Is PhD in pure math worth it?

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Daniel Duffy said:
The 'place' (aka branding...) is not all that important. Supervisor is more important.

A PhD in maths means you are good in a very very narrow area that 3 people (including you, excluding supervisor) know. No a-priori conclusions can be drawn about other aptitudes.

e.g. pure maths meets industrial computer programming.
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I love that you say excluding supervisor, because it is so true!
 
bigbadwolf said:
In some cases it can actually be an impediment as the habits of thought you've acquired (and which are now part of your nature) are very different to those you need in the other area. The habits of thought you acquire in class field theory or automorphic forms are not going to help you in any real-world occupation. What you've become is over-trained and over-specialised in one very narrow area that society is not willing to pay for.
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I really do not rate pure maths PhDs. Very narrow skillset, and they believe that every problem is solved by staring at a piece of paper with a pen for long enough.
 
John Marks said:
To OP do what you like. In the UK the applied math departments are mostly for mathematical physics. Statistics is in the pure math departments. James Simons has a Math PhD, I think he did pretty well.
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Einstein has a PhD in physics, he did pretty well, hence a PhD in physics is good training for life.
 
I think they mean that the specialization is in a pure math topic, the name on the degree isn't important.
 
Number theory, algebra, functional analysis, etc would be pure in my eyes. Linear algebra, numerical analysis, differential equations, statistics, computational mathematics, optimization would be applied.

The way I think of it is if the subject matter is directly applicable to solving real world problems, then it is applied math. If the subject matter develops the robust theoretical background for use in another another subject area, then it is theoretical.

For example, separation theorems in functional analysis are used to develop the theorems used in optimization which can be applied directly to solve problems. It's been a while, but if I recall correctly, Farkas' lemma (or perhaps the Motzkin transposition theorem) is proven using a separation theorem (or perhaps a corollary) and is used in proving the Fritz-John, and hence KKT, conditions.

That's my opinion anyway.
 
CandyOates said:
Number theory, algebra, functional analysis, etc would be pure in my eyes. Linear algebra, numerical analysis, differential equations, statistics, computational mathematics, optimization would be applied.

The way I think of it is if the subject matter is directly applicable to solving real world problems, then it is applied math. If the subject matter develops the robust theoretical background for use in another another subject area, then it is theoretical.

For example, separation theorems in functional analysis are used to develop the theorems used in optimization which can be applied directly to solve problems. It's been a while, but if I recall correctly, Farkas' lemma (or perhaps the Motzkin transposition theorem) is proven using a separation theorem (or perhaps a corollary) and is used in proving the Fritz-John, and hence KKT, conditions.

That's my opinion anyway.
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Numerical Analys is both pure and applied, can be. Same holds for PDE.

Maybe I missed the definition of 'pure' (it means nothing).
 
Great discussion.... While I don't count myself among people with much natural aptitude in math I have a lot of respect for this field. There are so many interesting problems. Right now I'm taking some graduate math courses at my school. If they work out, then I'll try for the PhD.

I noticed NYU is ranked highly by US News for Applied Math, but has no Applied Math PhD program.
 
"The Graduate Department of Mathematics at the Courant Institute offers balanced training in mathematics and its applications in the broadest sense. The Department occupies a leading position in pure and applied mathematics, especially in ordinary and partial differential equations, probability theory and stochastic processes, differential geometry, numerical analysis and scientific computation, mathematical physics, material science, fluid dynamics, math biology, Atmosphere and Ocean science, and Computational Biology. "

You should read
 
JesseLevermore said:
"The Graduate Department of Mathematics at the Courant Institute offers balanced training in mathematics and its applications in the broadest sense. The Department occupies a leading position in pure and applied mathematics, especially in ordinary and partial differential equations, probability theory and stochastic processes, differential geometry, numerical analysis and scientific computation, mathematical physics, material science, fluid dynamics, math biology, Atmosphere and Ocean science, and Computational Biology. "

You should read
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You should read too. All I was pointing out is that the degree is not called "PhD in Applied Mathematics" in spite of its focus on both pure and applied math. That's all.
 
Well that's not very good mathematical logic is it. You're pointing out a completely trivial fact that would be insignificant to anyone on this site and confusing them into thinking that the University doesn't have the degree in question.

You said the University did not offer a PhD in applied math. You can continue to wallow in bad judgement if you want but the statement was just false. They do in fact offer a PhD program in applied mathematics. Maybe they just stopped calling it applied to save you an application fee if you cannot comprehend this.
 

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