Just learned Sussman (author of SICP) also authored a monograph on differential geometry
And on classical mechanics
Moreover, the former followes the concept of Turtle Geomtry and states in its Prologue the approach I admired most since my early childhood: learning things by programming them, thus forcing oneself to be precise and exact in judgements and claims. I'm recalling right now again that first "lecture" on elementary notions of set theory the summer before admission to VSU... Constructing function as a set so it becomes more "tangible" an object. The Katharsis that followed. I didn't realize back then that it's same as in programming. Five years I've been living with guilt and shame that I started as a coder and not a Mathematician. Five years I felt programming is disgusting and despisable thing to do. And only now I truly realize that the thing I loved about it in those first years is the same thing I've fallen in love with Mathematics for that summer of 2014.
Also stumbled upon a tweet mentioning the following interpretation of Laplace operator as measuring average sign of a function around the point. Sort of trivial, and resembles how we derive sufficient min/max conditions, yet I did not notice.
Majority of these I found in: JAX cookbook
Update! Accidentally found these slides by Absil giving some historical propspect on the subject
For instance, the slides mention Luenberger (1973) stating that "we'd perform line search along geodesics... if'twere feasible". Now we're closer to the roots of the whole thing