Nash's Game-Changing Idea Marks 75 Years

Seventy-five years ago, a young mathematician and Carnegie Mellon University alumnus named John F. Nash Jr. changed the way we understand decision-making — and the ripple effects are still felt today in fields like economics, political science, computer science and artificial intelligence.

The Nash Equilibrium, published in his 1950 doctoral dissertation at Princeton University, showed how people make choices in competitive situations — from business negotiations to international diplomacy — when each person’s success depends on the actions of others.

Early years

John Nash with the Carnegie Tech Math Club. 1947

When Nash was in elementary school, he was doing arithmetic with larger numbers than his classmates.

“I would have several digits, and they would have maybe two or three digits,” Nash recalled. In high school he was reading “Men of Mathematics” by E.T. Bell, and was proving Fermat’s little theorem.

While his mathematical ability was evident early on, Nash set foot on Carnegie Mellon’s campus — then the Carnegie Institute of Technology — as a chemical engineering major. He soon found that neither chemical engineering nor chemistry suited his interests. Noticing his natural talent in mathematics, faculty in the Department of Mathematical Sciences assured him that he could have a good career as a mathematician and encouraged him to switch his major.

Nash excelled as an undergraduate mathematics student. He published articles on number theory and topology in The Carnegie Technical, a magazine produced by students in the College of Engineering and Science. And he participated in the William Lowell Putnam Mathematical Competition, winning an honorable mention in 1946 and placing among the top 10 in 1947.

A mathematical genius

Nash’s classmates recognized his talents. Raoul Bott, who earned his Ph.D. from Carnegie Tech in 1949, recalled taking Richard Duffin’s course on Hilbert spaces with Nash, who was an undergraduate at the time.

“We were reading von Neumann’s book on quantum mechanics, which developed Hilbert spaces at the same time,” Bott said. “And it soon became clear that Nash was ahead of all of us in understanding the subtleties of infinite-dimensional phenomena.”

Duffin had a long and influential career as a faculty member in the Department of Mathematical Sciences and knew Nash’s ability. In a letter recommending Nash for graduate studies at Princeton, Duffin didn’t mince words, “He is a mathematical genius.”

In addition to his mathematics courses, Nash also took an elective class at Carnegie Tech in international economics. That exposure to economic ideas and problems was the spark that eventually led to Nash’s interest in game theory.

Nash graduated with bachelor’s and master’s degrees in mathematics in 1948.

Nobel Prize and global recognition

After earning his doctorate at Princeton in 1950, Nash joined the mathematics faculty at the Massachusetts Institute of Technology beginning in 1951. He later returned to join the faculty at Princeton as a senior research mathematician.

In 1994, Nash won the Nobel Memorial Prize in Economic Sciences for his doctoral work on game theory.

The University of Oxford held a symposium in honor of the 75th anniversary of the Nash Equilibrium in July 2025. The event featured talks and discussions from researchers in a broad array of fields including Vincent Conitzer, professor of computer science at Carnegie Mellon, who discussed game theory for AI agents.

Conitzer has courtesy appointments in the Departments of Machine Learning and Philosophy and the Tepper School of Business. He directs the Foundations of Cooperative AI Lab (FOCAL). He received his master’s and doctorate degrees from Carnegie Mellon’s School of Computer Science and serves as head of Technical AI Engagement at the Institute for Ethics in AI and Professor of Computer Science and Philosophy at the University of Oxford.

Conitzer said that is remarkable that the foundation laid by Nash is still so key to game theory and so fruitful for ongoing research.

“In my lab, we consider interactions between AI agents. That would have been hard to imagine 75 years ago, and it does add a number of new twists that don't apply to human interactions,” Conitzer said. “But yet, the foundations of game theory are robust and flexible enough to adapt to this new setting and form a solid basis for our work.”

Carnegie Mellon recognized Nash’s accomplishments with an honorary degree in economics in 1999.

A lasting legacy

While John Nash is best known for the Nash Equilibrium, many mathematicians consider it a piece of his much broader legacy.

Later research in geometry and partial differential equations is widely regarded by mathematicians as his most important and deepest work. 

In 2015, Nash received the Abel Prize, mathematics’ highest honor, with Louis Nirenberg for “striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.”

“Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations,” wrote the Abel committee. “Their impact can be felt in all branches of the theory.”

Days after receiving the award in Norway, Nash and his wife, Alicia, died in a car accident in New Jersey. He was 86.