Monday, February 22, 2021

Good Names and Bad Names of Game Shows and theorems

 In my post on Alex Trebek, see here, I noted that Jeopardy! is not a good name for the game show since it doesn't tell you much about the show. Perhaps Answers and Questions is a better name.

The following game shows have names that tell you something about the game and hence have better names: 

Wheel of Fortune, The Price is Right, Lets make a Deal, Beautiful women have suitcases full of money (the original name for Deal-No Deal), Win Ben Stein's Money, Beat the Geeks. 

In Math we often name a concept  after a person. While this may be a good way to honor someone, the name does not tell us much about the concept and it leads to statements like:

A Calabi-Yau manifold is a compact complex Kahler manifold with a trivial first Chern class. 

A Kahler manifold is a Hermitian manifold for which the Hermitian form is closed.

A Hermitian manifold is the complex analog of the Riemann manifold. 

(These examples are from an article I will point to later---I do not understand any of these terms, though I once knew what a Riemann manifold was. I heard the term Kahler Manifold in the song Bohemian Gravity.  It's at about the 4 minute 30 second place.) 

While I am amused by the name Victoria Delfino Problems (probably the only realtor who has problems in math named after her, see my post here) it's not a descriptive way to name open problems in descriptive set theory. 

Sometimes  a name becomes SO connected to a concept that it IS descriptive, e.g.:

The first proof of VDW's theorem yields ACKERMAN-LIKE bounds. 

but you cannot count on that happening AND it is only descriptive to people already somewhat in the field. 

What to do? This article makes the  ballian point that we should   STOP DOING THIS and that the person who first proves the theorem should name it in a way that tells you something about the concept. I would agree. But this can still be hard to really do.

In my book on Muffin Mathematics (see here) I have a sequence of methods called

Floor Ceiling, Half, Mid, Interval, Easy-Buddy-Match, Hard-Buddy-Match, Gap, Train. 

There was one more method that I didn't quite name, but I used the phrase `Scott Muffin Problem' to honors Scott Huddleton who came up with the method, in my description of it. 

All but the last concept were given ballian names.  Even so, you would need to read the book to see why the names make sense. Still, that would be easier than trying to figure out what a Calabi-Yau manifold is. 


  1. I think the most famous example is Abelian group instead of commutative group.

  2. What's a ballian point?

    1. the article I point to is by Laura Ball and she is the one who made the points I am re-iterating.

  3. Convince me with a better short reference name for a Calabi-Yau manifold and the other things anyone would have to learn before they're even ready to learn about a Calabi-Yau manifold.

    1. Or almost any other concept in advanced math. The linked article cherry-picks some examples where it is possible to come up with a short but (at least somewhat) descriptive name, but I don't see that being the case in general.

      And does the name "Monstrous Moonshine" really tell anything meaningful about the mathematics involved?

    2. I agree the finding the right name can be hard to do.
      (Idea for another blog: GOOD names for math concepts.)

  4. Carrying the logic further, perhaps we should start giving babies descriptive names instead of non-mnemonic names such as Sophia or Liam. That might make it easier to remember the names of new acquaintances.

    More seriously, while I do think that mathematicians ought to invest more effort coming up with better terminology, I don't think that there is any easy solution. Do we really want to trade in "Kähler" for something like "complex symplectic positive definite"? Or "Calabi-Yau" for "compact complex symplectic positive definite flat null-cohomological"? There's a tradeoff between descriptiveness and convenience. And if one chooses a short word that happens not to be someone's name, there's no guarantee that it will be any more descriptive or mnemonic than a name. Ball gives "perfectoid space" as an example, but as far as its descriptive or mnemonic value is concerned, I have a hard time seeing how "perfectoid" is any better than "Scholze."

    In fact, an argument can be made that even if we make mnemonic value our primary criterion, using someone's name is better than using a freshly coined neologism. Mathematicians are human, after all, and all (okay, almost all) of us care about other human beings. I might have a more vivid memory that a particular polynomial is "the polynomial that Tutte introduced" than I have of the definition itself.