John von Neumann: The Man From the Future

By Paul Davis

The Man from the Future: The Visionary Life of John von Neumann. By Ananyo Bhattacharya. W.W. Norton & Company, New York, NY, February 2022. 368 pages, $30.00.

Members of the SIAM community may come to Ananyo Bhattacharya’s fresh and lively biography of John von Neumann—The Man from the Future—with a predictably positive bias. SIAM’s highest professional honor is the John von Neumann Prize, which is awarded for “distinguished contributions to the field of applied mathematical sciences and for the effective communication of these ideas to the community.” It was established to honor the Hungarian-American mathematician, physicist, and computer scientist whose seminal work helped found the field of modern computing. Winners are recognized at the SIAM Annual Meeting, where they deliver an associated flagship lecture; Leah Edelstein-Keshet of the University of British Columbia is the 2022 prize recipient.

For many of us, the foundations of our own research have at least one brick that has been shaped by von Neumann’s ideas. Bhattacharya’s account of von Neumann’s life, research, and varied collaborations will refine readers’ understanding of his impact on the larger scientific and social milieu in which he worked, as well as the continuing influence of his legacy long after his death.

Bhattacharya naturally begins with von Neumann’s birth in 1903 and his childhood among the elite in “sparkling Belle Epoch Budapest.” He honed a formidable intelligence among schoolmates like future economist William Fellner and physicist Eugene Wigner, in addition to older mentors such as Theodore von Kármán, a pioneer of fluid dynamics.

While preparing to leave high school (more precisely, “real school” — a variant of the European gymnasium) at the age of 17, von Neumann began his first major mathematical work. In a bold, early draft of what eventually became his doctoral thesis, he sought “to make Cantor’s ordinal numbers unambiguous and concrete.” The necessity of this task arose from the logical turmoil of Bertrand Russell’s famous set-theoretic paradox: Can the set of all sets that are not members of themselves be a member of itself? Russell’s paradox had materialized among the fallout from David Hilbert’s challenge to place all mathematics on an unshakable axiomatic foundation. The concepts of ordinality and cardinality that von Neumann developed in response to this challenge are still in use today.

Five years later and with a doctorate in hand (as well as a spare chemical engineering degree to relieve his father’s concerns about future employment), von Neumann followed a grant from the Rockefeller Foundation to Hilbert’s department in Göttingen — the center of the mathematical universe at the time. He stepped directly into another intellectual maelstrom: Werner Heisenberg’s matrix formulation of quantum mechanics was butting against Erwin Schrödinger’s wave theory amid no end of physically implausible behavior. Bhattacharya provides a vivid and accessible play-by-play account of the intellectual turmoil that von Neumann eased by deploying Hilbert’s spectral theory to reconcile the two apparently different mathematical formulations and begin untangling the physical conundrums.

The author’s rich account of quantum disputes among physics luminaries continues as he follows von Neumann to the University of Berlin, then to the University of Hamburg. In Berlin, the 23-year-old Privatdocent—the youngest ever appointed at the time—reveled in the city’s decadent post-war atmosphere. His childhood friend Wigner happened to be in Berlin at the same time, living as a scholarly hermit who only emerged to attend physics colloquia. He reported that von Neumann “was sort of a bon vivant, and went to cabarets and all that.”

In 1929, von Neumann moved briefly to Hamburg before receiving an invitation for a highly paid lectureship at Princeton University. He engineered a parallel invitation for Wigner, and the two arrived in the U.S. nearly simultaneously. Von Neumann was accompanied by both his new bride, Mariette Kövesi, and a prodigious reputation based on his foundational contributions to axiomatic set theory and quantum mechanics.

Wigner recounted that at their first meeting in America, he and von Neumann quickly “agreed that we should try to become somewhat American.” According to Wigner, the Johnny von Neumann who emerged “was a cheerful man, an optimist who loved money and believed firmly in human progress.”

With von Neumann in the U.S., Bhattacharya’s illuminating sketches of the personalities and events of early and mid-century European mathematics and physics expand to include America and the emergence of applied and computational mathematics during and after World War II. At this point, readers might feel as if they have stumbled into the story of a fictional time traveler from the Outlander series. Von Neumann somehow managed to be on location for every major mathematical happening; he was in Budapest long enough to start repairing an essential part of the foundations of mathematics, then moved to Göttingen just as Schrödinger’s cat began to prowl.

Once von Neumann crossed the Atlantic and plunged into America’s war efforts, his pace quickened. The mathematical traveler was in Los Alamos to compute shock waves within bomb detonators and dispassionately select targets for atomic bombs; in Aberdeen to automate the calculation of ballistics tables; in Princeton, Santa Monica, and elsewhere to develop game theory; and almost everywhere—Philadelphia, Poughkeepsie, and maybe even London for a surreptitious collaboration (who knows?) with Alan Turing—to crystallize the operational and design principles of stored-program computers.

Perhaps von Neumann’s most audacious stop was nominally in Pasadena, where he delivered the first major public presentation of his ideas about self-replicating automata. His abstract model was a universal Turing machine, and his thinking lay well ahead of what biologists knew about DNA and the mechanics of coding, copying, and replicating life forms. The entire conception seemed to draw science perilously close to science fiction — and to the future.

Throughout his book, the author’s descriptions of the surrounding scientific landscape are generally so deft and effective that readers may feel that they are learning more about the setting than the protagonist. On the other hand, Bhattacharya frequently blends the reach of the scientific challenges that intrigued von Neumann with accounts of his achievements in ways that ultimately provide shadowy silhouettes of both his character and his scientific powers. For readers of a certain age, this chronicle offers some of the same pleasures of reminiscing with an old family album and connecting legendary names, places, and events from previous generations to our own. It also reminds us of Hungary’s disproportionate gifts to 20th-century mathematics.

In addition, these accounts prompt questions—perhaps many are unanswerable—about the man, his life, and his work. Would von Neumann’s decisive selection of atomic bomb targets in Japan have been so dispassionate if Germany were still fighting? Would his classic Theory of Games and Economic Behavior with economist Oskar Morgenstern have ventured beyond collaborative games if he were not the quintessential centered European? If von Neumann had lived into the 1970s, might he have spoken of the RAND Corporation and its clones in a paraphrase of his famous comment about the relative simplicity of mathematics: “If you think your simple mathematical model explains everything, you don’t understand how complicated life is”? What ideas might he pour across a colloquium’s video screen today?

Von Neumann may indeed have been The Man from the Future who returned to steer his era toward what he had seen. Bhattacharya’s sweeping and well-informed biography makes an even better case that von Neumann was a genius of multiple talents who had sensed the future but never seen it fully. His conception of the future was sometimes imperfect, but it was shaped so well that disparate segments of the scientific and technical community could pull it toward realization, shape it to meet new complexities, and ride it to new opportunities. Bhattacharya adroitly describes many of the challenges that occupy applied and computational mathematicians while recounting one of our profession’s most important origin stories to a broader audience.¹ 

---

¹ Readers can find more specialized accounts in the accompanying article, “SIAM and John von Neumann.”

Paul Davis is professor emeritus of mathematical sciences at Worcester Polytechnic Institute.