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How does an aspiring mathematician stay motivated in researching pure mathematics?

Hi! I am a high school senior set on becoming a "pure mathematician." Ever since I learned the proof to the quadratic formula in 10th grade, I have been chasing abstract mathematics and working to improve my problem-solving skills.
Less than a year ago, I came across a very interesting problem and have yet to solve it; many of the teachers I ask for help are stumped and leave the "discovery process" to me. I have worked on the problem for about 7 months but after making no significant progress, I decided to stop. Therefore, I ask: how do I motivate myself to continue? How do I know if my problem will lead to nowhere? How much time should I be devoting to this problem?

#math #puremathematics

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Manuela’s Answer

Definitely read the book and watch the movie "The man who knew infinity". You will get a lot of inspiration.

IF you have the gene for math you will figure out in a blink of an eye if 3599 is a prime number or not by putting on an algebraic set of lens. You find the answer reading "Flash Boys" by Michael Lewis the author of "The Big Short", "MoneyBall" , "The Blind Side" and a few others. You saw the movie "The Big Short", didn't you?

You will be happy doing pure math but more fulfilled if you go on the applied side, meaning ... do something with the math.