Lessons I wish I had learned before teaching differential equations [pdf] (1997)

It's worse than that. I remember that when I was doing physics aged 14/15/16, they weren't allowed to assume that we were taking the maths course that included calculus, so while you could see these repeating patterns crop up (half-thing-squared, you say? How peculiar) they were effectively prevented from taking the time to explain it properly. It would have made things so much simpler.

Nearly every educator I've ever learned from has unconsciously insisted that learning material remain sterile, and never become as funny and opinionated as this essay. For most students, "learning" is outrageously boring until you get out of college (or into graduate school) and suddenly learn through essays and memoirs that what was presented to you for 12-16 years in a bone-dry format as established gospel truth was actually the life's work of sometimes dozens if not thousands of people, each of whom fought through their own careers, formed their own views on society, joked, married, divorced, died, squabbled, sniped, and felt immense passion for the subjects they ended up distilling into textbooks for us. Much of the information we learn as students was at the time of its discovery controversial in the extreme.

A few years ago I experienced a perfect example of this phenomenon in a glassblowing museum in Sandwich, Massachusetts. The museum takes visitors through the history of glassblowing in New England, mostly by static exhibits but also with live glassblowing demonstrations. At one point in the tour I read a placard that said something like "in 17XX, John Newenglishman invented a stamped glass method that allowed for much higher production rates of glass. The already-employed glassblowers resisted this development as it meant infringement on their industry." Then I looked up at the wall and read a quote from John Newenglishman that said something like "after demonstrating my stamped glass method, I hid in my room for weeks... gangs of blower-men hunted for me, no doubt to inform me by force their displeasure with my invention." I am paraphrasing in the extreme, but I was struck by how sanitized the placard was compared to the actual words of J.N. It reminded me of the history textbooks I used to read, which removed all of the flair and human-ness from the teaching of history.

If I could change one thing about modern education, I would somehow disabuse students of the notion that the development and archival of information has ever been "regimented" or "unbiased", and take great pains to expose them fully to the tremendous wit and wisdom of the past authors whose work they pore over. Anyway, great essay, saved.

(As a somewhat related point, I have also consistently found mathematicians and engineers to be much funnier than artists and authors, with the exception of artists and authors devoted to comedy. Somehow the tragic hilarity of writing math textbooks or working in a late stage engineering company never made its way into the material I was reading about math and engineering until I was out of my aerospace engineering degree by about three years.)

I agree that some published proofs are not as clear as they're supposed to be, but I disagree that formalizing things in computer-based proof checkers is the way forward there. Computer proof checking is cool, but its an augment to what we already do and not not a substitute for it.

The purpose of a published paper is to explain things to other humans, while that of a computer formalization is to explain things to computers. Just as it is generally not easy for a computer to understand a published proof, it is usually not easy for other mathematicians to understand the code you feed to Lean or whatever.

The stuff you need to focus on to get a computer to accept your proof is usually quite different to the stuff you want to focus on when explaining things to colleagues. Roughly speaking we care about why you're doing things, while the computer cares about the intricacies of what you're doing.

I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation.

I don't know how it is in the Math department, but in Physics there is almost a sort of hazing that goes on, where some subjects are just known for how grueling they are and how you just have to go through it

"To the contrary, we are delighted when someone shows even a spark of interest or aptitude" Not to read too much into it, but this kinda hints at the problem. You're delighted at the students that have passed your IQ test. There is generally very little care given to the 70%+ of students that aren't making the cut. The true horror is how many students are in the class and not getting it. And the teachers are not freaking out

From my university experience (which was a while ago) it was abundantly clear that most students hate their math/physics classes, were bored out of their skulls and the teachers are only interested in the engaged students that are getting it.

What you should be "delighted" by is when you find a new way to explain something that resonates with most of the class

The kind of people who fix fundamentals are not bothering to become math professors.