We write = as "equals", + as "plus", $\exists$ as "thereExists" and so on. Supplemented with some brackets everything will be precise:

$$\exists x,y,z,n \in \mathbb{N}: n>2 \land x^n+y^n=z^n$$

instead of writing:

ThereExists x,y,z,n from theNaturalNumbers suchThat 
     n isGreaterThan 2 and x toThePower n plus y toThePower n equals z toThePower n

What is the reason that we don't write all words as symbols (almost like a Chinese word system?)

Is it for redundancy? Clarity? Can our visual system process it better?

Because not only do we have to write the words, in order to understand them, we have to guess the real meaning of them.

If algebra and logic had been invented in Japan or China, might the words actually have just been the symbols themselves?

It almost seems like for each word there should be an equivalent symbol-phrase that it corresponds to that is accepted.

This question seems pretty close to why aren't symbols written in words, but there's still the question why don't we write everything in symbols, and leave natural languages behind?

  • $\begingroup$ @LordSharktheUnknown: he asks why is not all words. I ask why is not all symbols (symbols are great, aren't they?). The unanswered (sub-)question is why do we have this balance between symbols and words? $\endgroup$ Commented Jun 30, 2019 at 11:47
  • $\begingroup$ There has been books that were almost completely written with symbols, they were really hard to read and understand. Try doing it yourself and see how far you get, it isnt pleasent. $\endgroup$
    – jimjim
    Commented Jun 30, 2019 at 11:53
  • $\begingroup$ @Arjang: maybe they were difficult because people are not educated (yet) in reading all symbols math. $\endgroup$ Commented Jun 30, 2019 at 11:55
  • $\begingroup$ Yes I guess that must be it. $\endgroup$
    – jimjim
    Commented Jun 30, 2019 at 12:02

1 Answer 1


Neither clarity nor ambiguity or redundancy. Its just for brevity, frugality and scarceness.


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