The math does not have to self-referential to use complex expressions not amenable to writing in English. >Also you've picked a specific example where the objects of study are these long strings of symbolsĪvoiding the point. It's not true for everyone, especially professionals, that use some set of notation a lot. 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. In math they have well defined precedence, and math has parentheses to order correctly, unlike English. "Or" in English both can mean "inclusive or" or "exclusive or," yet most people simple write "or". The word "and" and "or" are ambiguous in common English, and have no common or even technical well-defined precedence. >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. 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. The simple English sentence case is a tiny part of what mathematicians do. As written it's concise and parseable without confusion for a logician. Convert to English (near impossible, certainly not possible without something like parentheses) and tell me it's easier for a logician to read. Without precise quantifiers you'd quickly get lost, make mistakes, and take forever to get anywhere.įor example, look at page 17 of the proof, at AG(6)(a) (after the "Thus"), where there is a long statement in logic.
Try converting something professional, such as Godel's incompleteness proofs, into English. English is far too sloppy, whereas the quantifier version is mathematically precise. But going the other way, expressing complex items in English, is a non-starter. Sure you can take simple English statements, and write them with quantifiers, and claim the English is simpler. I also find them much easier, faster, and more accurate to read, because it's from practice. Maybe you're not used to reading quantifiers.
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