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by cg30e 1692 days ago
This is very inspiring. I too am young and been in the work force for several years, but unlike the other comments in this thread I am not settled down as an older student returning to school.

I am willing to give up a high paying salary to return back to school as a PhD student and I am not tied down with a mortgage or anything else.

I find mathematics simply too interesting to not learn at the highest level. Working in industry will simply not teach me the material I want to learn. I’m considering going back for either a PhD in Math or a math heavy PhD in CS. I read math textbooks for fun and worked with tutors to ensure my proofs are done correctly. I can do this for hours on end without external motivation. I taught myself a lot of math and can see myself doing this as a career. I want to do research.

Most people my age say the same things in the comment sections in this thread (tied down to a mortgage, make too much money to return). I’m glad generalizations like these don’t apply to me and can’t wait to get back to school

4 comments

Some cautionary comments:

Often your advisor in grad school will force you to focus on what they want rather than what you want to learn. This is less likely in a math department, but more likely in a CS one. As with everything, it all depends on your advisor.

The PhD is replete with hoops you have to take that will be orthogonal to your goal of learning (e.g. spending a lot of your time doing HW on the professor's pet topic when taking a course). Someone I know who retired somewhat young (early 50's) enrolled in a PhD program because he loves to learn. He dropped out within two years because he found it fairly inefficient in learning the topics he wanted to learn about (he had a career on mathematical topics and can handle the math). Unlike younger folks, time is precious for him, and being efficient is more important to someone in their 50s than in their 20s.

If all you care about is learning and not the actual piece of paper in the end, it may be more efficient to get a less demanding job and use your spare time studying what you want to study. Do it right and you'll make more money than you would as a student, and potentially learn more than you would in grad school.

Finally, PhD is about research. Yes, you will learn a lot, but learning is not the goal. A lot of people drop out because they realized they loved learning much more than doing research, which will involve large chunks of your time being unproductive. If you plan to do a PhD, you will have to draw a line at some point and say "OK, those 10-100 things there that really interest me? I have to drop them forever so I can do research." If you opt not to do research, you can learn a lot more.

While everything else you say may be true, I take issue with efficiency being a function of age. Fundamentally you have no idea how many years you will get. Be efficient at all ages, and live like it might (and might not!) be your last year, regardless. Personally I’ve had close brushes with death a couple times in my life, and the dice roll could easily have gone the other way. I’m sure I’m far from alone in this.
I did not mean to imply one shouldn't be efficient at all ages - just that those doing their PhDs in their 20s do not value it as much as those in their 50s.

Also, those in their 20s often haven't lived long enough to know how to gauge their efficiency. The person who has spent decades working 40 hour/week jobs knows better the value of less free time.

PhD or not is one of those questions where if you find yourself asking it repeatedly (especially to others around you), the answer is no.

You are exactly the kind of person who should be doing it!

Good luck!

Thank you!
Where can people who are interested in learning math find math tutors? I'd like to engage a math tutor though i don't think I would pursue a math PhD :)
Do you mind sharing the books you found helpful to self learn math with a tutor?

I am looking to also go on a self study mathematical journey

For sure. I'll list some books for introduction to proofs, abstract algebra, real analysis, topology and category theory. These are not comprehensive, just listing books off the top of my head. I'll definitely be leaving off personal favorites other people have. You'll like some better than others. Some of these are beginner books and some are more advanced. A good tutor can help you get through the more advanced books. I tried to list the most beginner friendly book first in the list under each subject. Then the more advanced books later in the list.

Introduction to Proofs:

Just pick one of these that speaks to you the most. All three are good.

Discrete Mathematics with Applications - Epp

Discrete Mathematics and Its Applications - Rosen

Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al.

Abstract Algebra:

How to Think about Abstract Algebra - Alcock

Abstract Algebra - Pinter

Abstract Algebra: A First Course - Saracino

Algebra - Artin

Abstract Algebra - Herstein

Abstract Algebra - Dummit & Foote

Linear Algebra:

Maybe an engineering based book first if you haven't seen linear algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh).

Then:

Linear Algebra - Friedberg, et al

Linear Algebra Done Right - Axler

Linear Algebra - Hoffman & Kunze

Real Analysis:

How to Think About Analysis - Alcock

Understanding Analysis - Abbott

Tao's Analysis text

Principles of Mathematical Analysis - Rudin

Topology:

Topology - Munkres

Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson, and John Terilla

Check out this list:

http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others.

Category theory:

Categories and Toposes: Visualized and Explained - Southwell

Conceptual Mathematics: A First Introduction to Categories - Lawvere

Category Theory for Programmers - Milewski (if you like functional programming)

Programming with Categories - Fong, Milewski, Spivak (if you like functional programming)

Category Theory in Context - Riehl

There are a few others by Spivak which you may like.

If you don't know category theory whatsoever then I like Southwell the best (pair them up with his youtube videos). Eugenia Cheng also has a nice set of lecture videos.

If you already know math pretty well, then Riehl is a favorite.

Hope that helps!

I see you did a lot of analysis, but no Calculus, why is that?
Calculus is a subset of analysis. It's not really its own subject. Generally what people call calculus is a collection of results that are part of analysis.