Patience

 Patience. It's a word we use often but we don't quite know what it means.

In mathematics, particularly on the academia path, it's a big thing – you can't produce significant results without being patient. This goes to say that you are okay with reading a paper for 2 months, talking to people, instead of sitting in isolation in expecting yourself to do something fast and quick.

I think this is a skill that is heavily overlooked. Even the best high schoolers in math have trouble with spending longer than a day on a problem. And this is what sets apart people like Grigori Perelman and the other mathematicians who didn't make it. He spent 10 years on a single problem. He is an epitome of how a good mathematician should live his life. 

Now one might argue that it is not necessary to go into pure math and instead work in a "easier" field such as quantitative trading. You are right – it is a very good decision if you don't have a passion for thinking deep and hard. But even to solve the burning questions in quant, you need patience. The only difference between pure math and these type of fields is that pure math doesn't have much more of "fool around and do something random" whereas quant does – you can still make a living not being a very extraordinary quant guy who is actually working on the burning questions. Not to demean this choice, but just to highlight the differences.

Well, I'm still a high schooler. After talking to many other people with similar interests and that are around my age, I reached to a conclusion: one should spend their high school and undergraduate years exploring various things, from probabilistic combinatorics in math all the way to quantum information science (quant falls somewhere in the middle :P). This gives them an exposure to every subfield and allows them to make a well-informed decision at the end of their exploration. If one finds that something requires a huge amount of patience that is nearly impossible for them to bring within them, it's best not to go down that path. Many people make the mistake of singling out one particular field at a not-so-mature age because it "seems cool" and ignoring all other opportunities that come their way. Only later, they realize the qualities needed to succeed in the area and then they burn out.