Erdös Number 1 . . . for Mountain Climbing

Alfinio Flores

This article is published in the December 2011/January 2012 issue of MAA FOCUS.

The prolific mathematician Paul Erdös is at the center of a system of numbering mathematicians. Erdös had many coauthors; they are assigned Erdös number 1. Mathematicians who have coauthored with a mathematician who is Erdös number 1 are assigned Erdös number 2, and so on (see Erdös Number Project, oakland.edu/enp/, for details). Erdös was known for several eccentricities, but perhaps it is not as well known within the mathematical community that Erdös, as he visited places around the globe, liked to take hikes on nearby mountains, accompanied by local mathematicians. Thus, a similar numbering system could be devised for mountain climbing. People who climbed a mountain with Erdös would be given number 1, and so on.

When Erdös visited the Universidad Nacional Autónoma de México (UNAM) in Mexico City around 1978, he requested that he be accompanied on a hike on the highest nearby mountain that was not covered with snow. Víctor Neumann, the professor who had invited Erdös, declined to go himself because of health problems. So a group of six graduate and undergraduate students was recruited to walk with Erdös.

There are many remarkable mountains around Mexico City. Because of Erdös’s request of no snow on the mountain, majestic Popocatépetl (5,500 meters above sea level) and amazing Iztaccihuatl (5,286 meters) were not considered. We decided to take Erdös to Ajusco (3,930 meters), a beautiful mountain to the south of the city. It was not quite the highest mountain without snow around the city, but it was closer and more accessible than either Tláloc (4,158 meters) or Telapón (4,085 meters). So practical considerations took precedence over strict adherence to Erdös’s request. Of course, we did not tell him that Ajusco was not quite the highest mountain without snow around Mexico City.

Ajusco as seen from Universidad Nacional Autónoma de México. Photo by Ricardo Berlanga.

Erdös did not speak Spanish. Fortunately, each of the Mexican students on the trip, in addition to Spanish, spoke another language. Some spoke French, some English, and some German. Erdös was fluent in all these languages, and he asked each of us what language we preferred. We thought communication was going to be easy. Not quite. Erdös would forget what language each spoke, so he would address someone who spoke French in German, and someone who spoke English in French.

Another interesting aspect of the hike was that Erdös was already in his midsixties. Worried about his age, two of our teammates were adamant that we had to climb slowly. What had happened to Witold Hurewicz (who died in Mexico as a consequence of a fall from a pyramid) was already “one too many.” Erdös said that he would not have problems climbing up, but, because his ankles were not very sturdy, he would need some help on the way down. Indeed, Erdös went up slowly but steadily, without any help. He did not stop talking and did not stop to rest until he reached the summit.

On the other hand, the two team members who had worried about Erdös, although they exercised regularly, were heavy smokers. They had to stop a couple of times along the way to catch their breath and then rush to catch up with the group so that others would not notice.

On the top we enjoyed the view. Some of us remembered physicist George Gamow’s story about a group of Hungarian aristocrats who had lost their way when hiking in the mountains. One of them took a map and, after studying it, carefully exclaimed, “Now I know where we are! See that big mountain over there? We are right on top of it” (Gamow, One, Two, Three... Infinity, rev. ed., New York: Dover, 1988/1961, p. 3). Knowing where Erdös was from, we thought it better not to share the story with him.

As we started the descent, Erdös asked for support. Everybody offered to help. He did not choose any of the strong, athletic young males, but instead chose to lean on a beautiful 20-year-old woman. Go figure.

On the way down, all the young males strode ahead, but Erdös and his support lagged behind, because his ankle was hurting. It did not help that Erdös, instead of hiking shoes, was wearing sandals with socks. Great acclamation and laughter met their return to the base when they finally arrived; the young woman was leading Erdös by the hand.

Erdös was a little baffled by the laughter. The woman did not know how to translate the mocking jokes from her team members and instead asked Erdös whether he wanted anything. He asked for coffee, and we took him to a quesadilla stand. Erdös had two quesadillas and café de olla, the reinvigorating Mexican coffee sweetened with piloncillo (a dark brown sugar rich in molasses).

If someone took pictures along the hike, we did not see them. So we do not have any further proof that we had been with Erdös on a mountain and, thus, have Erdös number 1 for mountain climbing.

Alfinio Flores enjoys teaching mathematics and mathematics education courses at the University of Delaware. He thanks Claudia Gómez Wulschner, Francisco Larrión, Gilberto Flores, and Alejandro Uribe for contributing some information and sharing their memories about the trip; and Ricardo Berlanga for the picture of Ajusco.