Beautiful Minds

Being a mathematician in the 1900s was not an occupation that many people envied. Mathematicians often didn’t have much money, and by this point in history, it seemed like there was nothing new under the sun in terms of ideas or concepts to explore in the field. John Von Neumann, a Hungarian-American mathematician, was not fazed. He was determined to be unique and to study an interesting field within the seemingly boring subject of math. Although he made several contributions in more mainstream areas of mathematics, such as set theory (Poundstone), his most famous contributions were in the world of game theory. 

Inspired by his father’s banking career, Von Neumann quickly memorized several numerical patterns and became gifted at logistical math at a young age. Von Neumann was particularly talented in economics, quantum theory, and, most significantly, game theory. One of the puzzles he solved earlier in his career, for which he gained recognition, was the fly and bicycles puzzle. This fame didn’t come from the difficulty of the problem, as achieving the correct answer was relatively straightforward (the problem is below, in case you want to try it): 

“Two bicycles are traveling toward each other at the same speed until they collide; meanwhile, a fly is traveling back and forth between them, also at a constant speed. The bicycles start 20 miles apart and travel at 10 miles per hour, and the fly travels at 15 miles per hour. How far does the fly travel in total?” (Guillaume Chereau Website). 

Instead, he became famous for the way that he solved the problem. While the average person (myself included) would try a few approaches before realizing that the total time is one hour and multiply this by the speed of the fly (15 x 1 = 15 miles total), Neumann came up with the answer almost immediately with a different approach. At first glance, this appears to be almost impossible: What kind of madman would add up the distance of every interval that the fly flew and get the answer right away? Ironically, this is exactly what Neumann did. He had computed the sum of an infinite geometric series almost instantly, using geometry by plotting points on the intervals in a triangle, and using the distance of the first interval and the corresponding ratios to use the infinite series formula 1/1-r, all in his head. 

His brilliance and ingenuity didn’t stop there. He was also the pioneer and verifier of the minimax algorithm, the optimal strategy of a two-player zero-sum game (Chen et al.). The minimax algorithm has two main siblings: the Maximax algorithm and the maximin, but the minimax algorithm is the most optimal one to follow for this kind of game because cooperation is not possible and only one person can win in a two-player zero-sum game. The minimax algorithm is a revolutionary but relatively simple rule that follows the move path in a game that minimizes the maximum possible loss. Usually, situations in a game are assigned different number evaluations by engines, and engines derive the best move by utilizing the minimax algorithm and other factors in order to determine what the most optimal next move would be. It applies to many different strategic board games, including a millennia-old game that I specialize in: chess. Engines have simulated millions of games and have assigned numerical valuations for certain positions, pieces, and rank moves in a hierarchical order based on which moves lead to more favorable positions. Then, they play the moves that are the highest on their ranking. One instance of this is when an engine gives the starting position evaluation as +0.2, which means that White is slightly better in the position, and the moves that can be played from the starting position can change the evaluation. +0.2 in the position assumes that the best next move is played. 

Among Neumann’s many extraordinary contributions, it’s clear that his intellect and influence were great. While his convictions, particularly his support for the development of nuclear weapons and the militarization of scientific research, may be viewed as controversial, they reflect the complex context of his time and the weighty decisions faced by scientists of his era. His life serves as a powerful reminder that intellectual brilliance must be guided by ethical reflection. As we celebrate the immense legacy he left behind, we are also encouraged to pursue future innovations with a deep commitment to aligning scientific progress with moral responsibility.

Works Cited

Chen, Janet, et al. “Strategies of Play.” Game Theory, 2019, cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/Minimax.html.

“How Did John von Neumann Solved the Fly and Bicycles Puzzle?” Guillaume Chereau Website, 10 Apr. 2024, gcher.com/posts/2024-04-10-von-neumann-fly/. Accessed 17 May 2025.

Mérő, László. “John von Neumann’s Game Theory.” Moral Calculations, 1998, pp. 83–102, https://doi.org/10.1007/978-1-4612-1654-4_6.

Poundstone, William. “John von Neumann | Biography, Accomplishments, Inventions, & Facts.” Encyclopædia Britannica, 22 Apr. 2019, http://www.britannica.com/biography/John-von-Neumann.

Wikipedia Contributors. “John von Neumann.” Wikipedia, Wikimedia Foundation, 19 Nov. 2019, en.wikipedia.org/wiki/John_von_Neumann.