Review of books on 0,1,pi, e: here, Review of a book on i: here. Review of a book on square root of 2: here. Review of a book on phi: here. Review of a book on gamma (whats gamma?): here. If there is some mathematical constant that has had a book on it that I have not included, please comment.
Here is my choice ranked in order of how important they are.
- 0. Addition is more basic then multiplication so the additive identity comes before the multiplicative identity.
- 1. Multiplicative identity.
- -1. Negative numbers--- what would we do without them? One could even argue that subtraction is more important than multiplication and make this number 2 on the list. There is no book on -1 that I know of, but it is still too important to not put on this list.
- pi. Without pi we wouldn't have circles!
- e. Ah-ha- the pi vs. e debate. You can read about it here or even listen to a real debate here. I would go with pi since the level of math it is on is more basic then the level of math that e is on.
- gamma. What is this constant? It is the difference in the limit between natural log of n and 1 + 1/2 + ... + 1/n. How important is it? I read the book on it pointed to above. The book is pretty good but it mostly talks about related topics- logs, Zeta functions, pi. So I still don't see why gamma is worth a book. I suspect that there are more math constants that are more important that just happened to not have books written about them. Or they have and I don't know about them.
- phi. There is the notion that the Golden Ratio pops up in math and in nature all the time. And there are those who disagree.
- square root of 2. This is interesting historically as the first irrational number, but I don't think it has much mathematical significance.