Tanya Khovanova's Math Blog

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.

This story happened at a colloquium that was conducted during the Women and Math program at Princeton last year. The room was full of women waiting for the colloquium to start. A young man appeared at the door. He looked around in complete surprise. I watched the fear fade from his face when he must have decided that he had the wrong room. He disappeared, but reappeared at the door very soon. He had obviously checked the schedule and had realized that, in fact, he had come to the right room in the first place. His face started changing colors. He was terrified. A few minutes later, he left.

I sat there thinking: women have to deal with this type of situation every week. He could afford to skip just one lecture, but if a girl wants to do math she has to be courageous almost every seminar. I mentally applauded the girls around me for being that courageous.

Wait a minute! I am a woman myself. I went to seminars where I was the only girl hundreds of times. How did I feel? Actually I think my mind never registered that I was the only girl. I never cared. The first time I really thought that the gender of people in a room might be an issue was during that colloquium last year.

I started wondering why it had never bothered me. Could it be that the Soviets did a good job of teaching me not to pay attention to people’s gender? Could be. But wondering back in time, I remembered something else too.

When I was a child I wasn’t a girly girl. I was not interested in dolls; I preferred cars. I didn’t play house or doctor; I played war. To tell the whole truth, I actually did have a doll that I loved, but I never played with it. I liked having it. The doll was a gift from my father’s second wife and it was way beyond my mother’s price range. I think I had an admiration for the quality and the beauty of this toy.

So, while appreciating the courage that the other girls might have needed to do math, I was sitting there pondering my own indifference to the gender of people at seminars and my relative comfort with large groups of men. But this comfort had its own price. I felt comfortable with the group I wasn’t a part of, while I felt different from the group I was a part of. My price of being comfortable at math seminars was loneliness.