Question
Is it ever "too late" to significantly improve one's understanding of, and problem-solving skills in, mathematics (/physics/computer science), or a point after which it may become much more difficult?
Answer
There is good news and bad news for you. Since the question poster originally mentioned s/he was in high school, I'll try to focus at that level (you should mention that point in the question details).
The bad news first.
Yes, there are definite age effects. Pete Petrash provides a well-intentioned answer, but research does not back it up. Research by people like Dean Simonton at UC Davis shows a very clear correlation between age of peak achievement and discipline.
http://resources.emartin.net/blo...
Sure, this is correlation, not causation (you may not have encountered this idea in high school, it simply means that when two things happen together, it does not mean they are related). But there is reason to believe that there are genuine effects having to do with learning, aging, social factors and other factors that gradually diminish your ability to learn with the same efficiency. This is not absolute, but with very high probability, you will be less able to learn as you age. I find it wise not to bet against aging dynamics.
Mathematics in particular is definitely a young person's game. To the extent that physics and computer science are based on mathematics, those limits apply there as well.
The other big factor is simply getting in the famous "10,000 hours of deliberate practice" (research by K. Eric Anders showing that in most skilled disciplines, it takes about 10,000 hours of conscious practice to achieve mastery, which translates to about 10 years -- read Malcolm Gladwell's Outliers for a simple introduction to the idea). So the 10,000 hour race starts and ends early in different disciplines. In math, the best are off the blocks at a ridiculously young age. But we're talking prodigies here, not normal talent/skill levels.
All that said, here's the GOOD news. "Too late" in all these fields probably translates to about 28-30. I don't know anybody who started after that age and got good at any of these subjects. I've heard of a couple (they are like ghosts, it is always a friend of a friend who's met one of these late-starters), but the very weirdness and extreme blood-and-sweat in their stories tells you just how hard and unnatural that is.
If you're only in high-school (18 or younger), NONE of this applies. You are probably past the point of being able to achieve genius-level skills in mathematics, but there is no reason to believe you cannot get to ordinary excellence levels. Depending on the kind of physics and software you are talking about, you can get to excellent levels in those fields as well.
Time is on your side. You've got at least 10 years. More than enough time to pack in those 10,000 hours while your brain still has the ability to handle the stress.
So what can you do to reverse what seems to be a bad trend in the wrong direction?
That's the hard part. Unfortunately, the only things I can think of are:
a) Finding a really good teacher.
Someone who figures out a way to get through to you and hook your naturally most efficient learning style. Look for somebody at least 5 years older than yourself. Doesn't have to be a professional teacher or tutor. Just somebody who can get through ot you.
b) Doing it yourself.
This may be easier than you think. The key is to simply ignore school, bad teachers, tests, college applications expectations (which clearly aren't working for you) beyond a bare minimum, and learn to enjoy these subjects as hobbies. For math and physics, I'd recommend getting some of the famous books of problems (S. L. Loney for example or the books of Soviet authors like Irodov or Y. Perelman) and simply work through all of them, at whatever pace you can manage. You'll need to make sacrifices. It takes consistent practice at about 2-3 hours/day over a couple of years to get your intuition trained on these subjects. It's like a sport.
If you can do this with a friend, all the better. Ask a separate question about good books of problems if this path interests you. I am sure others will have recommendations.
For computer science, simply pick a language and start programming little projects. This is how I personally got good (but not great) at all these subjects. I had a vague idea of getting into a good school, but didn't seriously believe I could do it, so that took the pressure off. I ended up simply doing this for fun. I'd spend hours every day solving problems and programming just for fun. I kept up with my schoolwork too, but basically ignored my formal teachers. They were largely useless, as far as I was concerned. As it happens, I actually got good enough to get into that university I thought was out of my reach.
The great thing about path (b) is that even if you end up not doing well in high school or even going to college, the skill will stay with you. Unlike the humanities and social sciences, basic math, physics and programming skills hold their value whether or not you have credentials. You can simply get doors to open by building things using your knowledge.
I don't know anyone who got good at these things starting after age 30 like I said, but I do know tons of people who dropped out of college or high school but are excellent at these subjects, and making good livings off their skills. That said, I am not recommending that you drop out. Just saying that developing your real skills is a much higher priority than going through the motions and getting a piece of paper. Having skills and no pieces of paper is bad, but having pieces of paper and no skills is even worse.
The bad news first.
Yes, there are definite age effects. Pete Petrash provides a well-intentioned answer, but research does not back it up. Research by people like Dean Simonton at UC Davis shows a very clear correlation between age of peak achievement and discipline.
http://resources.emartin.net/blo...
Sure, this is correlation, not causation (you may not have encountered this idea in high school, it simply means that when two things happen together, it does not mean they are related). But there is reason to believe that there are genuine effects having to do with learning, aging, social factors and other factors that gradually diminish your ability to learn with the same efficiency. This is not absolute, but with very high probability, you will be less able to learn as you age. I find it wise not to bet against aging dynamics.
Mathematics in particular is definitely a young person's game. To the extent that physics and computer science are based on mathematics, those limits apply there as well.
The other big factor is simply getting in the famous "10,000 hours of deliberate practice" (research by K. Eric Anders showing that in most skilled disciplines, it takes about 10,000 hours of conscious practice to achieve mastery, which translates to about 10 years -- read Malcolm Gladwell's Outliers for a simple introduction to the idea). So the 10,000 hour race starts and ends early in different disciplines. In math, the best are off the blocks at a ridiculously young age. But we're talking prodigies here, not normal talent/skill levels.
All that said, here's the GOOD news. "Too late" in all these fields probably translates to about 28-30. I don't know anybody who started after that age and got good at any of these subjects. I've heard of a couple (they are like ghosts, it is always a friend of a friend who's met one of these late-starters), but the very weirdness and extreme blood-and-sweat in their stories tells you just how hard and unnatural that is.
If you're only in high-school (18 or younger), NONE of this applies. You are probably past the point of being able to achieve genius-level skills in mathematics, but there is no reason to believe you cannot get to ordinary excellence levels. Depending on the kind of physics and software you are talking about, you can get to excellent levels in those fields as well.
Time is on your side. You've got at least 10 years. More than enough time to pack in those 10,000 hours while your brain still has the ability to handle the stress.
So what can you do to reverse what seems to be a bad trend in the wrong direction?
That's the hard part. Unfortunately, the only things I can think of are:
a) Finding a really good teacher.
Someone who figures out a way to get through to you and hook your naturally most efficient learning style. Look for somebody at least 5 years older than yourself. Doesn't have to be a professional teacher or tutor. Just somebody who can get through ot you.
b) Doing it yourself.
This may be easier than you think. The key is to simply ignore school, bad teachers, tests, college applications expectations (which clearly aren't working for you) beyond a bare minimum, and learn to enjoy these subjects as hobbies. For math and physics, I'd recommend getting some of the famous books of problems (S. L. Loney for example or the books of Soviet authors like Irodov or Y. Perelman) and simply work through all of them, at whatever pace you can manage. You'll need to make sacrifices. It takes consistent practice at about 2-3 hours/day over a couple of years to get your intuition trained on these subjects. It's like a sport.
If you can do this with a friend, all the better. Ask a separate question about good books of problems if this path interests you. I am sure others will have recommendations.
For computer science, simply pick a language and start programming little projects. This is how I personally got good (but not great) at all these subjects. I had a vague idea of getting into a good school, but didn't seriously believe I could do it, so that took the pressure off. I ended up simply doing this for fun. I'd spend hours every day solving problems and programming just for fun. I kept up with my schoolwork too, but basically ignored my formal teachers. They were largely useless, as far as I was concerned. As it happens, I actually got good enough to get into that university I thought was out of my reach.
The great thing about path (b) is that even if you end up not doing well in high school or even going to college, the skill will stay with you. Unlike the humanities and social sciences, basic math, physics and programming skills hold their value whether or not you have credentials. You can simply get doors to open by building things using your knowledge.
I don't know anyone who got good at these things starting after age 30 like I said, but I do know tons of people who dropped out of college or high school but are excellent at these subjects, and making good livings off their skills. That said, I am not recommending that you drop out. Just saying that developing your real skills is a much higher priority than going through the motions and getting a piece of paper. Having skills and no pieces of paper is bad, but having pieces of paper and no skills is even worse.