## Perfect Math Notation

Notation is very important in your mathematical papers. Here are the most famous rules on how mathematicians use notation.

Do not explain your notation. Do not waste your time explaining your notation. Most of them are standard anyway. Your paper will look more impressive if you plunge right into your statements. So a good paper can start like this:

Obviously, p is never divisible by 6 …

Everyone knows that p is a prime number.

Use a variety of alphabets. This way you demonstrate your superior education, while expanding your notation possibilities. Not to mention that it looks so pretty:

sin2ℵ + cos2ℵ = 1.

You also get points for drawing a parallel between alpha and alef.

Denote different things with the same letter. It is very important to maintain continuity with the papers in your references, so you should use their notation. Besides, some notation is standard:

Suppose S is an ordered set. Elements of the permutation group S act on this set: for any s in S, sS is the corresponding action.

Mathematicians secretly compete with each other. The goal is to denote as many different things as possible with the same letter in one paper. My personal record was to denote six different things with the letter G. There are two versions of this competition to maximize the number of different meanings of one letter: it can be done either on the same page or in the same formula.

Use different notation for the same thing. The ultimate achievement would be to change your notation in the middle of your sentence:

Gauss showed that the sum of integers between 0 and k inclusive is equal to n(n+1)/2.

Replace standard notation with your own. Your paper will look much more complex than it is. Besides, if someone adopts your notation, they’ll have to name it after you:

Let us use the symbol ¥ for denoting an integral.

Denote a constant with a letter. Letters look more serious than numbers. You will impress your colleagues.

We will be studying graphs in which vertices are colored in only three colors: blue, red and green. For simplicity the number of colors is denoted by k.

As a bonus, when you prove your theorem for three colors, you can confuse everyone into thinking that you proved it for any number of colors.

Do not specify constraints or limits. When you use a summation or a integral, the limits look so bulky that they distract from your real formula. Besides, it’s time-consuming and too complicated for most text editors. Look at this perfect simplicity:

i2 = n(n+1)(2n+1)/6.

Everyone knows that you are summing the integers between 1 and n inclusive. Oops. It could be between 0 and n. But 02 = 0 anyway, so who cares?

Be creative. You can mix up these rules or invent your own.

Let us consider a triangle with N sides. Actually, it is better to replace N by H, because in Russian the letter that looks like English H is pronounced like English N. Let us denote the base of the triangle by X. By the way, that is the Russian letter that is usually pronounced like the English letter H, so sometimes I will interchange them. The height of the triangle is, as always, denoted by H.

By following these simple rules, you will earn great respect from your readers.

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1. #### Jason Dyer:

Brilliant!

(I’ve seen the no-limits-on-summation thing so many times I thought I was the only one who was grumpy about it.)

2. #### (x, why?):

I had a college professor a long time ago that insisted on pronouncing “psi” as “see”.
Okay, I realize that, technically, he was correct with that, but he never noticed the confusion he was causing, particularly in problems that were also using the letters a, b, and (you guessed it) c.

Frustrating enough that I almost switched to see-cology.

3. #### SpeedKills:

Yesterday I got a reproval for using i (as a square root of -1) and /delta_{i,j} (as the Kronecker symbol with indices i and j) in the same formula. How sloppy … 😉

4. #### Roman Cheplyaka:

https://gamma.pu.ru/user/aih/papers/lection.zip

5. #### Kathy:

One of my favorite quotes :

We will occasionally use this arrow notation unless there is danger of
no confusion.
— Ronald Graham, “Rudiments of Ramsey Theory”