Comment by umvi
8 hours ago
No, the problem with mathematics is that it is basically its own language separate from your native tongue. You have to learn dozens of symbols and greek letters and such and memorize what their meaning is in the context of mathematics in order to "follow" a mathematical conversation.
Mathematics would be much more approachable if it just used plain English like `sum(0, Infinity, my_func)` instead of a big Greek sigma with nested function nomenclature. But on the flip side, mathematics being its own language means that a mathematician from any country can read and understand mathematics from a different country without needing to translate words such as "sum" and "infinity"
Mathematics would be much more approachable if it just used plain English like `sum(0, Infinity, my_func)` instead of a big Greek sigma with nested function nomenclature
First of all, no, mathematics would be far less approachable if it did that. Most of the Greek letters used in mathematics don't have a universal meaning, they're context-specific and defined by convention or just prior to use.
Second of all, mathematics is optimized for hand calculation on paper, not long-term programming and code maintenance. Writing out long names over and over on a whiteboard gets tiring extremely quickly, so mathematicians prefer to stick to single-letter symbols.
To second this, most (non-applied) mathematicians work first with paper and pencil or on a chalkboard, and the act of writing out the symbols is a part of thinking about them. Typing doesn't wire into the brain in the same way. Think of how you learned algebra in school. You wrote out much of what you were thinking, often in ways that would be hard to flexibly format on a computer, and the act of writing your thoughts solidified them in your memory.
Mathematicians pretty much universally view typesetting as a distinct step from the thinking part of math, and something you do at the end once you have figured everything out.
Your translation only makes intuitive sense to you because you are well versed in programming.
I suspect if I showed a non-technical person with no background in either math or programming they would think both are nonsense until you explained it to them
> I suspect if I showed a non-technical person with no background in either math or programming they would think both are nonsense until you explained it to them
I doubt it. Greek letters convey almost no information, whereas (one hopes) the function and variable names are chosen by a programmer to help the reader. The Greek letters used by mathematicians (and physicists) weren't used to convey information, they were used because typesetting, publishing and paper were expensive. They are optimised for brevity over readability.
It was a perfectly reasonable trade-off at the time, but times have changed.
As an aside, some programming languages (such as APL, and to a lesser extent Perl) did emulate the old Greek letter style. "Line noise" is a typical description of the result. No computer language aimed at software engineers and computer scientists does that now.
The thing is that you basically cannot explain the math like you can the programming.
Tables, algos, and variables are all things people can generally quickly grasp. The construction is abstract but the function is tangible.
The math is working entirely on abstract objects, using abstract tools, governed by abstract rules. It's just all so desperately far away from anything even technical people have contact with.
My example was contrived, I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax. At a certain point though, your layman has to know the "atomic" (as in, you can't break them down further) mathematical concepts like "functions" and "infinity":
`sum function(x) from x=0 to x=infinity`
I am a research mathematician. In my field (abstract algebra, computational group theory), a sum or some such notation is like the most trivial of trivial things in terms of notation. There are a few things like sums that could in theory be made to "look more like what a computer programmer would expect", but that'd be just a tiny corner of it.
And if you think about how summation would look in Lisp or APL (which some smart people use to this day), I am not even convinced your argument for the "sum function" notation being superior holds in general.
I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax.
And somehow, none of the thousands of very smart mathematicians have done that, or if they had, it has not seen wide adoption. I recommend contemplating on this: if math could be made easier by changing notation, why hasn't this already happened?
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Capital sigma doesn't always mean sum and certainly lowercase sigma never means sum.
If mathematics used plain language, the ability to meaningfully manipulate and understand would go way down. Proofs would become massively tedius.
Of course, notation is hard. Any good mathematician should put a lot of work into it.