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I am 21 years old, with an unfinished degree in CS, and for this past year all I could think about was trying for a mathematics degree. I was miserable at my previous university for many reasons and hated the coding subjects in our program, but I always enjoyed the mathematical ones. Now after quitting, all I can think about is becoming a mathematician, to do research and hopefully teach at some place and I simply cannot imagine any other profession for myself.

Two worries essentially prevent me from acting on this impulse -- that I am too old to start from scratch at this point and that I am simply not fit for mathematics as a profession. The first one is pretty self-explanatory: if I were to for it, I would probably only be able to start next year, by which time I will be 22. Add to that 3-4 years of bachelor, 2 years of master and I would probably not be able to start PhD work untl I'm 28-29, assuming I've successfully make it that far. Meanwhile, the median age for most bachelor graduates is probably something like ~22, with most getting their PhDs by ~27 and I feel very threatened and outclassed by this. My other worry is that I'm not simply fit for the profession -- I feel like I'm not a particularly good problem solver and, in my mind, solving problems is the cornerstone of mathematics. I have a good memory and retain theory pretty well, but I consistently have trouble applying it (I usually can't solve more than half the exercises after each chapter in a textbook and whenever I actually solve any, I feel like it was too easy and even a dunce could do it). To summarise, I am worried that I have simply convinced/talked myself into wanting this and that if I do go for it, I will run into a dead-end, not having achieved anything remotely of note, trying unsuccessfully to make it in a profession for which I do not have the aptitude, while younger and more talented people reach heights unattainable to me.

I honestly am not so sure what I'm asking here. I suppose I'm looking for some kind of advice on how to proceed, from those of you who maybe started late in this field and had serious doubts about the whole thing, but still managed to make something of yourself.

Hilbert Jr.
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    People much older than you have had success as mathematics students. As to whether you are fit, really the only way to tell is to try. – Gerry Myerson Nov 11 '19 at 11:42
  • See also https://math.stackexchange.com/questions/1334946/am-i-too-old-to-reach-to-the-point-of-a-ground-breaking-research-and-achieve-it and https://math.stackexchange.com/questions/237002/too-old-to-start-math – Gerry Myerson Nov 11 '19 at 11:45
  • Thank you for the links, I will take a look at those. I know the post sounds incredibly whiny and insecure, and people probably will downvote it, but I honestly did not come seeking any kind of "validation" (in the "You can do it, champ!" sense). I am simply hoping to find advice from people who were once in a situation similar to mine and I want to know what they ended up doing. – Hilbert Jr. Nov 11 '19 at 12:29
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    Here's a relevant poem, though it's about writing, not mathematics. It's good advice though. – goblin GONE Nov 11 '19 at 13:25
  • "I am too old to start from scratch at this point" - you wouldn't be starting from scratch. Things that you've learned during your CS degree translate to mathematics.

    "I consistently have trouble applying it" - that's what a PhD course is for. You are meant to learn how to do research there, not to already have that skill.

    As a personal anecdote: I started my PhD at 28, finished at 31. I'm currently a professional mathematician with publications in highly competitive journals.

     – Randy Marsh Jun 26 '23 at 17:52
  • And since you're asking for advice on how to proceed, I would suggest that rather than focus on age or ability, you do some research about the state of the job market in mathematics, i.e. what awaits you after you get a PhD. – Randy Marsh Jun 26 '23 at 17:54
  • @RandyMarsh thank you for the comment, you and others like yourself are an inspiration to me. I am pleased to say that in the time since I posted this question I have quit the whining and have enrolled in a bachelor programme, which I will be ending soon (with plans for further education after). As for career prospects, I am not entirely sure at this point, but I will take it as it comes, don't want to do anything else in life. – Hilbert Jr. Jun 26 '23 at 17:55

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I am in my 30s and about to get my B.S. with high honors and currently applying to PhD programs.

I am not good at math, it is very challenging to me and that is also why I enjoy it so much. Like you I have asked this question many times, and waited years thinking I was too old.

There will be moments of doubt as you will be surrounded by incredibly talented people younger than you are... For the rest of your life, you will always feel that you might be "too old" or "not smart enough." Do not fall for this common feeling and trap. Do what you wish and do it with integrity and honesty. Otherwise, you will live with regret, which is far worse than failure.

No one here can advice you whether Math is right or wrong for you, and I understand this fear all too well. You must decide for yourself.

cemsicles
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    Thank you for your answer, you're right, I don't want to live my whole life wondering "what if...". I wish you the very best in your mathematical career! – Hilbert Jr. Nov 11 '19 at 13:32