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Comment by stepvhen | Hacker News Reader

I think math is "easier" to learn while it still holds a clear practical value, up to calculus and linear algebra. Past that, when you start to enter the world of "pure" mathematical s, it can be muh more difficult. The practical value of earlier subjects allows a student or what have you to draw connections between what they already know and this new concept. Something like group theory however is more difficult to find a "use" for, outside of solving problems in your text book.

There are some good texts out there for learning by yourself. I currently own 7 or so Dover Books on Mathematics, and I could understate my appreciation of them.

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My experience was the opposite. The more practical Mathematics was too easy to hand wave through so no one ever bothers with proof. But then when something goes wrong or you're not sure whether a particularly complicated calculation makes sense, you're SOL without a real formalism to go on.

I didn't really believe in calculus except on a case by case basis until after my first analysis course.

I think the only reason the less formal mathematics courses seem easier is because the thing being studied is also dead simple and the calculations are easy. But that approach doesn't scale.

Actually, group theory is not a very good example of a theory that has no or few practical applications; see https://en.wikipedia.org/wiki/Group_theory#Physics. In general, you would probably be surprised to learn how much of the modern mathematics (including category theory) has already made its way into theoretical physics and other sciences.

Ha, well then my class/texts have failed to mention these practical uses.

Sub-disciplines of mathematics don't blow up and become cornerstones of education if they don't have practical applications. Analysis, Topology, Algebra, Abstract Algebra, Linear Algebra, Statistics, Geometry... If something doesn't have a major practical use, it'll probably be named after somebody specific and studied in relative obscurity.

Number theory was a major field for centuries before people discovered there was a practical use for it.

Number theory has always had practical use. It used to just be called "Arithmetic", and it didn't become something else until that something else had demonstrated practicality.

The sort of number theory that mathematicians studied for centuries had no practical use until the development of cryptography and computing in the latter half of the 20th century.

That's why Hardy famously used it as his example of mathematics done with no consideration or hope of there ever being a practical application.

I'm talking about education. Mathematicians work on useless stuff all the time. They don't teach it as part of their core curriculum.

Either way, Hardy was wrong. Number theory became relevant because of the work of people who thought it could be. There was hope for a practical application, even if Hardy couldn't see it.

> latter half of the 20th century.

Nitpick - latter half of the first half.

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