I no longer understand my PhD dissertation

> I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition.

If it only happened on mathematical papers... It is all over the place, in books, classes, etc. Few professors tell you what are they doing and why; they just throw formulas, theorems and symbols at you. Intuition is not given its necessary importance, first because it's hard to grasp some concepts, and second because sometimes there's no easy intution behind them unless you have deeper knowledge in the subject.

Regarding "unit tests", or descriptive names... That's very difficult once you get into advanced math. Examples are probably going to be trivial or too contrived to be useful. And if you have to give a name to a theorem or lemma, you'll end up describing its full contents.

I can relate to this. My major was EE and I had similar experiences, but kind of liked diffeq. Fast forward some 25+ years later, I spend all day coding and look to my old math and some new comp sci books for fun. I keep an engineering notepad with different sections in it so I can just open it up and attack problems such as concrete math problems from graham knuth and patashnik or physics problems. Even though I code through business problems on a daily basis using X framework and Y API, I find the rigor involved is not as satisfying as struggling through finding the closed form of some equation. I want to solve a deeper problem, if that makes any sense.

It isn't the answer that I seek in doing this; it's the desire to know why the answer is what it is. I think I have become more interested in learning far after graduating from university.

> never mind five years!

Some bits of the DMD compiler back end go back 32, 33 years!

From my experience of both academia and life in general, I'd say traditional tertiary education -- meaning lectures and research work from undergraduate upwards in a university setting -- is actually quite a poor way to learn anything.

I'd say the ideal way to develop knowledge, understanding and skill in almost any field is a combination of systematic practice and receiving personalised guidance and training from someone who thoroughly understands the field itself to at least the level you are trying to reach and is able to share that understanding effectively based on your current level of understanding.

Sadly, this is usually hopelessly unrealistic, because there are nowhere near enough suitable trainers around to give everyone close to 1:1 training in that format. But the further we drift from it, the more impersonal and generic training becomes, the more isolated individual practice becomes, the less immediate and detailed feedback becomes, the less effective the training regime as a whole will be.

Given that neither undergraduate-style mass lectures nor postgraduate-style research are particularly efficient at conveying useful information, guiding practice, or promoting rapid and actionable feedback, I personally don't rate either particularly highly on an idealised scale. Perhaps a more practically useful question would be whether there are ways to improve university-level training that are realistic given the time and money constraints and, beyond a certain point, the lack of many if any people who actually are more knowledgeable or skillful in increasingly specialised fields than the research student who is dedicated to exploring them.