The author teaches maths to art students. The paragraph on maths research: But now I realize that, in maths research, you don’t just follow logical steps. If

The author teaches maths to art students. The paragraph on maths research: But now I realize that, in maths research, you don’t just follow logical steps. If you do, you’ll never get anywhere interesting. You have to use your gut instinct and feel your way through something first, and then back it up with logic afterwards. Opposite to TFA, in school, I gave up on maths because explanations were not provided; you had to take things on faith (e.g. algebra of limits, epsilon-delta proofs were not given), and the questions were carefully manufactured to be solvable by the given methods. i.e. puzzle-solving, not general powerful methods. Also, no proof of the uniqueness of prime factorization. TBF, it's hard to load proofs on to school students, and since Euclid was dropped, the focus is on technicians and results - not truth. But it can be done: spend the time on building foundations; or omit subjects where you can't. I'd like an axiomatic approach.