Fields Medalist Terence Tao famously said: "There is more to mathematics than rigour and proofs".[1] Look, I love proofs. But realistically, you can't expect m

Fields Medalist Terence Tao famously said: "There is more to mathematics than rigour and proofs".[1] Look, I love proofs. But realistically, you can't expect most people to ever learn multidimensional calculus before you teach them the basic fact that a circle maximises the area: something that can be intuited by drawing polygons of increasing degree. Discovering this fact through inductive reasoning, even if mathematically unsound, is still a good teaching method (and will stick well in memory) and is not just "memorising trivia". Incidentally, working inductively is also crucially important for working mathematicians, it's just that the insights gained by doing that need to be verified (and refined) by constructing a rigorous proof; but working towards a proof when you don't even know what you want to prove yet is often difficult, it might work in an optimisation case like this, but it won't in many other areas of mathematics. Also, if you compare how other mathematics is taught in high school (and in the US, even in undergraduate university classes), it's not like there is a heavy emphasis on proof either. You're not deriving calculus from the real number axioms, you're handwaving the existence of derivatives and integral and the formulas to compute them. I'll be the first to say that knowing how this actually works behind the scenes is fascinating, but realistically, that's not what most people will need. I'm not sure why kids discovering that circles maximise the area through inductive reasoning is worse somehow than them memorising calculus rules and applying them to find the result. [1]: https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/theres-more-to-...