“The world will never know what has happened—what a light has gone out,” the belletrist Lytton Strachey, a member of London’s Bloomsbury literary set, wrote to a friend on January 19, 1930. Frank Ramsey, a lecturer in mathematics at Cambridge University, had died that day at the age of twenty-six, probably from a liver infection that he may have picked up during a swim in the River Cam. “There was something of Newton about him,” Strachey continued. “The ease and majesty of the thought—the gentleness of the temperament.”

Dons at Cambridge had known for a while that there was a sort of marvel in their midst: Ramsey made his mark soon after his arrival as an undergraduate at Newton’s old college, Trinity, in 1920. He was picked at the age of eighteen to produce the English translation of Ludwig Wittgenstein’s “Tractatus Logico-Philosophicus,” the most talked-about philosophy book of the time; two years later, he published a critique of it in the leading philosophy journal in English, Mind. G. E. Moore, the journal’s editor, who had been lecturing at Cambridge for a decade before Ramsey turned up, confessed that he was “distinctly nervous” when this first-year student was in the audience, because he was “very much cleverer than I was.” John Maynard Keynes was one of several Cambridge economists who deferred to the undergraduate Ramsey’s judgment and intellectual prowess.

When Ramsey later published a paper about rates of saving, Keynes called it “one of the most remarkable contributions to mathematical economics ever made.” Its most controversial idea was that the well-being of future generations should be given the same weight as that of the present one. Discounting the interests of future people, Ramsey wrote, is “ethically indefensible and arises merely from the weakness of the imagination.” In the wake of the Great Depression, economists had more pressing concerns; only decades later did the paper’s enormous impact arrive. And so it went with most of Ramsey’s work. His contribution to pure mathematics was tucked away inside a paper on something else. It consisted of two theorems that he used to investigate the procedures for determining the validity of logical formulas. More than forty years after they were published, these two tools became the basis of a branch of mathematics known as Ramsey theory, which analyzes order and disorder. (As an Oxford mathematician, Martin Gould, has explained, Ramsey theory tells us, for instance, that among any six users of Facebook there will always be either a trio of mutual friends or a trio in which none are friends.)

Ramsey not only died young but lived too early, or so it can seem. He did little to advertise the importance of his ideas, and his modesty did not help. He was not particularly impressed with himself—he thought he was rather lazy. At the same time, the speed with which his mind worked sometimes left a blur on the page. The prominent American philosopher Donald Davidson was one of several thinkers to experience what he dubbed “the Ramsey effect.” You’d make a thrilling breakthrough only to find that Ramsey had got there first.

There was also the problem of Wittgenstein, whose looming example and cultlike following distracted attention from Ramsey’s ideas for decades. But Ramsey rose again. Economists now study Ramsey pricing; mathematicians ponder Ramsey numbers. Philosophers talk about Ramsey sentences, Ramseyfication, and the Ramsey test. Not a few scholars believe that there are Ramseyan seams still to mine.

Philosophers sometimes play the game of imagining how twentieth-century thought might have been different if Ramsey had survived and his ideas had caught on earlier. That exercise has become more entertaining with the publication of the first full biography of him, “Frank Ramsey: A Sheer Excess of Powers” (Oxford), by Cheryl Misak, a philosophy professor at the University of Toronto. Drawing on family papers and records of interviews conducted four decades ago for a biography that was never written, Misak tells a more colorful story than one might have thought possible so long after such a short life ended.

Ramsey’s father, Arthur, claimed that Frank, his eldest child, learned to read almost as soon as he could talk. His political sense was precocious, too. One day, little Frank told his mother, Agnes, that his younger brother, Michael, was, unfortunately, a conservative:

You see, I asked him, “Michael are you a liberal or a conservative?” And he said “What does that mean?” And I said “Do you want to make things better by changing them or do you want to keep things as they are?” And he said—“I want to keep things.” So he must be a conservative.

The two brothers later diverged in religious matters as well. Frank was an atheist by the age of thirteen; Michael entered the Anglican Church and became the Archbishop of Canterbury.

By the last year of Frank’s school days, he was apparently consuming books about economics, politics, physics, logic, and other subjects at a rate of almost one a day. On the holidays, he learned German, so that he could read some volumes of mathematics and philosophy in their original language. In his aptitude for math, he followed his father, a Cambridge mathematician and the author of textbooks in math and physics. But Frank’s temperament—he became known for his jovial spirits and loud, infectious laugh—was in marked contrast to that of his father, who was less notable for his academic work than for his sulkiness, quarrels, and rigidity. An obituary notice in the records of Magdalene College, where Arthur Ramsey was second-in-command for twenty-two years, described his rule as “austere.” In childhood, Frank’s way of dealing with his father’s foul moods was to slip calmly out of the room whenever the going got rough. Perhaps it was this pacific ease that, later in life, enabled Ramsey to cope better than most with Wittgenstein’s frequent fits of tormented umbrage.

At a time when few women went to university, Agnes Ramsey studied history at Oxford, and also attended the logic lectures of Charles Dodgson (better known as Lewis Carroll). She had been among the little girls whom Dodgson liked to take boating. More progressive than her husband, Agnes was an activist for left-wing and feminist causes. Frank was similarly inclined; at school, he was seen as an “ardent Bolshevik.” At university, he became involved in local politics and was a keen, though undoctrinaire, member of the Socialist Society.

The Ramseys were part of an intellectual aristocracy, in which Frank was comfortable from a young age. After his first meeting with Keynes, in Cambridge, Ramsey recorded that he found him “very pleasant”; on a walk, they had talked about the history of economics, the lamentable state of probability theory, and the difficulty of writing. Ramsey was seventeen at the time; Keynes was advising the League of Nations and the Bank of England, and lunching with Winston Churchill.