How to Read Mathematics

Through Tall, Dark and Mysterious, I found this web page on How to Read Mathematics by Shai Simonson and Fernando Gouvea. This quote says it all:

Students need to learn how to read mathematics, in the same way they learn how to read a novel or a poem, listen to music, or view a painting.

Some of my papers are said to be “hard to read” because I make ample use of mathematical notations, even when it is not strictly needed. Some reviewers, though they won’t admit to it, don’t like my papers because they can’t read them. Of course, there is no shortage of Ph.D.s who can read mathematics, so there is no reason to stop using mathematical notations. To me, a paper with a strict adherence to mathematical conventions and a thorough use of mathematical notations is far easier to work with than a paper which tries to describe everything in English. English is an ambiguous and dangerous language, especially if you are not trained in philosophy and have English as your third language. Mathematics, on the other hand, is a true universal language and it can be extremely precise if needed. And that’s what I try to give my readers: a precise description of what is and what is not, not just vague impressions. I’ll keep the vague impressions for this blog.

Now, as of students, last time I taught Calculus, I was told that I was using too many Greek letters. Well, I didn’t apologize for using Greek letters. I probably kept using them. Students: learn to work with Greek letters, there is nothing wrong with them and if you do a lot of complex work, you’ll find that 26 letters are not enough and that borrowing from other alphabets does improve the clarity of your documents. Plus, there are some universal conventions you just can’t get around. I could say that “e” is a small quantity, but “e” is Neper’s number. So, when I want to refer to a small quantity, I use the Greek letter epsilon. So do at least another million of crazy geeks.

The real question is, when will I start using mathematical notations on my blog? That’s coming soon… I’ll get MathML on this very page in the near future. With plenty of Greek letters!!!

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Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

4 thoughts on “How to Read Mathematics”

  1. I agree with both of the above comments. There’s a time when using symbols is a succinct and elegant way of expressing an idea – and there’s a time when using symbols is an unnecessary obfuscation, and is done for no apparent reason other than egotism. And Will Fitzgerald’s comment about CS people wanting to know why they should care, and what the implications of the material is, applies doubly to first year students who are only dubiously math literate.

  2. I completely agree that Math is Good, and that people need to know how to read Math. But mathematicians often find the math itself to be what is of interest; that’s fine, that’s their game. But there are two aspects of any paper that are often overlooked in math-heavy (CS) papers. One is: Why should I care? The second is: What are the implications? Math makes you think hard, and life is oh so short, so you need to give me a good reason to think so hard understanding *your* ideas instead of time working out my *own* ideas.

  3. Rigor is the important thing, not symbolism. The best mathematical expository writing is so good because it knows when not to use symbols and formalism.

  4. I prefer to read Math for it is more accurate and simple. But only when it is good
    math. Sometimes, people just play the game of formalization. And when a paper reviewed,
    the reviewer questions whether it is necessary and rejects the paper if they do not understand.
    So explanation is still needed, along with math.

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