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This list sounds like new programmers complaining about the difficulty of language syntax - which largely vanish once you know enough that it melts into the bac

This list sounds like new programmers complaining about the difficulty of language syntax - which largely vanish once you know enough that it melts into the background and poses no significant cognitive burden. They are valid observations, but they miss the point that (generally speaking) mathematics is about communicating ideas to other people who speak the language. Most high level mathematics involves both a great deal of implicit knowledge, and potentially introduces completely new ideas that may not be easily expressed with existing terminology.

wfo 11y ago
Yes. In general the mathematics that people bother to talk about is much, much more complicated than most programs. There is more complexity in a few words of mathematics than most programs that exist; mathematicians are drawing on thousands of years of constant labor and forward progress from the brightest people in human history with every word or symbol they write. Plus, they feel free to invent new notation to capture the creative ideas they require it for at will. If your idea isn't new enough to require new notation, it's not really difficult/creative enough to be worth writing a paper about. Mathematics is written to express ideas for other humans to read, not for machines to execute correctly to accomplish a task. You will find algorithms written in mathematics (to prove a certain fact, sometimes we exhibit a procedure that is guaranteed to accomplish it) and they are generally clear and easy to read with simple syntax, etc -- the actual mathematics is in the proof that the algorithm is correct, or always terminates.
rdlecler1 11y ago
That's sort of the point. We will come up with a new language when the old is no longer sufficient for the problem at hand. It's as if math is stuck using punch cards. I found thinking in terms of Mathematica and MatLab helped me think about math syntax as it is more complete.
- cgearhart 11y ago
  The syntax of any programming language is easier to grok because it is more concrete - not because it is more complete. It is not so much that "math is stuck using punch cards", but rather that you only really need as much formality as it takes to express the central idea - which is far short of what would be required for a concrete implementation.

wfo 11y ago

Yes. In general the mathematics that people bother to talk about is much, much more complicated than most programs. There is more complexity in a few words of mathematics than most programs that exist; mathematicians are drawing on thousands of years of constant labor and forward progress from the brightest people in human history with every word or symbol they write. Plus, they feel free to invent new notation to capture the creative ideas they require it for at will. If your idea isn't new enough to require new notation, it's not really difficult/creative enough to be worth writing a paper about. Mathematics is written to express ideas for other humans to read, not for machines to execute correctly to accomplish a task. You will find algorithms written in mathematics (to prove a certain fact, sometimes we exhibit a procedure that is guaranteed to accomplish it) and they are generally clear and easy to read with simple syntax, etc -- the actual mathematics is in the proof that the algorithm is correct, or always terminates.

rdlecler1 11y ago

That's sort of the point. We will come up with a new language when the old is no longer sufficient for the problem at hand. It's as if math is stuck using punch cards. I found thinking in terms of Mathematica and MatLab helped me think about math syntax as it is more complete.

cgearhart 11y ago
The syntax of any programming language is easier to grok because it is more concrete - not because it is more complete. It is not so much that "math is stuck using punch cards", but rather that you only really need as much formality as it takes to express the central idea - which is far short of what would be required for a concrete implementation.