On Wednesday, four mathematicians will receive the prestigious Fields Medal at the International Congress of Mathematicians (ICM) in Seoul. If you go to the kinds of parties I do, the Fields Medal will probably come up at the next party you attend, so here’s your guide for conversing about the medal with aplomb.

First, a few basics: the medal was endowed by Canadian mathematician John Charles Fields and awarded for the first time at the ICM in 1936 and every four years since 1950, when ICM meetings resumed after World War II. The first few years, the prize went to two mathematicians at a time. An anonymous donation allowed it to expand to up to four per congress starting in 1966. A total of 52 mathematicians have been selected for the prize, although one, Grigori Perelman, famously turned it down.

**Cocktail party tip: **A fun conversation topic would be which Fields medalist should get which number and suit in a novelty card deck featuring their pictures. Sadly, time is running out on this idea. We could push the limits this year by adding four jokers, but the jig is up in 2018.

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I suppose it is inevitable that any prestigious award will become known as the Nobel prize of its field. But the comparison between the Fields and the Nobel has always irked me far more than it probably should.

**Cocktail party tip:** A New York Times article by Michael J. Barany makes the argument that people started calling the Fields Medal the Nobel prize of mathematics in part to help protect Stephen Smale from political problems based on his opposition to the Vietnam War. It’s an interesting read.

The biggest difference between the Fields Medal and the Nobel Prize, and the reason the comparison bothers me so much, is the age limit. The details of the limit have not been consistent throughout the medal’s history, but currently, Fields medalists must be younger than 40 on January 1 of the year they receive their award. The Nobel Prize has no age requirement, other than the fact that the recipient must be living. The age limit is in place because in the letter establishing the endowment for the award, Fields wrote, “while it was in recognition of work already done it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others.” But Fields himself did not mention an age limit.

I don’t have a problem with the fact that an award with an age limit exists, but I do have a problem with us characterizing it as the highest honor in mathematics, akin to a Nobel prize. The age limit is an arbitrary cutoff, and it reinforces the stereotype that mathematics is a young person’s game, and that people whose career paths meander a bit, or whose research takes a while to get off the ground, will never enter the highest echelons of the field.

When you combine the age limit with the fact that the Fields Medal is awarded only every four years, the problem becomes even greater. Some people age out of the award at 36, while some don’t until 40. I’m sure there aren’t enough Fields Medals awarded to create a statistically significant bias, but it would be funny if people born in years that have a remainder of 2 when divided by 4 gradually became overrepresented in the list of Fields medalists, the way people with birthdays in January are overrepresented in some professional sports leagues.

**Cocktail party tip**: So far, the Fields Medal has been awarded to four mathematicians under the age of 30: Lars Ahlfors (age 29, 1936), Jean-Pierre Serre (age 27, 1954), Charles Fefferman (29, 1978), and Simon Donaldson (28, 1986). Now might be a good time to refresh that drink.

The age limit is not the only difference between the Fields and the Nobel. We mathematicians are far too pure of heart to care about filthy lucre, but the money associated with the Fields Medal, 15,000 Canadian dollars, is a pittance compared to the amount that the Nobel pays. It does, however, come with an attractive medal that's worth quite a bit as well.

**Cocktail party tip:** according to article from the Notices of the American Mathematical Society (pdf), Lars Ahlfors had to pawn his medal in the chaos at the end of World War II but was eventually reunited with it.

The Abel Prize, first proposed in the late 1800s and finally officially established in 2001, may be a better analogue to the Nobel Prize and is also frequently referred to as the “Nobel Prize of mathematics” by mathematicians and the media. It is awarded every year to one or more mathematicians who worked on closely related contributions, has no age limit, and carries the hefty sum of 6 million Norwegian kroner (approximately 1 million US dollars). If the Abel Prize had been founded first, the Fields probably wouldn’t be called the Nobel prize of math.

**Cocktail party tip:** If someone mentions the “Nobel of math,” start talking about your favorite theorem by Yakov Sinai, the dynamicist who received the 2014 Abel Prize. That’ll throw them off!

The hipster candidate for the “Nobel Prize of mathematics” is the Chern Medal, which was awarded for the first time at the 2010 ICM. It’s new, you’ve probably never heard of it, and it’s only awarded once every four years.

**Cocktail party tip:** Start following the Chern Medal now. In 20 years, you can talk about how you called the Chern Medal the Nobel Prize of mathematics before it was cool.

So why isn’t there a Nobel prize for mathematics? Sadly, we’ll never know for sure. There is a strangely persistent rumor that it was because Nobel’s wife was having an affair with Swedish mathematician Magnus Mittag-Leffler. That would have been quite a feat, as Nobel never married. It’s possible that friction between Nobel and Mittag-Leffler, who probably would have won the first mathematics Nobel Prize, contributed to the omission. But in an article about the 2004 Abel Prize, Keith Devlin writes, “the most likely explanation, I think, is that he viewed mathematics as merely a tool used in the sciences and in engineering, not as a body of human intellectual achievement in its own right. He also did not single out biology, possibly likewise regarding it as just a tool for medicine, a not unreasonable view to have in the late 19th century.”

**Cocktail party tip:** Laugh condescendingly at anyone who brings up the “Nobel’s wife” rumor.

The Nobel Foundation has spent a lot of time cultivating its brand, and it doesn’t like it when other prizes call themselves the “Nobel prize of” another field. They’ve sent letters to award organizations for copyright infringement over the issue.

**Cocktail party tip:** If you are an organization that confers a prize that you would like to be perceived as prestigious, be sure to refer to it as “often described as the Nobel prize of [your field here].” That way you shift the responsibility of the characterization to others and avoid any legal trouble with the Nobel Foundation!

The letter Fields wrote establishing the prize is worth a read. Fields was an idealist who wanted the prize to help further international unity and elevate the prestige of mathematics, and he would not have approved of the prize being called the Fields Medal. He wrote, “One would hear again emphasized the fact that the medals should be of a character as purely international and impersonal as possible. There should not be attached to them in any way the name of any country, institution or person.”

**Cocktail party tip:** When someone mentions the Fields Medal by that name, sigh deeply and mumble something about how insensitive people are to the wishes of the dead. Pointedly start your next sentence by referring to the Fields Medal as "the International Medal for Outstanding Discoveries in Mathematics.”

**Bonus cocktail party tip, apropos of nothing: **Cedric Villani, one of the 2010 Fields medalists, has been called the Lady Gaga of math, which means you can say that the Lady Gaga of math has received the Nobel prize of math. In my opinion, the Lady Gaga comparison doesn’t work too well—on a fashion level, Villani has a distinctive style, but it’s almost a uniform, while Lady Gaga’s style is much more eclectic—but neither does the Fields-Nobel comparison.