# Is there a standard way to write mathematics in words?

Asked by

PhiNotPi (

12677)
March 4th, 2012

This question is inspired by an earlier question regarding the meaning of “two times less than 16,” a meaningless statement. That made me think “is there a standard, *unambiguous* way to describe mathematics in words?”

What are some rules that you believe to be in a guide to how to write out math?

Part of the problem is how to denote parentheses without using unpronounceable punctuation or saying thinks like “opening parenthesis”. For example, how should 2/(x-1) be said?

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## 8 Answers

I don’t think that there *is* a standard way, but maybe there *could be* one. For your example, I would suggest “Two divided by x-minus-1” (the hyphens indicating that “x-minus-one” is a combined term just as the parenthesis would). I’m not sure this could be extended to all examples, however, which perhaps is one reason we have the formal syntax in the first place.

One question is whether we need it to be unambiguous without the knowledge that what is being described is a mathematical problem. This is analogous to an issue in logic: it’s one thing to have a standard way of translating logical sentences such that it is clear what they mean *if you already know you are looking at a sentence of logic*; it’s quite another thing to come up with translations that fit into a natural language as logical sentences *without indicating that this is what you are doing*.

For your example at the end I suppose I could say, “two divided by the difference of ‘X’ minus one” (but *someone* in the world will interpret that wrong; I just know it).

But I think mathematical notation is acceptable English usage, and is preferable to using words.

@HungryGuy Part of my reason is not just to be able to write it, but to speak it also.

@PhiNotPi – Then I would still go with, “two divided by the difference of ‘X’ minus one” as a way of speaking it. Likewise, “energy is the product of mass times the square of the velocity of light” is another way to verbalise a famous formula.

Though that could get *really* cumbersome with some complex formulas.

There’s no standard (even with symbols), but some say “2 divided by the quantity x minus 1.”

No, I don’t think so. That’s the whole point of math.

*x-minus-one, all to the minus one, times two.* = 2*(x-1)⁻¹

It gets a lot harder with more variables. e.g. noone would think I here mean (x-1)⁽⁻¹*²⁾ because youd say *all to the minus two*.

But if one said *x-minus-one, all to the minus n, times two*, it would be ambiguous whether one meant (x-1)⁽⁻ⁿ*²⁾ or 2*(x-1)⁻ⁿ

Larger stuff gets much more difficult to say unambiguously, and even if you do, most people would struggle to follow, making it much easier to simply write.

The Babylonians discovered how to solve quadratic equations, which was quite an accomplishment given their lack of symbolic representation. This may be slightly off topic, but here is a description of what they had to go through to describe what had to be done. This shows how mathematics is not just a means for solving problems, but a kind of language as well. Unfortunately, this language does not translate well into spoken language.

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