Too old to start math

Question

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could.

This is a question I've been asking myself now for some time. In most areas, there's a "cut off age" to be good at something. For example, you're not going to make the NHL if you start playing hockey at 20. It just won't happen.

So my question then, how late is too late to start studying math and make a career out of it? By "start studying math" I mean, to really try to understand and comprehend the material (as opposed to just being able to do well in a formal, intuitional environment).

I don't mean this from a "do what you love, its not too late" motivational perspective. I mean this from a purely biological perspective; at approximately what age has your brain's capacity to learn effectively and be influenced by your learning stop? When does the biological clock for learning new math run out?

My reasoning for asking this question is (for those who care): I love math. Really I do. But , having spent the first 21 years of my life in sports/video games/obtaining a degree in a scientific field which I care nothing of/ect, despite all my best attempts at trying to learn math, am I just too late starting to ever actually be good enough at it to make it a career? I've almost completed my second degree (in Math), but find that in many cases, despite how I look at a problem, I lack the intuition to comprehend it. I'm going to single him out (sorry), only as an example, but Qiaochu Yuan is my age.

Note 1: If this question isn't a suitable post, I won't be offended at all if you vote to close - I know this question borders what's acceptable to ask.

Note 2: Thanks to everyone for reading and taking the time for the great responses. Really appreciate it!

Answer 1

Karl Weierstrass was in his 40's when he got his PHD. There are a dozen other counterexamples, a number fairly recent. A good set of examples can be found in the thread on MO here: http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners

This myth of "science is a game for the young" is one of the falsest and most destructive canards in modern society. Don't listen to it. You only get one life and when it's over,that's it. When you're dead a hundred million years,you'll be dead the tiniest most infinitesimal fraction of all the time you'll ever be dead. So stop listening to career advice from teenagers,grab a calculus book and get to work. That's my advice.

Answer 2

21 is not old at all. I personally know heaps of people my age (32) who started out at 18 as salesclarks/BA or BCom majors/lawyers/bookeepers etc and ended up having a PhD degree in some advanced math areas and landed a job in academia or industry.

My personal case: I got a lousy BCom degree with little math at 22 and then worked in a primitive banking job. After a few years I realized I was growing stupid, so decided to do what I secretly always liked but never really had the balls to do: math and stats.

So I moved to another country, did a Masters degree in Computational Statistics, (2nd level honours) then started on PhD in Computer Science (mathematical modeling of AI). After 6.5 years of math I'm, like $n^n$ times smarter than I was at 22, I got a postdoc job in my area and got awarded a Doctoral degree this morning.

Answer 3

In Israel kids are expected to serve in the army when they are 18, and they serve for three years (men do, women serve two years). After this period it is common to find yourself questioning what you should do with yourself and not many people have answers. Therefore it is common to take another two years to work and travel the world before settling down and starting your academic education.

This means that most students in Israel begin their undergrad studies around the age of 23-24.

That been said there are considerably less mathematics students, and many of them start sooner. I started at 22, but I studied both with kids that didn't serve in the army and were 19-20 and people who took longer to settle for math and were 25.

So if you are just 21 and you want to start with mathematics, you're still younger than the average Israeli freshman.

Answer 4

Of course you can make a career out of it! When I started reading your question I though you were around 50, but 22 is not old at all to go after a career in anything but sports. This kind of time don't affect your brains ability to think at all. The only thing is, if you have great ambitions, you are probably not gonna be able to win the fields medal because it has an age limit, but apart from that there is nothing that can stop you from following a career in math and be great at it.

Answer 5

I'm not sure my personal experiences will be very helpful to a mere kid of 22, but here goes ...

I made a complete mess of being an undergraduate when I was 18 (until 21), and followed a career for some decades before I finally got round to seeing if I was actually capable of doing maths at a more advanced level.

I was almost 50 by the time I had published some research and gained a PhD in pure maths, so the effort could be considered a total waste of effort in terms of "my career", but it was hugely rewarding to me personally to have discovered that I was capable of finding out things in maths that professionals were interesting in reading - even if they were not in the same league as the millenium problems.

So - "go for it!" - you are never too old!

Answer 6

Oh my! $22$ years old?

You are still very young, and certainly not too old to pursue any passion, math or otherwise!

I've taken many (lengthy) breaks from math. But each time I've returned to serious and dedicated mathematical work (be it studying math, teaching math, or pursuing research), I've come at it from a fresh perspective.

Sure, when I've resumed mathematical work after taking "time off" from studying math, I've been a bit rusty at first, and have needed a bit of time to clear cobwebs from my brain. But that happens when taking time off from anything! So yes, "picking it up again" can feel discouraging at first, even perhaps overwhelming. But it's worth it; sometimes revisiting material you've encountered a few years back actually leads to a deeper and more comprehensive understanding of the material.

With respect to your impression that you "lack the intuition" to fully comprehend some of the problems you encounter, I doubt that intuition is "something you either have or don't have"; I'm convinced that mathematical intuition is something one can acquire/develop and honed over time, with practice and perseverance.

Take heart. Pursue your passions; with patience and persistence, the "cobwebs" will clear, and in no time at all, you'll feel very much at home in the mathematical world.

On a different note: I do think there is a myth floating around that you need to be a prodigy to excel in math, and there does seem to be a bias held by many academics that only the best and brightest among young students are worth investing in, in terms of mentoring, and/or admission into graduate programs. But perhaps the best way to defy such bias is by setting out to prove them wrong!

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Added $(1)$: Your question reminded me of the article Is math a young man's game?. (Of course, I'd prefer it was entitled: *Is math a young person's game?* - but that's another matter altogether!)

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Added $(2)$: On a light note, see xkcd for Too old for....

Answer 7

If your career means Fields medal, you're probably too old. But 21 is not too old for studying math and be successful, in the sense that you still have a great chance to become a professor in a descent university after say 15 years, 36 is not old at all, I saw lots of people got their Ph.D around 30. But I am sure you will fell frustrated sometime but if you can hold on to it, you will make it.

Answer 8

I am a couple of months away from being your age and I, as well, just started doing math. I also wasted a good amount of time playing games, sports, etc. I was a psychology major but changed my major a year ago to math -- not that I hate psychology, I still love it. Of course I struggle understanding some of the concepts in math but that alone won't deter me from accomplishing the goals I want. To be honest, I really don't care if it takes me 50 years to completely understand math. My advice will be work as hard as you can and don't look back.

Answer 9

OK, I understand nothing, but here's my opinion:

1. To be a star you should have already started as a child, out of your own accord, and should have found yourself devoting all of your time to profession of choice - be that a star video game player, a star lawyer, a star anything.

2. At the age of 21, after having completed a degree in a scientific field (for which you should have learned some math, regardless of caring for it or not) AND having almost completed your second degree in math, you are obviously qualified to make a career out of Math. Especially since you love it.

It might interest you to know that most (secular, non Arab) Israelis serve in the army till the age of 21-22, then usually take a one year vacation (backpacking around the world) and only then start their higher education. Didn't hurt us any.

As an obese person at the age of (OMG almost) 53 trying to survive Ninjutsu classes, I feel your pain :). I know I'll never be Sensei Hatsumi but I'm quite sure that had I decided to make a career out of it, I'd be able to reach instructor level.

Answer 10

Maths is life, when you start doing maths your age will be 0. Don't worry about age. Maths is life, live life as life whether its 10 days or 100 years.

All the best. I too started Maths very late :-), and after that only I rediscovered myself. As far as I remember, most of Euler's work done after he became blind (around 59 years ).

Answer 11

It depends on you!

I can take myself as an example, I started studying college math when I was 15 years old, I was sick of math when I was 19, so many things to study, I didn't have the maturity to study such a serious subject, now I'm 29 and I'm doing my master's degree in math after two bachelor's degrees: psychology (duration 6 years) and math (duration 4 years). I feel like when I was 15, the same difficulties, in fact, I think I am better now than I was 15, really. And now I feel like I can study anything I want, my brain is really fresh and new.

However, I have friends who are old inside, what do I mean? I mean they don't like thinking, don't like to discover new things, they only live to work hard and take care of their family, very difficult to teach something new to them.

So forget research which says your brain power becomes less as you age. The tests are correct in some sense, but we have to ask ourselves why a person with older age makes less points in tests than younger people, this happens because when they become older, they stop to study to work hard, have children and so on.

So what you have to have in mind is not to lose your interest to study new things and don't be contaminated by people who have lost their will of life and curiosity. If you do so, you NEVER lose your capacity to study new things.

I really don't know why mathematicians have this kind of prejudice. I've never seen this in any other areas of science.

So remember, your problem is not biological, your problem is social, the social can influence our brains.

Answer 12

We can be good at anything we set our minds to. If we make excuses, though, those become brick walls which hold us back from achieving greatness. In other words, if you approach math in the way that you'll be one of the best, and age won't matter at all. Plus, as someone who's researched mental decay, it tends to happen to people who let themselves mentally go, meaning that doing math or something mentally straining as you get older is great for your mind.

Answer 13

I am in graduate school now. Plenty of my classmates are aged over 30 and they performed very well. My mother went to college at 24 due to political reasons. She is a successful medical professor closing to retire now. I do not see any reason age should be an obstacle for your pursuit if you have passion, courage and following the right guidance.

Answer 14

It's easy to find any excuse to give up, but it's hard to slog it out and learn something in depth.

I'm almost 50, have never done physics before, but I'm slowly but surely getting my way through Special relativity, which is meant to be easy. After that I'll go through General relativity.

Years ago at uni, we had a guy who was 8o years old in his first year, he went on to do his masters and Phd in the German language, by that time he was 91.

Answer 15

The bigger problem for mathematicians is not age, but running out of ideas. There is a historic trend that the best work has been done my mathematicians while they were relatively young, and after that they just kind of floundered through the rest of their careers, riding on their past glory.

If you start late, you may still have a chance to go through the same thing, at a later age. The excitement of exploring something unfamiliar may be there for you, in contrast to others who have long burned out already.

This window of creativity may have nothing to do with age; it may just have to do with an individual's capacity, which is "emptied out" like a vessel, earlier or later.

Sometimes, the more you know, the more excuses you have to reject some idea or not to pursue some avenue of exploration. It's the young academics who make the advancements because it's a time for them where they don't have the breadth to get in the way of digging deeply in some direction.

Answer 16

Apart from age, this makes me think about this basic fear that if you're not enormously brilliant at doing logic and math puzzles, you're not going to make anything in maths, hard sciences or even applied sciences.

It's true that if you are not sure of being a crack, you are probably not one of them. But I see many people doing well in applied maths that are really not "cracks" (and I'm sure there are also some in very scientific fields).

Also, I usually hear about the major "super brains" in maths that they used help from fellow researchers on writing down theories, etc. (I was thinking about A. Grothendieck, sure you can find some examples).

So I think there is a place for "less genius brains" in science and maths.
And if you're thinking about applied maths, there is place to make money with maths today more than ever.
If you love maths, go for it (there are too few people like you!).

Answer 17

Pierre de Fermat was a French lawyer and amateur mathematician. I think he only started doing math in his late 20s. He is most famous for Fermat's Last Theorem, conjectured in 1637 and solved in 1994 by Andrew Wiles.

Answer 18

Knowledge is provided for whoever want it. Like a Chinese quote,'Live and learn until you become old or even death'. Somebody believe in IQ or gifted or talented. But i believe the quality of hardworking and never give up is the true path to success. If you know something is right, just do it.

Answer 19

When I started my undergrad degree, the head of the physics department was a guest speaker in another class I was taking. He told us that physicists don't come up with any ideas that are groundbreaking after age 40. So, even if a physicist were to publish a ground breaking paper at age 60, it is most likely based on ideas they first came up with when they were younger. I think this probably is true for the most part.

However, there are many things here to consider.

1. This statement isn't absolute. There are counterexamples. And, it is based on his observations and not on a statistical experiment that is well controlled and well documented.

2. You are still much younger than 40 and even after you get a PhD, I think you still will be, though I'm not sure about your age.

3. This is probably the most important one. Most PhDs in any field don't do anything that is groundbreaking at any age.

So, what is your goal? Do you want to be a world famous mathematician? If so, if you are a genius then it might not matter when you start (i.e., even if you do start late, your genius can make up for it). And, if you are not a genius, then it might not matter when you start (i.e., even if you started young you still probably won't do anything world famous).

Otherwise, if your goal is to be a professor and do research that is fun to you (but not groundbreaking or world famous) and teach other students, then you're definitely not too old for that. Where I go to grad school, half the students are 30+ when they graduate. And, most of the people I know in pure math in my department go on to jobs where they are required to do no research or are required to do limited research. This is something you could achieve. Is this what you want to do?

If you want to do more research, you could do it on your own, in your own free time. If you want your job to be doing research, then it's possible but not likely no matter when you start. Most of the professors where I am getting my PhD got theirs at schools like Berkeley, Penn State, Yale, Harvard, Illinois Urbana Champagne, Wisconsin-Madison, etc. They now work here, a research university, and a large portion of their job is research. Can you get a PhD from a top school? That can't be answered here. We don't know enough about you.

Answer 20

I don't think that age is an issue with you. This lack of "epiphany" and "intuition" you are having is not because of age. It is because of inexperience. You just have been out of touch with math for too long. Or maybe you were never exposed to enough mathematical thinking to begin with. Thinking logically is hard. And it can take a lifetime to get there.

So its not that your brain is incapable of being good at math. Its just that you need to spend some time in math mode. I have been buried in math consistently and constantly for the past 9 years and still at this point even if I just step away for one summer I start losing some of it. For me its exposure. If I see a problem, usually something in the past that I have seen helps me. Rarely I think of something truly original. So what I do is just expose myself as much as possible so my arsenal keeps getting bigger and bigger.

Very few people (like Gauss and Mozart) are truly gifted and rock the world as soon as they are born. The rest of us just learned and refused to give up. I think the only thing which you have no control over is creativity. Good GOOD mathematicians always had a lot of creativity and that is something you can't get with age or experience. That's the only thing you need to be born with.

Just keep at it and you will get better, guaranteed. Humans (including our brains) are remarkable at adapting.

Answer 21

If, on the other hand, if this being really good requires a tenure stream academic career, I believe you need to think about how most hiring committees would view someone starting out at the age you have completed your Phd.

Mine was planned for age 50 but delayed due to revisions for three years and I discovered that 53 was too late. Onetime I actually found out the committee decided they would prefer the younger candidate (no I did not sue) and the one position I was hired for, it was pointed out that I starting rather late for academe. It was a very good Department, but I chose to leave after the first year rather than relocate my kids just before they finished high school.

You should be done well before that, I wish someone had pointed this out to me.

Answer 22

I started working on my bachelor's in Computer Science at 24 at UCSD, and I came in with almost no knowledge of programming, and the highest level of math I had accomplished at that point was Pre-Calculus. So in addition to taking the entire CS curriculum, I had to take all 5 engineering calculus courses as well. I just tackled everything I needed to do, and with the help of good people around me, I finished with pretty good grades.

So, no. You're not too old.

Answer 23

1. You're never too old to learn anything.
2. You're only 22 -- These are the years you're supposed to be deciding what to do with your life, so if you're interested in mathematics, do it!

This is a similar situation to my own. I'm going for it, you should too!

Answer 24

This popped as a newsletter question, and it seems appropriate to share personal experience.

It is true that most significant math research seems to be done before 30. I remember Hirzebruch from my Alma Mater who had published 50% of his research by 25 - or at least that was what people said. At the same school, my Algebra professor, Jens Franke, was a year or two younger than me (see below), having already spent time at Princeton and Moscow before this. One of my teachers in grad school (economics) had 4 seminal papers in 4 different areas by 25 (and more or less retired after).

In my first semester of college, I was 25. In my first semester of math, I was 26. Being surrounded by people 7 to 8 years younger than me wasn't very encouraging - in particular the regrettable attitude of many math students to (falsely) claim that they solved an exercise you agonized over with no problem at all, and to spend 1/2 their time shortening and obscuring their arguments, probably because of a misunderstood understanding of what is elegant and cool. My first homework buddy told me what I never forgot, and have found quite true:

"If someone has a better solution than you, just assume he copied it from a better book than you had access to."

Given that my high school math education wasn't very good, for faults of my own and my teacher's, and I averaged I'd say a B+ (below my general average), with a glorious F in my final oral exam (my only F ever), I felt both inferior, and did objectively struggle at the beginning. Add to this that in informal rankings (there are no official ones in Germany) my school, Bonn, was considered one of the two best for math, and so attracted many former math Olympics participants (the most accomplished one had participated in grades 10-13, winning 2 silver and 2 gold medals). Before meeting them, I didn't even know there were math Olympics...

I worked very hard, and I think for most this is simply necessary in math. As a result, within about a year, in a crowd of about 200, I started being considered pretty good - certainly behind the math Olympics guys, but probably around there. I went on being admitted to a top 3 grad school in the U.S. - not for math as I still lacked the confidence, but with a goal to study the most theoretical part of economics (decision, game theory and such), which boils down to applying algebraic topology and other fairly hardcore math disciplines. My course work consisted mostly of taking the theoretical stats grad level classes of the first two years (in stats, my school was - then - traditionally considered as competing with Berkeley to be the top-ranked stats school), scoring consistently A's with the rare A-, and I did very well (ranked 'outstanding' and 'excellent' by my school the first two years). Being a rather troubled human being, I proceeded to boycott my own future as an academic (which is a different story not belonging here), but still my main thesis paper was 3rd rounded by Mathematics of Operations Research (with feedback "Clearly worthy of publication", asking to tie up details), before I stopped pursuing it, having gone to industry, not academia.

I'm now in my 40s, and am just done auditing algebraic topology at Columbia. 22 is certainly in itself not too old. While you say that you don't want a "do what you like!" pat on the back, I can't help giving you one. Just expect it to be tough originally, to have to work very hard (making it your life for a while), and to pretty much keep feeling that you should see things faster than you do. That's the doing math experience: every new problem is a true challenge.

Answer 25

While I think you are never too old to start anything, I really think Math sports needs to be learned and cultivated from a young age to be truly effective.

Answer 26

Gauss was pretty much the Lord of Number Theory by the time he published Disquisitiones Arithmeticae, at the tender age of 21. From that point on he turned to other endeavors. He did have a personal sponsorship from the Duke of Brunswick, but he was still afraid that this was cut off, and even he himself was clear at this point that number theory wasn't something that deserved such a sponsorship...

He still did publish some number theory stuff far and few between, and clearly he still cared about it, but it is obvious that he was full time engaged in anything but number theory from that age on.

So probably youth is only correlated with such results because at no other age is anyone naive enough to work on such subjects...

If you are somehow in a haphazard economic position and do mind to die poor and ugly, just don't...

EDIT1: Here is another fun historical anecdote: When Gauss's protege Dirichlet (number theorist) and his buddy Jacobi visited Gauss to celebrate the 50th anniversary of his doctorate, this happened (source page 31):

A highlight in those strained times was the participation of Dirichlet and Jacobi in the celebration of the fiftieth anniversary jubilee of the doctorate of Gauß in G¨ottingen in 1849. Jacobi gave an interesting account of this event in a letter to his brother ([Ah.2], pp. 227–228); for a general account see [Du], pp. 275–279. Gauß was in an elated mood at that festivity and he was about to light his pipe with a pipe-light of the original manuscript of his Disquisitiones arithmeticae. Dirichlet was horrified, rescued the paper, and treasured it for the rest of his life. After his death the sheet was found among his papers.

so it goes...

EDIT2: another option is to first get in shape and marry a rich wife and then do pure math...

EDIT3: another option is to make a website and sell each pixel for a dollar

EDIT3: another option is to become a millionaire by selling one of the first video streaming websites to Viacom but then to totally stop publishing stuff eh??...

Answer 27

I have looked through the answers so far, and don't see one from anyone really old. I am 82 and still learning maths, and lots of other stuff, as part of a hobby that includes electronics and amateur radio. I help with on-line tutoring on a UK course for those taking their exam for a Full amateur radio licence, and I have no trouble sorting out the answers to the problems students have. So age is not a hindrance.

From boredom and ill health, I just scraped though a Pass degree in Maths and Physics when I was 21. After ten years as an engineer I studied for a Teaching Certificate, and at the same time became interested (1964) in computing. I got a Master's degree in Technology (computer Science) at age 43, and thereafter taught computing at a Polytechnic that became a University (and a very good one) a few years before I retired.

My advice is to attempt what you fancy, age mostly brings maturity that makes it easier to study.