So I just learned about Mathematical Induction (one of the four fundamental proof techniques in math) for the fifth time (fourth in college) today and I’m kinda frustrated - and I wanna take you through my thought process 1/12

So, my first thought was “why are we talking about this in my upper level maths class?” Then “how is it possible that you (two students in the class of 8) hadn’t learned this?” “This should be prerequisite knowledge for this course” 2/12

The answer is actually pretty simple and it has to do with an education ideology that starts with the Renaissance ideology of (Liberal Civic) Humanism (happy to quibble over the name) - essentially, students should have some control of their course of study 3/12

Not the curriculum of the classes they take, but what classes they take when - this is good - learners control their learning and it can foster diversity of though (a fuller explanation for why it’s good would be too lengthy a tangent for this thread) 4/12

However, there are some downsides, particularly with prerequisite requirements - which is why I’ve “learned” (been lectured on) induction FIVE FUCKING TIMES - but I don’t think this is an issue with our education ideology, I think it’s an issue with our mathematics curricula 5/12

The vast majority of the maths curricula I’ve taken have been structured around a lecture which goes through the proofs of the field in order of entailment (i.e. you use the first theorem to prove the second, second the third, etc) - this SUUUCKS 6/12

If I wanted a list of the proofs of a field in order of entailment, just give me a book rather than have me dictate it into my notebook over the course of 10-15 weeks - but here’s the thing I DON’T WANT THAT BOOK! It’s boring and unhelpful 7/12

Most proofs are boring - there’s a very small number that are really interesting and worth spending time on - classic familiar example is the Fundamental Theorem of Calculus, every six months I start thinking about it, am totally befuddled, so I write a proof of it 8/

Instead of spending a week going through fifteen nameless proofs, let’s spend a week talking about the one named theorem you’d mention 9/12

Cause here’s the thing they’re named because they’re interesting and they’re interesting because they have some fancy technique or incredible result - let’s talk about those! 10/12

And it’s much more useful for me walking out of school to say “I know like 15 different proof techniques and 15 interesting results” rather than “I have 15 notebooks that lay out 15 sub fields (which the textbooks I bought already did)” 11/ 12

Some will say that you get a knowledge of those techniques and results FROM copying those textbooks into your notes - and I say, “yeah, maybe, but I bet there’s a faster, more direct, better way” 12/12