>No greater mistake can be made than to imagine that what has been written latest is always the more correct; that what is written later on is an improvement on what was written previously
I feel this way about math books a lot actually, especially calculus. When we really formalized the foundations of calculus using limits and epsilon delta arguments in proofs (instead of alternatives like Non-standard analysis see: https://en.wikipedia.org/wiki/Non-standard_analysis) I feel like a great deal of the intuition that actually built calculus was lost. I call it "differential reasoning", and I wish there was a class in just such a thing, formalized with operator theory and non-standard analysis techniques. It's still used a lot in physics but no one talks about the concept of a "ratio of differentials" in modern calculus.
Yeah, a book recommendation would be great! I’ve picked up this way of thinking over the last decade, but don’t know of a resource to recommend people.
I feel this way about math books a lot actually, especially calculus. When we really formalized the foundations of calculus using limits and epsilon delta arguments in proofs (instead of alternatives like Non-standard analysis see: https://en.wikipedia.org/wiki/Non-standard_analysis) I feel like a great deal of the intuition that actually built calculus was lost. I call it "differential reasoning", and I wish there was a class in just such a thing, formalized with operator theory and non-standard analysis techniques. It's still used a lot in physics but no one talks about the concept of a "ratio of differentials" in modern calculus.