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I am 26 now. I left study after completing school. Now I am thinking of doing a Bachelor's degree in mathematics. I purchased a basic Calculus book and I found it interesting.

So I took some advice from a PhD scholar. His straight answer was that I am not gonna be successful. He quoted some words from a mathematician, "Mathematics is young man's game".

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    $\begingroup$ I think mathematics is a young man's game probably on average because life begins to catch up with the "old men". If you, for example, have family responsibilities and non-research job responsibilities to attend to, even if mathematically oriented, these seriously eat into one's thinking and writing time. (This is one man's opinion!) What I'm saying is that at 26, you are closer to running into these kinds of obstructions to thinking than you would be at 19. This is, to me, the biggest reason that mathematics is a young man's game. Counterexamples to this require a very simplified lifestyle! $\endgroup$ – Jon Bannon Feb 3 '17 at 0:56
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    $\begingroup$ @jonbannon I disagree. Look at Mary Ellen Rudin. With four children she was one of the greatest mathematicians of her generation. I certainly didn't know her well enough to be able to say how she managed it but she certainly did. $\endgroup$ – DRF Feb 3 '17 at 8:49
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    $\begingroup$ @DRF: Indeed, there are always exceptional geniuses (I've heard from reputable sources that Mary Ellen was much smarter than Walter, for example...) Also, consider Maryam Mirzakhani! However, I know several very strong mathematicians who have tried to balance full-bore research careers with a healthy home life, with the result ending in heartache. What I am saying is, there is a cost to any high level career commitment, especially in a challenging discipline, and that it is not fair to attribute it to the inherent nature of mathematics and the age of the human brain! $\endgroup$ – Jon Bannon Feb 3 '17 at 13:41
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    $\begingroup$ @DRF (cont.) Furthermore, the apparent ability to flourish in mathematics despite advanced age is often due to very strong commitment of a person to mathematics in his or her younger and freer days. This experience certainly allows us to be productive even into old age. The question is whether one can manage to make that commitment in busier stages of life. It is certainly possible, but there are only so many hours in a day! E.g. Mary Ellen Rudin at age 17 became a student of R.L. Moore, so the foundation was laid early. The same, I know, is true of Mirzakhani. $\endgroup$ – Jon Bannon Feb 3 '17 at 13:49
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    $\begingroup$ @Taladris: I totally agree. As said in a great post on MO, you don't have to be Michael Jordan to play basketball! I wrote these comments to give a glimpse from the inside (I am a mathematician who knows many mathematicians) about mathematics being a "young man's game". $\endgroup$ – Jon Bannon Feb 3 '17 at 17:30
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Certainly someone your age (or even much older) can learn Calculus, even get a degree in mathematics. And get a good job afterward.

That "young man's game' quote refers to doing mathematical research at the highest level. There is some validity to it, but there are also well-known counterexamples. (And even most young men never make it there.)

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    $\begingroup$ +1 especially for the comment "And even most young men never make it there." While it seems anecdotally that most great mathematicians start young that can be explained away by a number of confounding factors and given how few of those studying mathematics ever "make it big" (~50-100 in a generation) it's hardly reasonable to give up, since you likely won't be one of them no matter when you start. $\endgroup$ – DRF Feb 3 '17 at 8:50
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    $\begingroup$ I also know some very successful women in mathematics, if we're really caring about this scholar's pithy quote that much. $\endgroup$ – djechlin Feb 3 '17 at 22:42
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For sure you are not too old. If you are really interested and if you are motivated to work hard, then you can have a shot. Maybe you try some of the exercises in the book to get an impression, how well you are in teaching yourself maths.

A friend of mine is a philosopher and he started with maths, when he was older than 30 and it worked quite well.

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No, it is not too late.
Not even close.

I failed at my first attempt at college, went back at 28, initially only part-time, and eventually ended up with bachelors degrees in math, physics, and CS. Now I'm in the Ph.D program in CS. You might not be as prepared/ambitious/indecisive/whatever as I was, but it's not too late for you to learn math. I also studied with quite a few classmates who were coming back for another degree or who switched majors late, or who had worked in industry for years (or decades in a few cases). If anything, the older ones were more interested and more focused.

I'm not sure what your Ph.D. scholar friend had in mind; depending on why you're interested and how it goes it's not unlikely that getting a Ph.D. in math won't be for you. But if a Ph.D. isn't for you it won't be because of your age. If you can spend the time and money and are interested in the subject, you can learn it. And you don't even have to be a full-time student.

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    $\begingroup$ How are you able to tell OP that it's not too late with the information that they've given ? Surely they should state what foundations they already have in place etc, as well as saying what they want? Of course it's never too late to learn some mathematics, and no one learns all of it... But there's certainly a large area where, if you haven't a sufficient foundation it's going to be extremely difficult to get anywhere with the subject I don't understand why so many seem to throw out blind support on this type of question. $\endgroup$ – baxx Feb 19 '17 at 12:14
  • $\begingroup$ @baxx, I suppose in my mind getting a bachelor's degree is learning some mathematics. IME, when people can't make it through an undergraduate math program it's not because they run out of ability but because they run out of patience or interest. What I said about getting a Ph.D. applies there as well: if it isn't for you it won't be because of your age. Here in the U.S. math is feared and hated even by the schoolteachers entrusted to give our children its foundation; it seems like a terrible idea to discourage the rare few who take interest despite that. $\endgroup$ – ShadSterling Feb 19 '17 at 14:51
  • $\begingroup$ I understand that if someone don't want to do maths then they're not going to, but that's a bare minimum. I would argue against that wanting to do it and working hard is enough, because I don't think it is. If someone doesn't have the foundations in place in almost all cases undergraduate mathematics isn't going to be an option. I often see statements such as "Oh it's only high school maths you'll be fine!" etc etc. I assume that people saying such things have no comprehension of the work involved to learn the subject from near scratch later on (continued) $\endgroup$ – baxx Feb 19 '17 at 19:30
  • $\begingroup$ If someone hasn't done high school maths it's extremely challenging, and trying to do that on top of other commitments really isn't practical for most. I also get the impression that many take the easy option by telling people that they can do it, and I don't like it. I get that the intention is for it to be encouraging and so on, but often kthe statements are pretty empty as there hasn't been enough information exchanged for a meaningful review. (continued) $\endgroup$ – baxx Feb 19 '17 at 19:30
  • $\begingroup$ And what's worse is that the ideas are often along the lines of "if you work hard enough you'll be able to do it", which just seems crazy to me. A lot of the people doing the subject at University have been working fairly hard for the past 10 years, I don't understand why people assume that some one can just catch up on the back of some encouragement. Of course there are edge cases, but for most I would say that it's not really an option if they don't have a decent foundation. $\endgroup$ – baxx Feb 19 '17 at 19:31
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It really depends on what your goal is. If you want to be the best Mathematician, it may be hard no matter when you start.

I guess the major reason why you want to study Mathematics is just to enrich your way of thinking. No one is too late for that purpose. Also there are many benefits of studying math, like logical thinking and abstraction.

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Just a little example on this topic - when I got into studies(at the age of 18), I was top student in my generation along with a student who was 40 years old, decided to give it a try at that age and who has family. He got top scores in all math subjects (algebra, analysis etc.), so it means you can definitely succeed if you are interested enough. I find math beautiful and enjoy every bit of it, so as long as you are interested enough and have even a slight talent for it, you should give it a try.

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It is never to late to expand and exercise your mind. The stimulation alone will keep your brain young. Math is exercise for the brain. How strong you want to be is largely up to you. The more you learn the more potential you have to learn.

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A good answers is the personal story of Barbara Oakley who change from Language to engineering after 20.
There is a TED talk : https://www.youtube.com/watch?v=O96fE1E-rf8 and a MOOC Learning how to learn : https://www.coursera.org/course/learning

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You can start learning to any subject at any age of your life, as long as you are interested toward the subject age doesn't matter.

The quote you mentioned here " Mathematics is young man's game".

where ; YOUNG word is not always concern with your body age, If you are looking forward to learn something your mind and brain is young always, no matter how old you are.

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Firstly, check out Ed Witten; ok, he was 22 not 26 when he switched to maths and physics, but I think it is still a reference point.

The young man's game thing is a common prejudice. I have wondered whether any truth in this is more on the lines of many people do peak early in their maths careers and given typical age profiles this means many have success ata a particular age.

I do not think this is the same thing as saying someone in their mid twenties is too old. What is necessary is the ability to immerse yourself in your subject.

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