“A Kiss and Its Consequences,” English carte de visite, 1910.

In 1965, Caltech computer scientist Donald Knuth privately circulated a theorem that, “under special circumstances, 1 + 1 = 3”:

Proof. Consider the appearance of John Martin Knuth, who exhibits 
the following characteristics:

Weight      8 lb. 10 oz.      (3912.23419125 grams)         (3)
Height      21.5 inches          (0.5461 meters)            (4)
Voice          loud               (60 decibels)             (5)
Hair         dark brown       (Munsell 5.0Y2.0/11.8)        (6)


He conjectured that the stronger result 1 + 1 = 4 might also be true, and that further research on the problem was contemplated. “I wish to thank my wife Jill, who worked continuously on this project for nine months. We also thank Dr. James Caillouette, who helped to deliver the final result.”

(From Donald E. Knuth, Selected Papers on Fun & Games, 2011.)