In early May 1952, 73-year-old Albert Einstein took a break from his three-decade pursuit of a unified field theory to provide a 14-year-old some help with a geometry problem.

The request for aid had arrived in the mail from Johanna Mankiewicz, a high school sophomore at the Westlake School for Girls in Los Angeles. Johanna was the daughter of Herman Mankiewicz, a writer who collaborated with Orson Welles on the movie *Citizen* *Kane*. Her uncle was the famous producer and director Joseph Mankiewicz. Some of her schoolmates, like Jane Fonda, would become movie stars.

Johanna’s Hollywood surroundings probably contributed to her willingness to contact the biggest celebrity of all in the American scientific scene when she and her geometry classmates were stumped by a tricky homework problem. Surely a star like Einstein would be far better to ask than the never-to-be-known-for-anything Westlake mathematics teacher. In her letter to Einstein she wrote, “I realize that you are a very busy man, but you are the only person we know of who could supply us with the answer.” After stating the problem for Einstein, she commented: “I think you will agree it is the hardest thing!”

Although Johanna would not have known it, Einstein had a consistent history of answering letters from children and others from the general public that he felt were genuine. He would often scrawl a reply on paper, and Helen Dukas, his personal secretary, would either type the reply or just send off the written response as he wrote it.

**A puzzling response**

In reality, Johanna was asking for help with a standard Euclidean geometry problem involving an application of the Pythagorean theorem. It was a question one might reasonably find in any high school mathematics book of the time: What is the length of “the common external tangent of two tangent circles of radii 8 inches and 2 inches”?

Einstein used the back of Johanna’s letter to write his response. He sent his letter by airmail but forgot to use the correct postage of 6 cents (or perhaps he ran out of stamps and thought, with his characteristic rebelliousness, that the 3 cents would work well enough). A reproduction of Einstein’s handwritten answer is shown in figure 1.

The handwriting below the diagram states the following:

The radius

rof_{3}Kis the differenz_{3}r=_{3}r–_{1}r._{2}

The tangentO–>_{2}Kis || to the tangent on_{3}Kand_{1}Kand_{2}

can be easily constructed. This gives the solution.

A. E.

Einstein’s native German language made two small intrusions in the response. The word *differenz* is the German spelling. More subtly, the circles were labeled with the letter *K* (probably for *Kreis*, German for circle).

A properly proportioned version of Einstein’s diagram is shown in figure 2.

Einstein’s logic in the solution was as follows:

**Step 1.** Construct (using a protractor, for instance) the dashed circle having a radius equal to the difference of the two lengths given. In this case, *r*_{1} = 8 inches and *r*_{2} = 2 inches, so the dashed circle has radius *r*_{3} = 6 inches.

**Step 2.** Draw a tangent to the dashed circle from the center of the smaller circle. The normal radius to circle *K*_{1} must also be the normal radius to the dashed circle *K*_{3}. Therefore, a tangent to *K*_{3} can be constructed (using the compass) that is equidistant and therefore parallel to the tangent between *K*_{1} and *K*_{2}. Einstein marks this tangent with a dashed line. Furthermore, if the dashed line ends at *O*_{2}, the center of *K*_{2}, it must be the same length as the tangent whose length is required in the problem.

**Step 3.** It seems at this point that Einstein could not bring himself to divulge the complete solution that the teenager surely desired. Any more information and he would be doing the problem outright for the girl. So Einstein abruptly closed the reply with “This gives the solution.”

What would Johanna have had to do next to get her answer? Crucially she would have had to remember the given information that Einstein did not mention: that the circles were tangent circles, meaning they had to kiss at a single point. In figure 3, we take a look at the two-circle state of affairs when all of the given information is included and Einstein’s construction is in place.

The kissing circles present a right triangle formed by the intersecting three lines: *O*_{1} to *K*_{1} (stopping at *K*_{3}); *O*_{1} to *O*_{2} (the hypotenuse); Einstein’s dashed line.

Using the Pythagorean theorem for this triangle, the required tangent length is simply $\sqrt{{({r}_{1}+{r}_{2})}^{2}-{({r}_{1}-{r}_{2})}^{2}}$ or equivalently $2\sqrt{{r}_{1}{r}_{2}}$. With the supplied numbers plugged in, this gives the common tangent length as 8 inches.

Einstein’s symbolic solution, giving only an implicit resolution, seems somewhat pedagogically incommensurate with the intended recipient’s assumed knowledge base. His solution neither references the supplied numerical lengths nor pinpoints the use of the Pythagorean theorem for the constructed triangle. Furthermore, he does not incorporate the kissing constraint, even though that information is necessary to find the solution. The sentiment to help is laudable, but the execution implies a lack of common sense with respect to the preparation level of a high school student who would write such a letter.

**The press weighs in**

Given her parents’ connections, newspaper reporters quickly learned of Einstein’s reply and avidly pursued Johanna’s detailed account of the experience. The resulting human-interest stories focused on Einstein’s willingness, despite being the world’s foremost scientist, to correspond with a teenager who wrote to him about the trouble she was having in solving a school geometry problem.

Both the* Los Angeles Times* and the *New York Times* featured the story on their front pages on 16 May 1952. The *New York Times* rounded off Johanna’s age and led with the headline “Einstein sends QED to problem of schoolgirl, 15.” The article began with the affirmation that Einstein “took time out from investigating the mysteries of the universe.” The *LA Times* led with the headline “Stuck with geometry, girl turns to Einstein”; the story continued on page 6 with Einstein’s diagram. Johanna’s story was even front-page news in Australia’s *Sydney Morning Herald *under the banner “Dr. Einstein solves a geometry problem.” Based on an internet search, some version of the story appeared in at least 82 newspapers in the US alone. In today’s jargon, we would say Johanna’s story went viral.

The day after the story broke, the newspapers had a new angle, one not so positive toward Einstein or Johanna. The 17 May *LA Times* story was headlined “Einstein flunks out as geometry teacher.” The article informs us that although Johanna was grateful for Einstein’s reply, she still did not understand the “hieroglyphics” in his answer. That same day, the Spokane *Spokesman-Review* had a short article with the heading “Einstein helped her, but not enough,” accompanied by a photo (below, left) of Johanna sitting with an open binder and holding up the letter from Einstein. Another widely published photo (below, right) clearly demonstrates Johanna’s confusion over Einstein’s answer. In trying to reproduce the solution on a small slate chalkboard, she misreads Einstein’s handwritten *r* symbols as square-root symbols, which results in an irrelevant and meaningless equation.

Surprisingly, a Los Angeles dentist soon became part of the saga. Leon Benkoff, who had a side interest in recreational math, jumped into the fray after reading coverage in both the *LA Times* and the paper’s afternoon tabloid edition, the *LA Mirror.* Benkoff concluded that something was off with Einstein’s answer. He is quoted as saying, “Well, I looked at the postcard sketch pictured in the newspaper, and Einstein wasn’t right either. He gave an answer to a different problem. He described how to construct a tangent to a circle, but the problem was to compute the length of the tangent.”

Benkoff phoned the* Mirror* and told them of the “error.” The editors were skeptical. But a visit by a reporter to Benkoff’s house to check his credentials was enough to land him on the front page of the *Mirror* the next day. The headline read, “Einstein ‘fails’ in math, but still has Nobel Prize.” As Benkoff related it, he became known around the city as “the man who corrected Einstein.”

It’s obvious from the second-day reports that Johanna ultimately realized that she was stuck solving the cursed geometry problem in the mundane way that her noncelebrity teacher had explained to the entire class the day before Einstein’s letter arrived. Despite the intervention of the world’s most famous living scientist, she did not have a genius solution with which to impress people.

Making things worse, her teacher and principal were not pleased with her now-public statement that Einstein was “the only person we know of who could supply us with the answer.” The *New York Times* follow-up article noted that Johanna was rebuked by school authorities for writing to Einstein. The principal, Helen Temple, even adopted a finger-wagging tone toward Einstein for encroaching on her turf. “Great scientists should be bothered only with great problems,” she reportedly said.

It is not clear how Einstein felt—he declined comment on the hullabaloo.

*David R. Topper is a retired professor at the University of Winnipeg who taught history of science and art history for 42 years. He is the author of four books, the latest being *Einstein for Anyone: A Quick Read* (2016). Dwight E. Vincent is an associate professor of physics at the University of Winnipeg. He has interests in cosmology using higher dimensions as well as an interest in Einstein’s scientific work as manifested through his various blackboard photographs.*

*Editor’s note, 19 December: The article was modified to correct the German word for circle.*