[Shosty123]

I've had a MathAcademy subscription for some time and it's quite good. I'd say it's best at generating problems and using spaced repetition to reinforce learning, but I think it falls short in explaining why something is useful or applicable. I don't know, most math education seems to be "here's an equation and this is how you solve it" and MathAcademy is undoubtedly the best at that, but I wish there were resources that were more like "here's how we discovered this, what we used to do before, why it's useful, and here's some scenarios where you'd use it."

[Nevermark]

I have so wanted such resources for years. I have found some and should make a list.

The first time the difference between understanding some math, and understanding what the math meant, was after high school Trig. The moment I started manually programming graphics from scratch, the circle as a series of dots, trigonometry transformed in my mind. I can't even say what the difference was - the math was exactly the same - but some larger area of my brain suddenly connected with all the concepts I had already learned.

While ordering the "Mathematica: A Secret World of Intuition and Curiosity" I came across these books, which looked very promising in the "learning formal math by expanding intuition" theme, so I bought them too:

Field Theory For The Non-Physicist, by Ville Hirvonen [0]

Lagrangian Mechanics For The Non-Physicist, by Ville Hirvonen [1]

The Gravity of Math: How Geometry Rules the Universe, by Steve Nadis, Shing-Tung Yau [2]

Vector: A Surprising Story of Space, Time, and Mathematical Transformation, by Robyn Arianrhod [3]

[0] https://www.amazon.com/dp/B0CN7HMTJN

[1] https://www.amazon.com/dp/B0CN7HMK38

[2] https://www.amazon.com/dp/1541604296

[3] https://www.amazon.com/dp/0226821102

Excited to read each (based on their synopses & ratings), and if I will get compounding fluency across both math and physics between all five books.

[Shosty123]

Burn Math Class follows that tradition, although it starts pretty basic, so it requires some patience.

https://a.co/d/fZnWUU8

[auxbuss]

If you're interested in how vector calculus developed, and who was instrumental, all the way from Newton/Leibnitz to Dirac or so, by way of Hamilton, Maxwell, Einstein and others, then Robyn Arianrhod's 'Vector' is brilliant.

But be warned, it gets progressively harder, along with the concepts, so unless you're conversant with tensors, at some point you will have to put on your thinking cap.

The reviews on Goodreads – including my own – are worth reading to get a flavour: https://www.goodreads.com/book/show/202104095-vector