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> There are so many _symbols_ used in mathematics. It's all as if they're spells written by wizened greybeard wizards and passed down to apprentices throughout
by gspr 5y ago
> There are so many _symbols_ used in mathematics. It's all as if they're spells written by wizened greybeard wizards and passed down to apprentices throughout the centuries.
It's a misconception commonly held by non-mathematicians that the symbols are somehow the key to mathematics. I often see complaints, particularly on HN, of it being "impossible to read" research mathematics due to "all the dense symbols".
This isn't how it works. You learn the mathematics. That's hard. As you go along, you realize that some things that require a lot of words can be condensed. So you make up symbols, or, more likely, the source that you're using teaches you some commonly-agreed-upon symbols. Now, once you've learned the math at hand, the symbol isn't the issue anymore.
(Sure, it's a bit of a pain when people disagree about symbols for concepts that everyone agrees should be abbreviated, but in the big picture it's minor)
- genewitch 5y agoJapanese is easy, you just learn Japanese and the symbols that are commonly agreed upon to represent it.
- Koshkin 5y ago> That's hard.
- injb 5y agoThis isn't a good analogy, because if you have a human brain then you already understand all the concepts that Japanese is used to represent (except maybe some cultural things that are hard to translate). In contrast, the language of mathematical notation is used for expressing concepts that are utterly unfamiliar and unintuitive. As a language, mathematical notation is nowhere near the complexity of a full human language, or even a programming language. It's much simpler than that. But the concepts behind it don't come naturally and have to be studied carefully.
- samatman 5y agoWhile this is true, it doesn't help that postwar mathematics seems to have run out of useful names for things. Understanding what an algebraic group "really is" (with variations and extensions e.g. Lie groups) is more than one lifetime's work, but if you know what "group" means in English, well, you won't be disappointed. "Ring", even "field" kind of work this way. If I ever really develop an intuition for what a magma is, and I doubt it, this will not resemble the molten core of the earth. Or will it?
- deleted 5y ago[deleted]
- gspr 5y agoOne of the reasons that Japanese is hard (for a westerner) is that all the symbols used to write Japanese text are unknown. Mathematics is expressed in logic, and that logic is most often expressed in a human language that the reader knows (such as English) plus some symbols. Those symbols are usually either known, or are introduced on a supportive framework of logic, a human language, and known symbols.
- whythatis 5y agoSymbols in math come cheap. Many different books and papers use different symbology for the same idea. Is why a lot of math books have a list at the outset for agreement on what symbol would stand for what idea. On the other hand, you cannot use non-standard symbols to represent a sound in English. For example, nobody reading an English text will pronounce the letter "k" as "d" whereas mathematicians might do something like that, but they'll let you know in the opening pages of their book.