How to become more creative in problem solving?

Question

I am 16 years old and I am doing everything to improve in mathematics and one day try to do something important as I want to become a mathematician. Many say that the fundamental character for being a top mathematician is being creative and having divergent thinking but these are characteristics that do not reflect me. How can I be more creative in math, is there any way to improve this? Do you have any books to recommend or even advice?

Answer 1

(1) At age 16 you can not yet truly know what are the characteristics that reflect who you are. Even if you somehow have the wisdom to know, you can work at changing those (at any stage of your life).

(2) Creativity has somehow taken the meaning of a trait that allows you to come up with fresh original ideas in the moment, and at any time. However, people that are termed creative geniuses often for each piece of art or science have hundreds or thousands of hours of work that the public never gets to see.

The best selling music album of all time, Michael Jackson's Thriller, has 9 songs on it. However, in the process of writing the album, 30 songs were written and hundreds of ideas were explored. No one except Michael Jackson, his collaborators for Thriller and the few very very hard-core fans heard all other 21 songs. Not to mention that by the time recording for Thriller started, Michael Jackson, at that time aged 24, was already doing music for 20 years.

Prince (the musician) published 39 albums over the course of his career. However he meticulously recorded probably every bit of music that he thought of. In his home there is a vault that contains enough material for at least 10 unreleased albums, 50 unreleased music videos and at least 1 documentary directed by Kevin Smith. Why that material was not released, nobody truly knows, but it stands to reason that it wasn't up to Prince's own standards for artistry.

Going back to mathematics, it took Andrew Wiles some 8 years to prove Fermat's Last Theorem. But he was thinking about it for at least 20 years before attempting the proof. He was also a very successful mathematician before he attempted to prove Fermat's Last Theorem, with tens of thousands of hours of experience in his craft.

(3) To summarize, you get better at mathematics by doing mathematics. This is true for all human endeavors. However, search for proper guidance. You should read books suggested in the comments, but books alone will not make you into a top mathematician, they won't even make you into a mediocre one. The most important thing to do beside practicing is to talk about mathematics with other people. If you don't know any, websites like this one can be a temporary substitute before you start university studies in mathematics.

Answer 2

You just need to become creative in anything. For example, fishing. Learn to be a creative fisherman. It will help eventually. Alternatively, you can become a creative sportsman. Ping-pong and tennis are good for this. (American football and rugby are not that good because these can cause head injury, and the head is important when doing mathematics.)