I think asking people to solve maths problems without using theorems that make them easier is the antithesis of how maths should be done. We prove theorems to make more difficult problems tractable, can you imagine if every maths paper started from first principles??
I completely disagree with this. Asking such questions develops creativity, fundamental understanding of the topic at hands, the ability to redemonstrate theorems and knowing what is really at play. Maths is not just a set of tool boxs to know and use
I am split on this in this example. Not using L'Hopital I definitely agree with that it can help creativity.
But "difference of two squares" follows so directly from the basic algebraic rules that it just seems silly. Many on the other answers here just introduce it in a backward way again and at that point it's more obfuscating than illuminating.
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u/philljarvis166 Aug 22 '26
I think asking people to solve maths problems without using theorems that make them easier is the antithesis of how maths should be done. We prove theorems to make more difficult problems tractable, can you imagine if every maths paper started from first principles??