And I suppose you are implying a lot of math is illogical. :-)
> Heck, coding CRUD apps
Yeah, I hear the "bad notation" argument frequently from programmers, precisely for the reasons you describe: because you can't read a mathematical textbook with a programmer's IDE.
Some mathematical texts will do you the favour of having a list of some notation that they consider to be idiosyncratic to their own text, but few would go as far as to letting you look up the definition of plus and minus. In general, though, mathematics isn't programming, despite some similarities and analogies between the two. The symbol for the partial derivative is used nearly universally to mean partial derivatives of some kind, so there's a lot of tradition that writers of mathematical texts expect you to know.
Programming has similar traditions that are baffling to outsiders but as invisible to the programmers as water is to fish. For example, in programming it is understood that everyone is capable of easily handling plain text files. Have you ever seen a newcomer try to write source code in Microsoft Word? I have.
Wikipedia and other online mathematical texts can help a little by hyperlinking the text to explain new notation or terminology, and sometimes texts are just plain bad in that they use idiosyncratic notation without explanation. In the last case, it takes effort to work out from context the likely meaning of a symbol.
In general, though, I stand by my thesis that notation is not the biggest obstacle to mathematics just like learning to use a text editor or IDE is not the biggest obstacle to programming. The fundamental ideas behind the practices of each are much deeper than the superficial aspects of text and notation.
> Normally going from no calculus to the multivariable chain rule as applied to differentials or as a best linear approximation takes at least three semesters in university.
Multivariable chain rule is much simpler than the 18 months learning curve would imply. It boils down to figuring out what a function is, what a derivative is, what the chain rule is and generalizing to multiple dimensions. We could probably teach it to a sufficiently logically apt high-schooler within a week, provided we could find a sufficiently motivating use-case.
The lack of compelling use-cases being the other major obstacle in learning math. Why bother rote memorizing tens of concepts and hundreds of factoids, when a lot of math texts pride themselves of building the perfect theory in abstract, decoupled from the original motivations.
I personally don't find a lot of motivation to learn calculus because engineers in the 19th century needed to figure out how to make better steam engines or cannons or because physicists wanted to understand electromagnetism. My own motivation was: okay, neat, derivatives. This says a lot about a function! What happens now if we try to do this with more variables? Oh, wow, look, the chain rule gets all weird now and grows additions it didn't have before!
For other people, I guess you need to find a different motivation. Maybe neural networks will do it for some. I must admit that I picked up a neural networks text in 1995 because I wanted to build robots, didn't understand a word of it, and ten years later I got a degree in mathematics having long ago forgotten about the neural networks book which I only recently picked up again. But regardless, ever since I was a little kid, mathematics is just something that naturally attracted me.
We should not minimise the intrinsic interest of the subject itself either. There is an artistic side to mathematics, where we do it because it's beautiful for its own sake. Not all mathematics needs a purely practical reason to justify its study.
> Multivariable chain rule is much simpler than the 18 months learning curve would imply. .... We could probably teach it to a sufficiently logically apt high-schooler within a week, provided we could find a sufficiently motivating use-case.
Supposing this were the case, given that there's no shortage of homeschooling and "alternative" high schools out there, can you find a case where this has actually happened.
And I suppose you are implying a lot of math is illogical. :-)
> Heck, coding CRUD apps
Yeah, I hear the "bad notation" argument frequently from programmers, precisely for the reasons you describe: because you can't read a mathematical textbook with a programmer's IDE.
Some mathematical texts will do you the favour of having a list of some notation that they consider to be idiosyncratic to their own text, but few would go as far as to letting you look up the definition of plus and minus. In general, though, mathematics isn't programming, despite some similarities and analogies between the two. The symbol for the partial derivative is used nearly universally to mean partial derivatives of some kind, so there's a lot of tradition that writers of mathematical texts expect you to know.
Programming has similar traditions that are baffling to outsiders but as invisible to the programmers as water is to fish. For example, in programming it is understood that everyone is capable of easily handling plain text files. Have you ever seen a newcomer try to write source code in Microsoft Word? I have.
Wikipedia and other online mathematical texts can help a little by hyperlinking the text to explain new notation or terminology, and sometimes texts are just plain bad in that they use idiosyncratic notation without explanation. In the last case, it takes effort to work out from context the likely meaning of a symbol.
In general, though, I stand by my thesis that notation is not the biggest obstacle to mathematics just like learning to use a text editor or IDE is not the biggest obstacle to programming. The fundamental ideas behind the practices of each are much deeper than the superficial aspects of text and notation.