modeling for biology). The math department is larger, and offers separate courses like linear optimization, discrete optimization, 3-course topology series, etc. Do you think applied math major in my case would still apply to what you are saying?

The specific requirements of applied math programs will differ depending on the college/university you attend, so I am not really qualified to answer here. In my alma mater, the applied math program is offered through the math department, and there is considerable overlap with the math department in terms of required courses.

What you may want to ask is whether, as an applied math major, you are able to take additional courses offered by the math department.

 

[WWGD]

If you do pure Math, there are jobs for Math Annotators for AI.

 

[jbergman]

TL;DR Summary: Wondering which of Pure Math or Applied Math would be better for AI/ML.

Hey everyone, I've been on this forum a while but never posted. I essentially have the choice to major in math or applied math, and was wondering which would be better for machine learning or AI as a career.

Well, AI usually is done mostly in Computer Science and Statistics departments so I would tend to say neither at leat at the graduate level.

For undergrad either pure or applied would work. The most related subjects are probability, linear algebra, differential geometry, pde, optimization, statistics and numerical methods.

 

[member 757689]

The specific requirements of applied math programs will differ depending on the college/university you attend, so I am not really qualified to answer here. In my alma mater, the applied math program is offered through the math department, and there is considerable overlap with the math department in terms of required courses.

What you may want to ask is whether, as an applied math major, you are able to take additional courses offered by the math department.

I see, okay. That makes sense, I think I am able to. However, since I took a bunch of college math courses in high school, I'm halfway done with the pure math major, and would essentially have to start over since the applied math department has separate courses from the math department (and as such requires completion of those, even the intro courses). I'm not really worried about time, but I'm planning to double majoring in electrical engineering and would think having a math degree might help in higher-level ee coursework.

 

[Hornbein]

I see, okay. That makes sense, I think I am able to. However, since I took a bunch of college math courses in high school, I'm halfway done with the pure math major, and would essentially have to start over since the applied math department has separate courses from the math department (and as such requires completion of those, even the intro courses). I'm not really worried about time, but I'm planning to double majoring in electrical engineering and would think having a math degree might help in higher-level ee coursework.

Seems like a good plan. Higher-level EE is all about complex numbers and vector calculus, something I have been unable to learn.

Machine learning AI is so hardware intensive that to meet its energy requirements Bill Gates is trying to reactivate the notorious nuclear power plant at Three Mile Island.