Mathematical Diseases

From Terry Tao’s blog (thanks to Michael Trick via Peter Haas for bringing it to our attention):

There is [a] type of “bug” that affects mathematicians—the attempt to solve certain problems. These problems have been called “diseases,” which is a term coined by the great graph theorist Frank Harary. A mathematical disease [has these symptoms]:

1. A problem must be easy to state to be a MD. This is not sufficient, but is required. Thus, the Hodge-Conjecture will never be a disease. I have no clue what it is about.
2. A problem must seem to be accessible, even to an amateur. This is a key requirement. When you first hear the problem your reaction should be: that is open? The problem must seem to be easy.
3. A problem must also have been repeatedly “solved” to be a true MD. A good MD usually has been “proved” many times—often by the same person. If you see a paper in arXiv.org with many “updates” that’s a good sign that the problem is a MD.

Improbable Research