2 ms·

This is a real question for anyone who might know: Have mathematicians as a whole ever thought about moving from the age-old formulas using various Greek symbol

This is a real question for anyone who might know: Have mathematicians as a whole ever thought about moving from the age-old formulas using various Greek symbols to something more akin to a programming language? What I mean is, instead of writing π to instead use "pi", or "summation()" rather than using the capital sigma? Functions like sin(), cos(), etc. already look like that, I wonder why the derivative sign and others haven't been changed. Superscript and subscript as well, and prime marks. It all seems superfluous. I guess what I'm asking is there an alternative to traditional mathematical notation that's commonly used?

dodobirdlord 7y ago
None that are widely used. What you're suggesting has no advantage over the existing approach and would significantly reduce the speed at which practitioners can read and write mathematical expressions. This is somewhat evident in your example of sin() and cos(). Even in situations like the trig functions where concepts aren't represented with special sigils (because there are too many of them and it would be silly), they are abbreviated in standard ways. sine -> sin() cosine -> cos() tangent -> tan() cotangent -> cot() secant -> sec() hyperbolic sine -> sinh() hyperbolic cotangent -> coth() etc.
BeetleB 7y ago
>What I mean is, instead of writing π to instead use "pi", or "summation()" rather than using the capital sigma? Mathematicians would like to use one symbol for one entity. Is pi the same as π or just p multiplied by i? As for summation vs Sigma? It'd take much longer to write, and probably a bigger pain to read. Having double summations is extremely common, and triple summations are fairly common as well. If you're doing mathematical manipulations/derivations with these, you'll have them on each line. The terse syntax exists for a reason - it's efficient. If you read fairly old math books (e.g. from the Arabs, or even more resent), you'll see that they were very expressive. The use of symbols for algebra was a significant advancement in math.
agumonkey 7y ago
MIT SICM book does try this. Iirc sussman (and maybe Steele), weren't happy about the syntax. Thus re-expressing Lagrangian mechanics in a scheme.
- russellbeattie 7y ago
  Nice, thanks.
antonvs 7y ago
> "summation()" rather than using the capital sigma? Why do you think that would be an improvement?

dodobirdlord 7y ago

None that are widely used. What you're suggesting has no advantage over the existing approach and would significantly reduce the speed at which practitioners can read and write mathematical expressions. This is somewhat evident in your example of sin() and cos(). Even in situations like the trig functions where concepts aren't represented with special sigils (because there are too many of them and it would be silly), they are abbreviated in standard ways. sine -> sin() cosine -> cos() tangent -> tan() cotangent -> cot() secant -> sec() hyperbolic sine -> sinh() hyperbolic cotangent -> coth() etc.

BeetleB 7y ago

>What I mean is, instead of writing π to instead use "pi", or "summation()" rather than using the capital sigma? Mathematicians would like to use one symbol for one entity. Is pi the same as π or just p multiplied by i? As for summation vs Sigma? It'd take much longer to write, and probably a bigger pain to read. Having double summations is extremely common, and triple summations are fairly common as well. If you're doing mathematical manipulations/derivations with these, you'll have them on each line. The terse syntax exists for a reason - it's efficient. If you read fairly old math books (e.g. from the Arabs, or even more resent), you'll see that they were very expressive. The use of symbols for algebra was a significant advancement in math.

agumonkey 7y ago

MIT SICM book does try this. Iirc sussman (and maybe Steele), weren't happy about the syntax. Thus re-expressing Lagrangian mechanics in a scheme.

russellbeattie 7y ago
Nice, thanks.

antonvs 7y ago

> "summation()" rather than using the capital sigma? Why do you think that would be an improvement?