Fame

There are two types of fame categories for mathematicians: those who are world-famous...and everyone else. If someone asked you to name all of the mathematicians you've ever heard of, your list would probably max out at six names and include Stephen Hawking, Isaac Newton, maybe the guy Benedict Cumberbatch played in that movie, and a few Greeks. Even in our modern, science-crazy society, most mathematicians will fly under the radar.

If you make a groundbreaking discovery that changes the way humanity perceives their collective existence on Earth, then maybe...you'll be the answer to a Double Jeopardy question. That's typically the extent of your world famous-ness.

That's not to say there's no fame in the world of mathematics; that holds true with research mathematicians. The field is littered with highly intelligent, highly creative people who take an active interest in the pursuits of their colleagues. If you work hard and build your reputation on respectable techniques and interesting papers, then those people may just be talking about you at all their fancy cocktail parties.