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This reminds me how I went through classes about fluid dynamics, quantum physics, & many more random things when I was in school, and I still have no idea how any of it works or even what it is really about, because 100% of the curriculum was about low-level mathematical details.https://twitter.com/fchollet/status/1055678774530822144 …
I remember quantum physics classes in particular as being about solving linear algebra exercises without understanding what any of it meant. Forgotten by the following semester
This! I still shudder at the bracket notation
Do you think that quantum physics is about something else ;) Anyway a good school for those who have to face complexity.
Do you think that perhaps, this is not a problem of mental models vs math but of mental models for math? Ie there are none really, just naked symbol manipulation, not particularly motivated or even fully derived steps & overly calculation heavy? Especially for analytic PDEs.
Maybe you should check out some quantum ML papers then. 
At least there is more context
Here's one where we cooked up a quantum algorithm that uses simulated Schrodinger dynamics instead of gradient descent to optimize DNN's/QNN's:https://arxiv.org/abs/1806.09729
As a physics student I would argue that doing the math was necessary for me to develop a good mental model. Intuition does not really work for QM. Doing the math and seing how things actually behave feels crucial. That said there should be a stronger focus on developing a model.
I had the same experience with fluid dynamics. I forgot all of it within a semester and the worst part is as you get older and know the useful application of all this knowledge, you’re self-learning many parts of it but are in a less ideal time of your life to be just learning.
I like to think of low-level math as screws and parts. Knowing how to attach a washer does not tell you how and why it works, and it is not clear when to use it. That said, if you do know how it works and what problems it solves, you are better off to build beautiful things.
Pfft come on
That reminds me of Richard Feynam view on understanding quantum mechanic(QM) I don't know if we currentrly understand more about QM, because of quantum computers and other devices using QM as core principle of working. https://www.youtube.com/watch?v=SczWCK08e9k …
Also there is a fragment the same lecture, where he talks more about difference between understanding and knowing how calculate something. He presents it on example of mayan calculations of astronomical events.https://www.youtube.com/watch?v=6TI1M3abAM8 …
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