The great thing about math research, or really research in any field, is that it's highly parallelizeable. There are a few geniuses like Terry Tao exploring specific directions of thought, but there are so many things to think about and problems to solve that even the best researchers can only focus on a very small fraction. For every genius there are hundreds of other researchers who are only, say, 10% as productive (this is maybe your typical professor at a top-20 school), but through virtue of numbers they can explore a much wider range of problems and have a large aggregate impact. Fetishizing of genius makes for fun pop-science articles but is not really reflective of how the bulk of research gets done.

Of course, even if it doesn't require genius, making serious research contributions in mathematics does typically require many thousands of hours of training and hard work (usually in the form of a PhD) which most people are not going to dedicate their lives to. Given this, I really like Bill Thurston's perspective, from the famous essay "On proof and progress in mathematics" (http://arxiv.org/abs/math/9404236), which is that proving new theorems is only a small part of the project of mathematics. The real goal is to increase humanity's mathematical understanding, which does not necessarily grow monotonically: there are plenty of results proved 100 years ago that are not known or understood by any currently living mathematician, thus have been "lost" to the mathematical community. And of course there are new people born every day who know no math as all, so understanding of mathematics will tend to decrease unless people actively work to sustain it. In this view, understanding and communicating mathematical insights is just as important and valid a part of the intellectual process as proving new theorems, and requires a different set of talents. Plenty of great researchers are not great communicators, and vice versa. (Terry Tao actually is an excellent writer, but again he's only one person and there's a ton of math out there to be shared). You may not know as much math as Terry Tao, but anyone on HN probably knows more than the vast majority of adults (the bar here is really low), and the world at this moment is certainly not suffering from a surplus of mathematical thinking. So whatever your background and abilities, there are almost certainly lots of useful ways to contribute.

We all have our intellectual strengths and weaknesses. Do not worry too much about how much smarter a man like Terence Tao is compared to you (or me).

Work hard and learn what you need to learn to do what you want to do. The rest should fall into place.

Some vanishingly small percentage of people are prolific geniuses. If you aren't, no real sense worrying about it! Just hang in there and keep learning and doing.

On a similar note, how should one feel when reading/ learning about people like this?

I mean, on one hand, it's rather inspiring to read about the amazing thing that another human is achieving. On the other hand, I can't help but feel ... helplessness, like whatever I do, it doesn't really matter (add on with the guilt of squandering my time, and wondering if I could ever have been that good).

When I was younger and have less (or no) ambitions, it was easy to brush off everytime a story like this comes up: well, they're genius, and ... so what? But interestingly, since I've learned that I might be able to do more than I thought I could, everytime I read a story like this, I just feel extremely mediocre, even pathetic of myself.

The brain is surprisingly plastic...all the way into 40s and beyond. If you have the passion, will, and the discipline to learn what you want to learn then amazing things can happen.

Five years is generally how long it takes to be noted as talented in something...so I guess patience is another virtue.

No matter how smart you are, there are always going to people somewhere smarter than you. You should not look at this as a tragedy.

In most fields, raw brainpower isn't what's needed to make an impact. Grit, determination, empathy, creativity, exploration, there are numerous attributes. Hell, even in D&D they separated intelligence and wisdom into two attributes!

Geniuses come and go, but being able to show up and execute still counts for a lot - in math as elsewhere.