> there is a way, in which I understand math better than in university lectures. That way is through computer programming.
Do you have examples of mathematical concepts that you developed an understanding of this way?
It is not exactly the same thing but it reminds me of a 1986 interview with David Blackwell[1] in which he went into great detail about how computers helped his own mathematical learning:
I have a little computer at home, and it's a lot of fun just to play with it. [...] Jim MacQueen was telling me about something that he had discovered. [...] He has an interesting algebraic identity. [...] Also, I had a conjecture that some stronger result was true. I checked it for some numbers selected at random and it turned out to be true for him and *not* true for what I had said. Well, that just settles it.
You may be interested in the ideas in Papert's book Mindstorms and the application of Logo to education through "microworlds". Given rules and systems to work within (or possibly to define themselves), students are given the opportunity to explore the systems and the way things interact. Most people only seem to remember Logo for its turtle graphics, which allows an exploration of geometric and (through the connection of geometry and algebra) algebraic concepts. But there were also microworlds for physics (dynaturtles) and others.
> Most people only seem to remember Logo for its turtle graphics
i got taught a tiny bit of logo in elementary school - just the very basics of moving the turtle, drawing a straight line, turning an angle, and drawing polygons.
The final challenge of the class was to draw a circle. It blew my mind when i figured it out.
I suspect that must be the inception of my love for programming.
I really wish schools would offer various ways to reach for a concept. In programming, as college students, it's not rare to understand an idea better through use of different paradigms. It seems an efficient way to tickle the brain.
After SICP Sussman wrote Structure and Interpretation of Classical Mechanics. The text is available free online, and it covers some (advanced) areas of classical mechanics by way of simulation.
Another interesting piece he wrote is The Art of the Propagator, which is also freely available. His CSAIL page has more of his publications: https://groups.csail.mit.edu/mac/users/gjs/
Do you have examples of mathematical concepts that you developed an understanding of this way?
It is not exactly the same thing but it reminds me of a 1986 interview with David Blackwell[1] in which he went into great detail about how computers helped his own mathematical learning:
[1] https://projecteuclid.org/journals/statistical-science/volum...