# Russian-Israeli Mathematician Solves Decades-Old Math Problem

by
findingDulcinea Staff

Avraham Trakhtman solved “the road coloring problem.” A former security guard, he is the latest mathematician to overcome hardship through intellectual brilliance.

## 30-Second Summary

Once employed as a mathematician in his hometown of Yekaterinburg, Russia, Trakhtman immigrated to Israel at the age of 48. Having a hard time finding work in his original field, he took up employment as a night watchman.

At the ripe age of 63, Trakhtman solved the “road coloring problem.” This mathematical stumper is based on the implausible assertion that given a finite number of roads, a “universal map” can be drawn so that people starting from any point can arrive at the same destination simultaneously.

The problem was first posed in 1970. Trakhtman solved it in a year.

“In math circles we talk about beautiful results––this is beautiful and it is unexpected,” Stuart Margolis, a mathematician who recruited Trakhtman to Bar Ilan University, told The Guardian.

Trakhtman is not the first mathematical genius to overcome adversity. Srinivasa Aiyangar Ramanujan came from a poor Indian village to become a mathematics scholar at the University of Cambridge, writing theorems in beat-up notebooks.

Sophie Germain fought the cultural mores of 18th-century France to gain the respect of her contemporary Carl Gauss, considered one of the greatest mathematicians of all time.

At the ripe age of 63, Trakhtman solved the “road coloring problem.” This mathematical stumper is based on the implausible assertion that given a finite number of roads, a “universal map” can be drawn so that people starting from any point can arrive at the same destination simultaneously.

The problem was first posed in 1970. Trakhtman solved it in a year.

“In math circles we talk about beautiful results––this is beautiful and it is unexpected,” Stuart Margolis, a mathematician who recruited Trakhtman to Bar Ilan University, told The Guardian.

Trakhtman is not the first mathematical genius to overcome adversity. Srinivasa Aiyangar Ramanujan came from a poor Indian village to become a mathematics scholar at the University of Cambridge, writing theorems in beat-up notebooks.

Sophie Germain fought the cultural mores of 18th-century France to gain the respect of her contemporary Carl Gauss, considered one of the greatest mathematicians of all time.

## Headline Link: ‘Security Guard Solves 38-Year-Old Maths Poser’

Avraham Trakhtman solved the “road coloring problem.” This theory could have applications in mapping and in computer science. Before he was recruited to Bar Ilan University, Trakhtman was working as a night watchman.

#### Source: The Guardian

## Historical Context: Genius over adversity

**Srinivasa Aiyangar Ramanujan (1887–1920)**

Srinivasa Aiyangar Ramanujan came from a destitute family living about 400 kilometers from the Indian city of Madras. He showed great talent in math in high school and was awarded a scholarship to the government college in the town of Kumbakonam, but it was not renewed and he attended for only a year. Said Ramachandra Rao, one of the founders of the Indian Mathematical Society, where Ramanujan came looking for work, Ramanujan “was miserably poor ... He opened his book and began to explain some of his discoveries ... He said he wanted a pittance to live on so that he might pursue his researches.” In 1914 he went to study at Cambridge. He returned to India in 1919 and died a year later.

#### Source: St. Andrew’s University

The University of Florida publishes The Ramanujan Journal, which is devoted to the areas of mathematics covered by Ramanujan.

#### Source: University of Florida

The Institute of Mathematical Sciences-Chennai has a compendium of Ramanujan’s works, including many of his famed notebooks in which he scrawled his theorems.

#### Source: The Institute of Mathematical Sciences-Chennai

In 2007, two mathematicians at the University of Wisconsin solved two of Ramanujan’s mock theta conjectures. According to the Mathematical Association of America, the solution links “Ramanujan’s functions to mathematical objects known as modular forms,” which “have recently played important roles in number theory, including the proof of Fermat's last theorem.”

#### Source: Mathematical Association of America

**Sophie Germain (1776–1831)**

Sophie Germain was intrigued by Fermat’s last theorem, which is based on the Pythagorean theorem x² + y² = z². As a riddle for future mathematicians, Fermat proved that there are no whole number solutions for similar equations. He kept the proof to himself, however. Germain took classes at Paris’ Ecole Polytechnique under the name of a male student who had dropped out. Esteemed mathematician Carl Gauss convinced the University of Gottingen to give her an honorary degree, but she died of breast cancer before it was awarded. Her death certificate read, “single woman with no profession” rather than “mathematician.”

#### Source: NOVA Online

## Reference: The road coloring problem and its solution

Avraham Trakhtman’s full solution to the road coloring problem is available from ArXiv.org, a math and sciences service from Cornell University’s library.