Tropical geometry is a funny one. When I first learned of it, I had two reactions: first, I hated the name, and second, I thought it was unmotivated and was really just generalization for the sake of generalization.
I was wrong, on both counts.
Let’s talk first about the name, before we get into what Tropical geometry is and why I was wrong about its motivation (or lack thereof). It is named in honour of Imre Simon, a Hungarian-born mathematician living in Brazil. Since he was one of the pioneers in this field, and since he lived in the tropics… whence the name.
I’ve actually heard someone say further that he lived and worked on opposite sides of the tropic of Capricorn, which was also part of the name. That said, I’ve only heard this part once, and so I’m not sure how much I believe it.
Anyhow, originally I disliked the name due to its frivolous nature. Perhaps part of this was due to my initial dislike of the subject, but either way I was bothered by how un-descriptive it was. By contrast, mathematical terms are typically named either after a mathematician or in some descriptive manner. Hilbert space. Sheaf. Étale. Gromov-Witten theory. Solvable. Space-filling curve. Markov process.
In particular, the descriptive naming is something that works very well. The name itself tells you something about what you’re studying, which helps a lot in remembering the ideas involved.
However, one problem that occurs frequently is that mathematicians as a group can be strikingly unimaginative in naming their objects, and so we end up with a proliferation of “normal” objects, or “regular” ones. And one of the most infamous examples, of course, is that it is perfectly reasonable to describe something as being both reduced and irreducible.
By contrast—or even hypocritically—I had always loved the whimsical nature of some of the names coming from physics. I love the name quark, and even more than that I really love their names—strange, charmed—although I would have preferred that they stuck with the “truth” and “beauty” quarks instead of the “top” and “bottom” quarks.
And of course, here is a problem. On one hand, I disliked the term “tropical” for its irreverence, but lauded physicists for their whimsical name choices.
In the end, the name won out, at least to me.