Daniel Lemire's blog

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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!!!