> Mathematics has always operated this way, going back to + and -.
Wikipedia says[1] the earliest use of characters resembling + and - was in 14th century. From what I remember, math books were light on special notation until (at least) 18th century, and another poster here says it could be even newer (beginning of 20th century).
> and the answer is the proof which, being a mathematical proof, is in math-speak.
There are many, many proofs in Euclid's elements, and the only unusual (ie. not in plain natural language) notation used there (from what I remember and after a cursory glance now) is using clusters of capital letters to denote line segments.
Proofs are just logic, and logic was used for millenia (I think?) before someone decided that `∧` is better than "and" and we should all use it.
What I'm trying to say is that the "math-speak" is (or should be?) defined by what you're talking about, not in what syntax. And if this is true, then using more familiar syntax would be better for lowering the barrier to entry.
On the other hand, as Twisol notes, the modern terse syntax probably has its merits for experts. I'm a casual user - I won't be writing papers or checking their correctness - so I get all the bad (unfamiliar, strange symbols, context dependent syntax) without any good parts. :(
Wikipedia says[1] the earliest use of characters resembling + and - was in 14th century. From what I remember, math books were light on special notation until (at least) 18th century, and another poster here says it could be even newer (beginning of 20th century).
> and the answer is the proof which, being a mathematical proof, is in math-speak.
There are many, many proofs in Euclid's elements, and the only unusual (ie. not in plain natural language) notation used there (from what I remember and after a cursory glance now) is using clusters of capital letters to denote line segments.
Proofs are just logic, and logic was used for millenia (I think?) before someone decided that `∧` is better than "and" and we should all use it.
What I'm trying to say is that the "math-speak" is (or should be?) defined by what you're talking about, not in what syntax. And if this is true, then using more familiar syntax would be better for lowering the barrier to entry.
On the other hand, as Twisol notes, the modern terse syntax probably has its merits for experts. I'm a casual user - I won't be writing papers or checking their correctness - so I get all the bad (unfamiliar, strange symbols, context dependent syntax) without any good parts. :(
[1] https://en.wikipedia.org/wiki/Plus_and_minus_signs