It was reported on May 16, 1952, that 15-year-old Johanna Mankiewicz, who lived at 1050 Stone Canyon Rd in the Bel-Air neighborhood of Los Angeles, California, was stumped by a problem that her geometry teacher had assigned. So were all of her classmates.
Johanna decided that the best thing to do would be to get some help from someone really smart. Make that really, really, really smart. She decided to write a letter to the famed physicist, 73-year-old Albert Einstein at the Institute for Advanced Study in Princeton, New Jersey.
She wrote, “Our geometry class found itself at a loss today when no one in the class could do a certain problem. I realize you are a very busy man, but you are the only person we know who could supply us with the answer and let us keep ourselves busy at our other business.
So, if you could possibly work this problem for us, we would be very grateful. Here is the problem:”
“The common external tangent of two tangent circles of radii 8 inches and 2 inches is —. I think you will agree it is the hardest thing!
“Very respectfully yours,
“Johanna Mankiewicz (Secretary of the sophomore class.)
“P.S. I think you knew my grandfather, Prof Frank Mankiewicz of CCNY.”
Surprisingly, Einstein took the time to sketch out a diagram on the back of Johanna’s letter, which he said would lead her to the solution. His reply was sent back via airmail. Einstein, like all good teachers, did not provide her with the exact answer, so the students set to work on coming up with an answer. Their solution was 8 inches, which, according to my calculations, is the correct answer.
Shortly after this story appeared in the national papers, an Athens, Ohio high school math teacher named Harold Lee wrote to say that Einstein had made a mistake in his diagram.
“I am not one to challenge Dr. Einstein on his knowledge of mathematics,” Lee wrote, “but his diagram does not agree with the statement of the problem.”
He added, “Einstein’s solution is correct for finding the external tangent to any two circles, but is not the best solution for this specific problem.”
Basically, Einstein’s error was that he did not touch the two circles together. The problem specifically specified that the two circles had to be tangent or touching one another.
Lee concluded, “He probably just missed that word, ‘tangent.’”
Even geniuses make mistakes sometimes…