I am reaching the tail end of reading Eugenia Cheng’s new book, Is Math Real?. It’s been an enjoyable read so far. The book reminds us that mathematics is not just a sterile set of rules to memorize, but a fertile and fun playground for the imagination backed by rigorous thinking.

However, the book also helped me realize that there is another component to mathematics as a subject that is usually not brought up. It is to learn a common language for us to talk about mathematics. Puzzling out math and thinking about all the different ways to think about a particular mathematical object is fun, but without a common language, you will have a very hard time talking about it with other people.

You can’t just conjure up your own notation or ways of expressing math
and expect others to understand. If you don’t believe that,
try to understand what the following means:^{1}

00000000011011011 00001011010001100 00110100100111000 01110010010000010

I suspect a large part of why math is such a problem for many people is that one basically has to learn a second language as part of math. At least the most widely used portions of this language is a very simple language, but there is still plenty that is not frequently used by the general public that is still taught up to high school. And for many, learning a second language is not easy.

I hope this is what many people mean when they say they are not good at math or that they hate math. Hopefully, they mean that they had trouble with learning and understanding the common language used for expressing math and not that they eschew good logical thinking and prefer sloppy thinking. It is unfortunate that some of these people actually do prefer sloppy thinking or even simply making things up and dressing them up as truth, but I hope such people are a tiny minority.

Perhaps if school could teach math so that math as a way of thinking and math as a common language are not so intertwined as being the same thing, fewer people may feel like they are bad at math itself, but instead not so good at learning the common language of math as a second language. It would be nice if they still liked mathematical thinking itself.