Who Was Frank Ramsey?

By James Case

Frank Ramsey: A Sheer Excess of Powers. By Cheryl Misak. Oxford University Press, Oxford U.K., March 2020. 544 pages, $32.95.

Frank Plumpton Ramsey was born in February 1903 and died in January 1930, leaving behind a wife and two infant daughters. He is remembered as a towering genius—compared by some to Isaac Newton—who made significant contributions to mathematics, economics, and philosophy during his short life. In Frank Ramsey: A Sheer Excess of Powers, Cheryl Misak explores his experiences and career.

Ramsey was born into the Cambridge branch of what is known as the British intellectual aristocracy. His father Arthur was a recognized mathematician who served as master (second in command) at Cambridge University’s Magdalene College for many years. Ramsey’s mother, Agnes Wilson Ramsey, was a university graduate at a time when few women attended college. She was politically liberal and active in feminist causes, the latter putting her in contact with the mother of John Maynard Keynes. Keynes was quick to recognize young Ramsey’s remarkable talent and made every effort to advance his career.

Ramsey was a schoolroom prodigy who stood at the top of virtually every class, despite being three years younger than most of his classmates. He won prizes at Winchester College (read: prep school) in Latin, German, and math, the latter of which was taught by L.M. Milne-Thomson, an emerging expert on fluid mechanics and aerodynamics. Ramsey considered him to be a “bad teacher and bad explainer,” but a generous soul who loaned him books like Louis Couturat’s Die Philosophischen Prinzipien der Mathematik and Hermann Weyl’s Raum, Zeit, Materie. According to his diary, those were but two of almost 50 books that Ramsey read between January and March during his final year at Winchester.

Even before his last year at the school, Ramsey was well acquainted with Principia Mathematica, a multi-volume treatise by Alfred North Whitehead and Bertrand Russell on the foundations of mathematics. Fascinating though it was, it seemed to raise more questions than it answered. However, it did ignite Ramsey’s lifelong interest in the foundations of mathematics, economics, probability, and knowledge itself. The latter topic belongs to philosophy, and it is as a philosopher that Ramsey is best remembered today.

Upon graduating from Winchester in 1920, Ramsey enrolled in Trinity College, Cambridge to study mathematics. At Keynes’ behest, he was soon invited to join the Apostles, a somewhat elite debating society at the university. He also explored several other undergraduate debating societies that dotted the Cambridge landscape, including the famed Cambridge Union. It was their debates, which primarily consisted of aspiring politicians, that Ramsey found uninteresting; Keynes’ Political Economy Club and the so-called “Heretics Society” were more to his liking. He spoke and/or “read papers” at a number of the meetings before confiding to his diary that he loathed his “perverted ambition” to excel at debating merely for “recognition.” The purpose of debate, Ramsey felt, was to generate insights that might lead listeners a bit closer to whatever truth they were seeking. He also attended almost every meeting of a socialist organization known as CUSS during his first year at school.

Ramsey met most of his lifelong friends at Cambridge, including his eventual wife. She was the treasurer of the Heretics Society, and he thought her both beautiful and “nice” upon their first meeting. They did not get together right away but remembered each other well when their paths crossed again.

When he first arrived at Cambridge, Ramsey was seriously considering a career in economics. However, he was soon persuaded that there was more glory—and more lasting glory—in the venerable Mathematical Tripos. While a mind like his might exhaust a subject like economics in just a few years, math would always provide appropriately daunting challenges. As such, Ramsey chose to pursue a degree in—and later teach—mathematics, all while dabbling in economics, probability, and whatever else caught his fancy. But his passion was always philosophy, and he had hoped to complete his magnum opus in this subject by the age of 30.

As an undergraduate, Ramsey was asked to translate Ludwig Wittgenstein’s all but incomprehensible Tractatus Logico-Philosophicus into English. Upon seeing the result, Wittgenstein declared Ramsey to be the only person in the world who understood his book. After finishing the Tripos in 1923, Ramsey travelled to Vienna. There he met Wittgenstein, was befriended by several members of the wealthy Wittgenstein family, and underwent psychoanalysis (by an associate of Sigmund Freud) to relieve him of his anxieties concerning sex. Ramsey became a fellow of Kings College in 1924, was appointed as a university lecturer in mathematics in 1926, and later became Director of Mathematical Studies.

Misak, a professor of philosophy at the University of Toronto, is eminently qualified to comment on Ramsey’s philosophy, his life and times, the circumstances surrounding his untimely death, and his on-again-off-again relationship with Wittgenstein. She does all of this in welcome detail. However, she is not a mathematician, economist, or expert in probability and has therefore enlisted several specialists in Ramsey’s fields to provide brief summaries of his more lasting achievements. Perhaps the most interesting of these, at least for SIAM members, was written by the late Ron Graham about “Ramsey theory,” which builds on a theorem that Ramsey proved in a paper published posthumously in 1931. One of the theory’s consequences concerns a complete graph on \(n\)-vertices, each edge of which is colored either red or blue. If \(n \ge 6\), one of the triangles in the graph must be either all red or all blue. Thus, 6 is the “Ramsey number” for the monochromatic triangle property; \(n \ge 18\) for the monochromatic quadrilateral and \(43 \le n \le 48\) for the monochromatic pentagon. Graham asserts that there seems to be little hope of anyone ever finding the Ramsey number for monochromatic hexagons. Other Ramsey numbers, associated with additional graph-theoretic properties, have been found. The subject lay largely dormant until 1947, when Paul Erdős introduced his powerful “probabilistic method” for establishing bounds for Ramsey numbers on graphs.

Another summary concerns Ramsey’s paper on “Truth and Probability,” also published posthumously in 1931. Ramsey argued that one need not infer probabilities from a record of past events when placing bets on the occurrence of one or more inherently unpredictable eventualities, such as the potential orders of finish in a horse race. Subjective probabilities are simply numbers that are meant to reflect a person’s degree of confidence that a certain event or combination of events will occur. A carelessly formulated (i.e., internally inconsistent) list of probabilities is all but certain to include the ingredients of a Dutch book — a combination of wagers that guarantee the bettor a sure profit. There will be no such book only if the assigned probabilities obey Bayes’ rule \(P(A \& B)=P(A|B)P(B)\) for each pair \((A,B)\) of potential outcomes. Although Bruno de Finetti is usually credited for this observation, careful scholarship reveals that Ramsey got there first!

Ramsey’s two contributions to economic theory were just as pathbreaking and are equally well described by guest commentators. The first concerned an optimal tax code—one that raises a target amount of revenue with minimal damage to public utility (also known as satisfaction)—while the second identified an optimal allocation of current national income between present consumption and future investment. Both ideas were too mathematical to be understood by economists of the day (the first utilized a Lagrange multiplier and the second employed the calculus of variations). However, thanks to later economists who rediscovered them in the aftermath of World War II, the concepts are now recognized precursors of presently active subdisciplines.

To address Ramsey’s findings in the field of philosophy, Misak quotes several living philosophers, all of whom arrived at some illuminating new insight — only to find that Ramsey had beaten them to it. She has crafted the sort of in-depth intellectual biography that, regrettably, will likely never be written about John von Neumann. Having been born in the same year, the two were almost exact contemporaries and were launched on parallel career tracks by the time of Ramsey’s death in 1930. Ramsey was a don at age 21 and von Neumann was the youngest privat-docent in German history. It was possible for Misak to write such a book because interviews that were recorded more than 40 years ago for a never-written biography of Ramsey remain intact, and because many of the notes he exchanged with friends and colleagues are preserved. It seems implausible that one could assemble a similar trove of material on von Neumann.

It is interesting to speculate about the path that history might have taken if von Neumann had died in 1930 while Ramsey lived on. They shared an interest in the foundations of mathematics, and Ramsey likely would have been just as quick as von Neumann to appreciate the significance of Kurt Gödel’s theorems. He would also have known of Alan Turing’s solution to the Entscheidungsproblem, on which he himself had already begun to work. Ramsey would almost certainly have been assigned to the code-breaking unit at Bletchley Park—along with Turing, his teacher Max Newman, and several Cambridge colleagues—after the outbreak of World War II. While there, he would surely have been cognizant of Colossus, the world’s first fully programmable computer. But unlike von Neumann, he would not have been at Los Alamos to work on the atom bomb, and his interest in computer development might or might not have survived the war.

All that aside, Misak has written a splendid biography of a rare genius who might have accomplished far more had he been granted his biblical three score years and ten.

James Case writes from Baltimore, Maryland.