I will leave one little story here, as it relates to this video. If you are someone that feels like you are not smart enough to succeed, then this story is for you.
I was one of the worst students back in my middle school. I remember being the only one not able to understand stuff in math class that basically everyone understood. The teacher even pulled me aside to talk to me. Failing lots of tests, from multiple subjects… even though I studied a decent amount of time… Eventually, I realized I needed to increase my intelligence. This is different from getting good grades. This is about increasing your comprehension, creativity and brainpower. I thought that math problems, not those from school, were the path. So I started at them. I started easy, getting the easiest math olympiad problems I could find. Some are really easy, but even those took me lots of time reading the solutions to understand.
But eventually, these started to actually become understandable to me… so I started ramping up the difficulty… I spent hours and hours everyday solving these problems, and eventually reached IMO level (International Mathematical Olympiad - though I did not make it to the actual team, I was selected as one of the potential participants, but basically everyone on the team selection tests were at least bronze level). I also became one of the top students from my country, and also a National Math and Informatics Olympic medalist. I studied for free at the top school, by getting the highest markings on the scholarship competition. It took a few years of daily study, but patience is a huge monster skill to have. Your brain just takes time to build itself. You wouldn’t think of rushing a broken arm, right?
Afterwards I got scouted by a top investment bank… at their best trading desk. Got the top score on their logic test by a mile. But this is getting out of topic.
What I want to teach with this story of mine is that even if you are not too smart now, you can become a top tier intellectual being by sheer effort, unless maybe if you have a special condition. But in general, if you do this, solve lots of math problems, ramping up difficulty until you reach international level, you WILL become a supreme genius. Every one of the math champions that I met worked very hard to reach that level. All of them entered top schools, top jobs, etc.
It really is a matter of putting in the hours… I did maybe 2 or 3 hours of math solving everyday, some days on vacation from school I did 4, 6 or 10 hours… It is a lot of work, but I guess most of the great rewards come from hard, grueling work. And mind you, I was in middle/high school.
Some practical tips: get easy problems first, and try to learn one per day until you get the habit. Note that I used “learn” instead of “solve”. Focus on raising your understanding, not on immediately being a top solver. Try all your obvious ideas first, and if that does not work, than start a timer for 15 minutes. Think for 15 minutes, searching for new ideas. Then read part of the solution, and try to finish the rest. Keep doing it until you get the entire solution. Also, try to understand how you could have reached that solution. How did the guy who solved it think about such an esoteric idea? You need to ponder these kinds of things, to increase your intuition. Sketch a lot. You need pen and paper. Read how the top math champions came to be and read their tips.
Hope this helps someone, and also that I did not come off as arrogant. It is hard to talk about these experiences without causing the impression of “showing off” or something like that. But I also believe it may help someone. I for sure would have liked to read these words back in the day. Would have sped up my progress.
If you feel you do not have a future, please believe that you can have a great life. I know it seems hopeless sometimes, but our comprehension gets limited when attacked by extreme stress and sadness. Work hard, have patience, it takes a few years, but if you put in the effort on the right things, you will most probably achieve “success”. Though by then your definition of success will probably be different.