Some thoughts about learning/teaching math history

It may worth to specify to whom the math history is written. I assume the history is written to students no higher than secondary school, and it may be true that the younger the reader, the better the effect, i.e., the understanding of the math knowledge, some concepts, and of course, some stories.

However, it is also true that unlike stories of other findings, stories of math findings are usually boring and hidden under other findings. I received a gift from my grandpa in my 12th birthday. It is a book recording stories of most major math and scientific (mainly physics, chemistry, and biology) findings. I still remember the feelings when I read those math stories: boring. The first math story was about Pi. At that time I have learnt Pi in school, but why should I be excited when an ancient spent all his life finding some values of Pi? I mean, there are more vivid stories like Archimedes' principle of buoyancy, the stories of a number are something not as interesting as the others.

However, the story of using wheat to fill up a chess board is intersting (2^0, 2^1, 2^2, ... 2^64). It demonstrates how fast exponents grow as well as how stupid the king was. And so does the story of square root 2, in which a man was killed by being thrown into the ocean. Similar math stories are rare; but if there is one, it must be the story rather than the math finding itself that attracts my attention.

At this moment I carefully examine my feelings of reading this book. I notice that I can clearly remember some math findings, but all of them are story-related. Here is the most important feeling I believe: math is everywhere in this book, but my feelings of math is only that it is powerful. I feel that it is the stories that touches me rather than the math. Right now I am trying to imagine the feelings if I encounter a chapter full of mathematical proofs. I would just skip the chapter in that age.

Then about the teaching the math history. No doubt this will help students understand math. In fact no matter what we teach, as long as they are willing to learn, they can always make improvements. I would suggest if we can combine the math history with some non-math components, like science findings and real applications, and less proofs and calculations. As long as we implement a feeling that math is powerful in students' heart, and even more, if we let them think the power of math outweighs the struggles of learning math, we succeed.