Richard Feynman

Richard Feynman Uses Runge-Kutta Methods to Approximate Solutions to Differential Equations, a Rare Manuscript Page from the Nobel Prize Winning Physicist at the Dawn of the Computer Age

Nobel-Prize-Winning Physicist Feynman Develops Computing Steps to Use Runge-Kutta Methods to Approximate Solutions to Differential Equations


RICHARD P. FEYNMAN, Manuscript Document. Steps for approximating solution to a differential equation. 2 pp., 5.5" x 7.75", in red ink. Very good.


Feynman illustrates how a computer program can approximate a solution to a differential equation using a first-order Runge-Kutta method and a second-order Runge-Kutta method. Both pages also include flow diagrams and a numbered sequence of computer commands.


Developed around 1900 by German mathematicians Carl Runge (1856-1927) and Martin Kutta (1867-1944), the Runge-Kutta methods are a group of iterative methods that include the Euler Method to arrive at approximate solutions of ordinary differential equations. Leonhard Euler (1707-1783) was a Swiss mathematician and physicist who published his namesake method in a 1768 work; it is a numerical method to solve first order first degree differential equations with a given initial value and has often served as a basis for the construction of more complex methods.


Prior to a small archive of Feynman’s papers hitting the market, only one single page manuscript appeared in the auction rooms, selling for $15,000 at Sotheby’s in 2008.  Also, at RR Auction in 2018, a tiny signed sketch the size of a quarter sold for over $6,000!  The most recent small group that arrived on the market fetched astounding prices, even up to $125,000 per page.  Here is an opportunity to acquire a genuine handwritten Feynman manuscript with stellar provenance at a reasonable price.  He is sure to be as celebrated and revered as Einstein. 



Richard P. Feynman (1918-1988) was born in New York City into a Lithuanian Jewish family who were not religious. He received a bachelor’s degree in physics from the Massachusetts Institute of Technology in 1939 and a doctorate in 1942 from Princeton University, where he studied under John Archibald Wheeler. In March 1943, Feynman joined the Manhattan Project in work on the atomic bomb at Los Alamos, New Mexico, where he was a group leader in the Theoretical Division. After the war, Feynman joined the physics faculty at Cornell University. At a 1948 conference, he first used his namesake “Feynman diagrams,” pictorial representations of the mathematical expressions describing the behavior of subatomic particles. Initially rejected, Feynman diagrams ultimately revolutionized nearly every aspect of theoretical physics. As a formal language, Feynman diagrams are applied primarily to quantum field theory but can also be used in solid-state theory. After spending a sabbatical year in Brazil, Feynman joined the faculty at the California Institute of Technology in 1952, where he became a popular professor and advisor to dozens of graduate students. He also popularized physics through lectures, often published as books.  He shared the 1965 Nobel Prize in Physics with Julian Schwinger and Sin-Itiro Tomonaga for their “fundamental work in quantum electrodynamics.”



Ex-Richard Feynman Papers, Sotheby’s.




Item: 65837

Price: $15,000.00
Richard FeynmanRichard FeynmanRichard Feynman
Richard Feynman
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