# What Is the Best Scientific Paper Ever Published?

"What is the greatest scientific paper ever published?"

Taken as worded, this is clearly an impossible question to conclusively answer, so we'll start by defining what exactly makes a paper "great."

Tony Padilla, an associate professor of physics at the University of Nottingham, provided a beautifully simple criterion in a recent episode of Numberphile: "impact per word." A short paper that was highly influential.

By that definition of "greatness" (which is, of course, open to debate) the best scientific paper ever written was probably John Nash's "Equilibrium Points in N-Person Games", published in January of 1950 to the *Proceedings of the National Academy of Sciences*. In just 333 words, Nash, then a 21-year-old graduate student at Princeton, outlined what became the cornerstone principle of game theory: the Nash equilibrium.

Nash would further elucidate the concept in his doctoral dissertation, published a year later. In essence, it states that in any competitive game or scenario, equilibrium is achieved when all of the players are making their best choices, whilst taking into account the strategies of all the other players. Motorists obeying traffic signals and driving on the right side of the road are two real-world examples of Nash equilibria. Nash demonstrated mathematically that these equilibria exist in any competitive situation with a finite number of players and strategies.

Nash developed his idea in the light of John von Neumann and Oscar Morgenstern's foundational work on game theory. When told of Nash's work, von Neumann initially dismissed it as "trivial," a tremendous blunder in hindsight.

"Game theory, with the Nash equilibrium as its centerpiece, is becoming the most prominent unifying theory of social science," economists Charles Holt and Alvin Roth wrote in 2004.

As veteran science writer Erica Klarreich summarized:

"The Nash equilibrium concept has become a benchmark by which economists and other scientists measure both rational behavior and the extent to which humans depart from pure rationality. Over the years, this concept has illuminated questions in economics, psychology, and even biology. In 1994, it earned Nash the Nobel prize in economics."

And now, in 2017, the Nash equilibrium has given Nash the distinction of authoring the greatest scientific paper ever published!