Most of the time as a student, we are exposed to timed problem-solving. Exams and homework are nice examples of this. Therefore, it is perhaps natural for us to rather focus on the ‘solving quickly’ part, rather than the ‘thinking for a long time’ part.

Since exams and homework are usually assigned with a due, many of us (including myself) usually forget about the thing and move onto the next homework or so, which are again due at some future point. This cycle continues.

Although regular homework and exams may contribute to enhancing the techniques of the student, but it may potentially have little effect on the robust thinking.

It was a pleasure for me to have the opportunity to meet many great mathematicians during my undergraduate course in KAIST. Particularly memorable bright mind includes Ji-Oon Lee, a mathematics professor working on fields of Physical Mathematics and Stochastic Theory.

I wanted to share a story of him-actually a conversation we had in 2020- about problem solving. I was a curious sophomore and asked him some questions on the attitude we should embody when dealing with maths.

Without any hesitation, he replied: Consistent thinking.

From here, i would share the (which relies on my poor memory) the direct quotes. J stands for prof Ji-Oon and H for me.

H: why are you so good at maths? Sometimes you scare the class out of us.

J: You should think about the problem carefully.

H: Carefully… a bit ambiguous, open-statement.. could you explain further?

J: You have to admit maths is not so nice as you have seen in High school. Everything is ‘under the rug’ or ‘handwave proven’ during high school. They just blind you with most details. Exams- the answers themselves are so nice, aren’t they? They are (mostly) integer answers. This makes the student think maths is just some holy subject which admits such concise solutions.

H: this is what i thought. Proofs are more important you mean?

J: Well, both. You should now get used to the environment of claiming some intuitive assertion of yours, and check that is indeed true with a proof. And this process take usually very, very long.