If this is so obviously preferable, why have mathematicians so obdurately not adopted this style?
Mathematical notation is not an archaic practice that is followed out of a respect for tradition, or a doctrine that has been developed from first principles, it is something that has evolved (and continues to do so) because it has been useful.
We do have f(x, y) in mathematics notation, as well as notations like { a, b, c }, ( 1, 2 ). The inventor of vector and matrix notation finally had the brilliant idea of dropping the silly commas [ i j k ]. Think of how ugly matrices would look with commas.
Now in mathematics, there is no equivalent of a 200,000 line piece of software. The number of identifiers a mathematician works with in any given work is small, even if the work is large (many pages of derivation).
Mathematics notation is ambiguous and inconsistent. One letter names are preferred so that xy can denote the product of x * y. So much so that mathematicians reach for other scripts like Greek rather than make a multi-letter name. Then, inconsistently, we have things like sin(x).
Consider that xy(z + w) is likely interpreted as the product of x, y and z + w. It has the same syntax as ln(z + w), the natural logarithm of z + w, not the product of l and n.
Professionally printed mathematics resorts to the use of special fonts to visually resolve these things. This problem is so serious that everyone who is anyone in mathematics goes to the trouble of professional typesetting, even in minor papers.
In software, the program-defined functions form vast vocabularies. They cannot all be assigned to infix operators without creating mayhem. Many functions have 3 arguments. Seven argument functions are not uncommon. Those also cannot be infix.
In spite of what the author may say, real Python code is chock full of "import foo" and "foo.bar.baz(this.or.that(), other.thing())".
Calling people’s use of LaTeX to type their homework “professional typesetting” seems like a stretch. Professional typesetting would be something like: send your hand-written manuscript to a full-time typesetter, and wait for them to do the work.
A better description would be “goes to the trouble of using math typesetting software designed by experts”. But is this really so strange? People use even more sophisticated software than that for making image collages of cats with mustaches, for modeling platonic solids, for adding their favorite song to a frivolous home movie, ....
Well mathematics notation largely follows speech. People say “one plus two” — largely because speech doesn’t have closing parentheses, so we need to speak in a way that makes it clear when we’re done talking — so that’s how we write it. But for a computer, prefix notation is great because it’s unambiguous and clear even without knowledge of PEMDAS. Similar to how Americans write MM/DD/YYYY because that’s how we say dates, but we can still acknowledge that YYYY-MM-DD is the best format for computers.
I wonder how much is the reverse: we now tend to say mathematical expressions as they are written, but before this was standardised, you would just explain the steps.
Probably not "one plus two" -- I think + is essentially a variant of & which is a ligature for "et", and I guess most languages put "and" between the things being combined. But I'd be surprised if (x/y)^2 was said "x over y all squared" by many people before this notation. But the notation is clearly more designed for thinking on paper than for explaining down a phone line.
1. Mathematicians have different priorities than programmers, and they use different tools. Working with an equation on a whiteboard, it's easier to write "a+b+c" and then cancel terms as needed. When writing a formula on my computer, cancelling terms is something I almost never do, so it would be silly to use a notation that's been optimized for that.
When I am doing algebra on my computer, I hope I have a tool like Graphing Calculator (not "Grapher"!) that lets me simply drag a term from here to there, and automatically figures out what needs to happen to keep the equation balanced.
2. They have, except they use Σ for the prefix version. When it's more than a couple terms, and there's a pattern to it, Σ (prefix notation) is far more convenient than + (infix notation).
If programming languages look like they do because they're taking the useful notations from mathematics, why doesn't your favorite programming language have a Σ function? Who's being stubborn here?
Most programming languages do have some variant of `sum(seqence)`. Python certainly does. Or, like, loops, which do the same thing.
But they're optimized for different things. Using the same tool for infinite length sequences and fixed length sequences doesn't make a whole lot of sense. We often have different types for them (tuple/record vs. list/array) too.
Having done addition in both infix and prefix varieties on my computer, over the past few decades, I don't understand why prefix notation is considered 'optimized' for indefinite (not 'infinite') sequences and infix notation is considered optimized for definite length sequences.
What exactly "doesn't make a whole lot of sense" about (+ a b)? (It doesn't look the same as you wrote it in school? Neither does "3+4j", or "math.sqrt".)
Being able to use the same tool for different types of data is precisely what makes high-level programming so powerful. As Alan Perlis said, "It is better to have 100 functions operate on one data structure than 10 functions on 10 data structures." Having only one way to add numbers (in languages that do that) is a great feature.
Python's insistence on these pre-selected groupings of functionality has always made it frustrating for me to work with. The two ways to add numbers look and work nothing alike. Does "TOOWTDI" not apply to math?
(Yes, I'm also frustrated and confused that Python has built-in complex numbers, and a standard 'math' module with trigonometric functions, but math.cos(3+4j) is a TypeError. What possible benefit is there of having a full set of complex-compatible functionality, but hiding it in a different math module, with all the same method names?)
The zen never says TOOWTDO, it says TO(APOO)OWTDI. (That's "there's one, and preferably only one, obvious way to do it.)
`reduce(op.add, [x, y])` works. Python could remove it's infix ops and use only prefix ones. But prefix ones aren't obvious. And as Guido says, readability matters.
This really isn't a good argument it just looks like one on the surface. In fact while computer science is a branch of math its pretty clear that most applied software development has substantial differences from theoretical math.
Further there is no reason to suppose that any group of humans act optimally in this area when they clearly act on the whole so illogically and sub optimally in every other area of human endeavor.
It asks respondents to prove the much more complex question of why different groups may prefer a particular notation instead of taking the much more simple and direct route of explaining why the poster prefers a particular notation.
Mathematics uses infix notation literally everywhere. Just because you prefer some notation doesn't mean people who have used infix notation since they were 5 years old will like it. Also, I avoid lisp mostly because S-expressions are almost unreadable to me.
Mathematics uses prefix, infix, suffix, circumfix, and some more complex notations; basically any pattern any computer language uses probably is inspired from math even if math doesn't use the notation for the same operation or operator symbol.
Mathematical notation is not an archaic practice that is followed out of a respect for tradition, or a doctrine that has been developed from first principles, it is something that has evolved (and continues to do so) because it has been useful.