[ChrisLomont]

As a math PhD I disagree. I can read math notation far faster and more accurately than ambiguous English. We don’t translate symbols. If anything, when reading English we have to translate into symbols.

For example, reading 5-7, I don’t have to translate the - symbol to the word “subtract”. I know this is -2. And I don’t translate the - in that to the word “negative,” and certainly not to the word “subtract”. And it’s vastly faster to agree 5-7=-2 is correct than “5 subtract 7 equals negative 2.”

Symbols are how mathematicians think.

[Smaug123]

I think you've got the same misconception as quietbritishjim above. Start stacking quantifiers, and the symbols get hairy much faster than the English does.

[ChrisLomont]

Maybe you're not used to reading quantifiers. I also find them much easier, faster, and more accurate to read, because it's from practice.

Sure you can take simple English statements, and write them with quantifiers, and claim the English is simpler. But going the other way, expressing complex items in English, is a non-starter. English is far too sloppy, whereas the quantifier version is mathematically precise.

Try converting something professional, such as Godel's incompleteness proofs, into English. Without precise quantifiers you'd quickly get lost, make mistakes, and take forever to get anywhere.

For example, look at page 17 of the proof [1], at AG(6)(a) (after the "Thus"), where there is a long statement in logic. Convert to English (near impossible, certainly not possible without something like parentheses) and tell me it's easier for a logician to read. It's not. As written it's concise and parseable without confusion for a logician.

The simple English sentence case is a tiny part of what mathematicians do.

[1] https://web.yonsei.ac.kr/bkim/goedel.pdf

[Smaug123]

Look, do you really want me to wade through sixteen pages to discover the notation first (written by someone who doesn't know about \langle and \rangle, either)? I would consider it bad argumentative form of the same water as Euler's apocryphal "does God exist" debate with Diderot.

At the very least, you will struggle to persuade me that the use of \wedge is easier to understand than the English word "and" with line breaks.

Also you've picked a specific example where the objects of study are these long strings of symbols. Of course any paper worth its salt is going to use them - they're literally the things that the paper is there to examine. It's the metamathematical statements in this context, not the quotation of the formulas under study, that I want to replace with English.

[ChrisLomont]

>do you really want me to wade ....

No - just pointing out that no matter how hard you studied that an English equivalent of such a terse expression will be a mess, vastly harder to understand.

>At the very least, you will struggle to persuade me that the use of \wedge is easier to understand than the English word "and" with line breaks.

You're making my case for me :)

The word "and" and "or" are ambiguous in common English, and have no common or even technical well-defined precedence. "Or" in English both can mean "inclusive or" or "exclusive or," yet most people simple write "or".

In math they have well defined precedence, and math has parentheses to order correctly, unlike English.

The only reason you find English easier to understand is you have used more than math symbols at a ratio that makes that true for you. It's not true for everyone, especially professionals, that use some set of notation a lot.

>Also you've picked a specific example where the objects of study are these long strings of symbols

Avoiding the point. The math does not have to self-referential to use complex expressions not amenable to writing in English. This expression is not complex because it's a meta argument. Such expressions can occur in all sorts of places.

At this point I'm sure your present these red herrings to avoid considering that your opinion is not common among professionals that can read symbols much faster and more accurately than can be done in English.

No sense in continuing.

[Smaug123]

> No sense in continuing.

On this we agree, at least!