Introduction to Paul Erdős: The Mathematical Nomad

Good [morning/afternoon], everyone! Today, we’re going to explore the life and legacy of one of the most extraordinary mathematicians of the 20th century—Paul Erdős (pronounced Air-dish). Known for his unparalleled collaboration, eccentric（古怪的） lifestyle, and profound contributions to mathematics, Erdős’s story is as fascinating as the problems he solved. Let’s dive in.

Who Was Paul Erdős?

Born in Budapest, Hungary（匈牙利）, in 1913, Erdős was a genius. By age 3, he could calculate how many seconds a person had lived; by 20, he had a doctorate in mathematics. But Erdős wasn’t just brilliant—he was a nomad. He famously owned no home, carried his life in a suitcase, and crisscrossed the globe（在全球往返）, staying with colleagues to work on math problems. His motto is “Another roof, another proof.”

The Extraordinary Influence

Erdős transformed mathematics into a global conversation. He co-authored papers with over 500 collaborators from 65 countries—physicists, computer scientists, and even a geneticist. This gave rise to the “Erdős number”, a playful academic status symbol:

  • Direct collaborators have Erdős number 1 (e.g Turán,Rényi).
  • Direct collaborators’ collaborators have Erdős number 2 (e.g Einstein,R&S&A).
  • Direct collaborators’ collaborators’ collaborators have Erdős number 3 (e.g Tao,Pauli).

More relevant information can be found at https://en.wikipedia.org/wiki/Erd%C5%91s_number.

Mathematical Contributions

Erdős’s work spanned number theory, combinatorics, graph theory, and probability. Key contributions include:

  • Probabilistic Methods: Using randomness to solve deterministic problems.
  • Ramsey Theory: Proving order exists in chaos (e.g., “Every party has a group of people who all know each other or all don’t”).
  • Random Graphs: Foundational work on random graphs, critical in network science today.

He has published over 1,500 papers, more than anyone else!

The Eccentric Genius

Erdős’s quirks were legendary:

  • He called children “epsilons” (a math symbol $\varepsilon$ for small quantities).
  • Referred to marriage as “captured” and divorce（离婚） as “liberated.”
  • Women were “bosses” who “captured” men as “slaves” by marrying them.
  • Survived on coffee and amphetamines（苯丙胺）, working 19-hour days. Once, after a bet, he quit pills for a month but complained, “Mathematics set back by a month!”
  • His colleague Alfréd Rényi said, “A mathematician is a machine for turning coffee into theorems”.

A Life Shaped by History

Erdős’s Jewish heritage forced him to flee rising antisemitism（反犹太主义） in 1934, which may save him from the Holocaust（大屠杀）. The murder of his mother in Budapest and the loss of colleagues during WWⅡ deeply affected him. Yet, he channeled grief into mathematics, calling it a refuge of beauty and truth.

Legacy

Erdős died in 1996 at 83, collapsing mid-conference—a fitting end for a man who lived for math. His legacy lives on in theorems, collaborations, and the Erdős Number Project, celebrating his belief all around the world.

In an age of specialization, Erdős was a polymath who connected ideas—and people. He showed that mathematics isn’t just about numbers; it’s about curiosity, community, and the relentless（不懈的） pursuit of the “Book’s” eternal truths.

He is also the subject of George Csicsery’s biographical documentary film N is a Number: A Portrait of Paul Erdős, made while he was still alive.

Closing Reflection

Erdős once said, “The purpose of life is to prove and conjecture.” But perhaps his greater lesson is this: Knowledge grows not in isolation, but in the shared pursuit of beauty. Whether you’re a mathematician, artist, or student, his story invites us all to keep our brains—and hearts—open.

Good Luck & Have Fun

  • Ramsey number like $R(6,6)$
  • Erdos-Turan’s Conjecture