Is "Axiomatic/Pure" Math really all that necessary?

[Ridge Rider]

I've been thinking recently about the way math is taught just from talking to my cousin who is in 10th grade. I sometimes think math education puts too much emphasis on getting the correct answer by the approved method on the first attempt. I don't think every stage of doing mathematics has to be perfectly rigorous.

That's one reason I like computational tools and AI. You can graph something, calculate hundreds or thousands of examples, change parameters, run simulations, and basically experiment with mathematics. Maybe you notice a pattern and think you've discovered a rule. Then you find an example where it fails. Now you have a new question: why did it work in all those other cases, and what is different about this one?

I think that's a very different experience from treating mathematics as a finished collection of definitions, axioms, formulas, and proofs that you're supposed to reproduce correctly.


This also seems closer to how mathematics connects with programming, science, engineering, modeling, and other applications.

So maybe math software can encourage a different attitude toward mathematics itself: play with ideas, experiment, make mistakes, look for patterns, ask questions, and then figure out what is really going on.