Interconnected: Erdös Numbers

December 7, 2025

Eva Zaman

Thomas A. Edison CTE High School 

11th Grade

With almost 8.2 billion people in the world, it is impossible to not be connected to complete strangers in varying ways. Whether by coincidence or interconnected relations, everyone and everything is connected. Erdös Numbers was named after Paul Erdös, a famous mathematician who wrote over 1500 publications, collaborating with over 500 co-authors. What started as a simple joke among mathematicians has now evolved into a concept to understand how people in several fields are connected through one man. 

Paul Erdös was born in Budapest, Hungary, on March 26, 1913. He was born as the only son to Anna and Lajos Erdös, who previously had two daughters that would go on to die from scarlet fever. Due to his sister's deaths, Erdös was kept very sheltered throughout childhood and was only homeschooled. He had a particular upbringing, especially due to his Jewish heritage during a time of extreme political and social instability as World War 1 had begun. His father was taken to Serbia as a prisoner of war, resulting in his mother and a German governess raising him alone for six years. Nonetheless, this would not stop his thirst for education. From a young age Erdös was taught mathematics, physics, history, biology, English, German, French, and Latin. It was evident, though, that while he was a prodigy in several fields, he strove the most in mathematics. By four he was multiplying three-digit numbers and manipulating negatives, only an eighth of his childhood capabilities. Erdös would grow up to be labeled a peculiar man, as he never married nor even had a permanent address; his entire life was focused on his beloved math. From referring to teaching math as preaching to calling children epsilons, he had many strange habits. 

His behavior, while considered odd, has no sway on his genius. His first time being recognized among mathematicians was for his PhD thesis at the University Pázmány Péter of Budapest, in Hungary. There he found a simpler method for the proof of a prime number-related theorem by Joseph Bertrand, Bertrand's postulate. After earning a fellowship at the University of Manchester in England, he began to focus on number theory, a topic he would spend much of his life writing on. To flee Europe before the start of World War 2, Erdös would get a fellowship at Princeton in the United States. There he created a series of theorems with mathematicians Mark Kac and Aurel Wintner that would become the basis of the probabilistic method. The probabilistic method is used in several mathematical branches, but in the modern world it holds the most importance in discrete mathematics—vital to analyzing and designing algorithms for computer science. After Erdös was rejected from continuing his fellowship at Princeton, he would travel around the world working with many colleges and research opportunities. This led him to collaborating and writing hundreds of papers from all forms of mathematics studies. Through this, the Erdös number was born; anyone that co-authored with Erdös would have a number of 1, anyone that co-authored with a co-author would get the number 2, and so on. It is a respectable number to be associated with and connects the world and people of mathematics with one another. 

Through Erdös's substantial studies, passion for math, and encouragement of others to pursue mathematics, he was able to bring several STEM fields together on the basis of wishing to learn more.