Real life mathematics . . . requires barbarians: people willing to fight, to conquer, to build, to understand, with no predetermined idea about which tool should be used.
—Bernard Beauzamy
That would have to wait. Not even the most important master’s thesis ever written and publishable work in genetics were enough for a PhD. Like every other MIT student, Claude Shannon had to pass his mandatory language exams. So he returned to Cambridge, and in between his teaching duties in the mathematics department and his first sketches on telegraphs, telephones, radio, and TV—whatever a mathematician might have to say about four means of communication that had precious few “fundamental properties” in common—he wrote out his stacks of flash cards. French was easier; he failed German before passing on the second try.
In the midst of a thoroughly numeric life, his recreations were the opposite. He developed a passion for jazz, especially for the improvisations he called “unpredictable, irrational.” In Gaylord, he played brass horn in the marching band; in Cambridge, jazz clarinet in his room. Playing backup to his record collection was his main distraction from the “intelligence” project, which increasingly cost him late nights and late mornings rolling out of bed. He put up with two roommates in an apartment at 19 Garden Street, not far from Harvard Square. We can imagine him forced up from his desk by the low roar of conversation whenever they threw a party, unpracticed in small talk, fond of walls and doorways. In fact, he was standing in his doorway at just such a party when a popcorn kernel hit him in the face.
Norma Levor, who threw the popcorn to get the attention of the tall, silent young man in the doorway, was only nineteen, but she was easily the most worldly person Shannon had ever known. She was born in a penthouse on New York’s Central Park West, her mother the heir to a pincushion fortune, her father an importer of fine Swiss fabrics. Tutelage in Upper West Side left-wing politics from her cousin, a “red” Hollywood screenwriter and playwright, and her sister at Columbia Law (where the radical students were Trotskyists, she said, and the mainstream students were just regular communists), then a summer in Paris as a reporter before her parents brought her home in advance of war (“That’s why I was there,” she told them, but they wouldn’t listen), then on to study government at Radcliffe, and then on to this terribly boring party, where a gaunt young man was standing at the edge of his bedroom, listening to his own jazz on his own record player.
“Why don’t you come out here where everybody is?” she asked. He answered, “I like it here, got some great music.”
“Bix Beiderbecke, you got him?”
“My favorite.”
And that was that. Norma was drawn, she recalled, to Claude’s “Christ-like” looks. Christ by way of El Greco, maybe, stretched out across a long frame—but Norma had good taste in most things. And Claude had twenty-four-hour access to the differential analyzer room. It was the scene of much of their courtship, compressed as it was—too short, probably, for Norma to weigh the costs of leaving school, or to discover anything in Shannon’s personality other than the odd genius that was his universal first impression, and so short that Claude’s entire experience of romance before marriage was the first unstable flush of early-twenties love. Liberal and uninhibited as Norma was, she was the obverse of everything he had left behind in leaving Gaylord. “We spoke to each other in our own private intellectual-silly language,” she wrote. “He loved words and repeated ‘Boolean’ over and over for the sound of it.” He wrote her poems, some naughty, all lowercased in the style of e. e. cummings. She said she was a third-generation atheist. He replied, “How can you be anything else?”
They were inseparable to begin with, to the point that Norma ran into “big trouble” sneaking back in the mornings to her Radcliffe dorm. In the beginning, Claude “was so loving and so darling and so funny and so sweet, so full of fun and such a joy to be with, so great all the time, night and day for months and months and months.” The popcorn hit him in the face in October 1939; January 10, 1940, was their wedding day, in a Boston courthouse with a justice of the peace. The honeymoon in New Hampshire was only marred by an anti-Semite hotel keeper who denied them a room (Norma was Jewish; Claude apparently looked it).
Shannon seemed pleasantly befuddled with the speed with which it had all happened. He wrote to Bush, “I did not, as you may have anticipated, marry a lady scientist, but rather a writer. She was helping me with my French (?) and it apparently ripened into something more than French.”
In the spring, he put on cap and gown to celebrate his simultaneous master’s and doctoral degrees, and the National Research Fellowship he had won, with Bush’s help, to spend the following academic year at the famous Institute for Advanced Study (IAS) in Princeton. Asked how the prestigious fellowship came about, he was more than usually sarcastic: “Well, I applied for it and that’s how it came, you applied for these things. Tell them how great you are, how smart you are.” Norma left her senior year at Radcliffe to follow him—not an unusual decision for a wife in those days, but one that would prove progressively more galling. In her own fields of left-wing politics and writing, Norma’s intellectual ambitions were a match for her husband’s, but they were put on hold.
Before Princeton, though, the pair would have a brief summer’s stop in Norma’s childhood home: Manhattan. The summer of 1940 was Claude’s second invitation to the Bell Laboratories. Now, though, he returned not as a first-year graduate student but as an award-winning PhD with Vannevar Bush as a patron. He was headed to what was perhaps the world’s foremost technology company—and the home of the best communications minds in America.
Had he wanted, Shannon could have continued the glide path through academia, collecting fellowships, amassing awards, and working his way to tenure and a lifetime of professorial comfort. But Shannon had proven himself the kind of mathematician who could stand on his own two feet outside the academy, whose work might result in more than a university chair. Shannon’s foremost mentor, Bush, understood this, too, and he set out to shape the course of Shannon’s life accordingly.
It helped, of course, that Vannevar Bush was, at the time, the high priest of applied mathematics. He may not have groomed Shannon explicitly in his own image, but he understood that Shannon’s talents, properly harnessed, would serve him well outside of a university setting, the same way Bush’s talents had taken him to a position of national prominence. It was Bush who had hired Shannon to work on the differential analyzer; Bush who pushed Shannon to apply his studies in mathematical logic to theoretical genetics; and Bush who, in 1938, put Shannon to work on the microfiche rapid selector, a “light-sensing reader system to allow speedy retrieval of microfilmed information”—a far cry from any of Shannon’s graduate work, but yet another chance to force his student to flex his mathematical muscles in an unfamiliar domain. Bush, too, had a tinkerer’s instinct, and he set to work on Shannon as a tinkerer might: a fresh problem here, a new research topic there, and eventually Shannon would be transformed into an applied mathematician of the first rank.
After his acceptance to the Institute for Advanced Study, but before leaving for Bell, Shannon wrote to Bush seeking career advice. Bush was emphatic: “The only point I have in mind is I feel that you are primarily an applied mathematician, and that hence your [research] problem ought to lie in this exceedingly broad field rather than in some field of pure mathematics.”
But Bush wasn’t the only one who understood that Shannon’s true potential lay somewhere other than pure math. Thornton C. Fry, head of the Bell Labs mathematics group, had taken notice as well. Fry was “a very careful and formal person.” That was the charitable way of saying he was a stiff: while working at the National Center for Atmospheric Research, he “rather frowned on the informal western clothing of the NCAR staff,” though “this never influenced his respect for their work.” Fry’s manner reflected his roots as the son of an Ohio carpenter. By 1920, he had managed to escape the family trade and had finished a tripartite PhD in mathematics, physics, and astronomy.
It was a combination of luck and skill that helped Fry turn that training into a job at Western Electric, AT&T’s equipment manufacturer and one of the country’s leading engineering organizations. Interviewed by Western Electric’s research chief, Fry was caught unusually flat-footed by the questions. He wanted to know: how familiar was Fry with the work of the era’s most influential communications engineers? As Fry later recalled his fiasco of an interview: “Had I ever read the works of Heaviside? I’d never heard of Heaviside. . . . He asked me if I had ever heard of Campbell. I’d never heard of Campbell. I think he asked me if I’d ever heard of Molina. I hadn’t. Whatever he asked me, I hadn’t.” Still, something about this too-formal young man was impressive; Western Electric rolled the dice and gave Fry the job. He excelled at it, and after the Western and AT&T research divisions were spun off to form Bell Labs, Fry found himself running the Labs’ mathematics research group.
Bell Labs “was where the future, which is what we now happen to call the present, was conceived and designed,” wrote Jon Gertner in The Idea Factory, his history of the Labs. Other appraisals struck a similar note: “the crown jewel”; “the country’s intellectual utopia.” By the time Shannon joined Bell Labs, the curious mix of techniques, talent, culture, and scale had turned the modest R&D wing of the phone company into a powerhouse of discovery. It was an institution that churned out inventions and ideas at an unheard-of rate and of unimaginable variety. In Gertner’s words, “to consider what occurred at Bell Labs . . . is to consider the possibilities of what large human organizations might accomplish.”
Its founder was a tinkerer of an earlier era: Alexander Graham Bell. United States Patent No. 174,465—for “the method of, and apparatus for, transmitting vocal or other sounds telegraphically . . . by causing electrical undulations, similar in form to the vibrations of the air accompanying the said vocal or other sound”—earned Bell the title “inventor of the telephone,” worldwide recognition, and a considerable fortune. He founded a phone company, American Telephone & Telegraph (AT&T), whose goal was suitably immodest: turn Bell’s invention into a nationwide network of phones, lines, and transmitters. The result: within a decade, the telephone went from lab demonstrations to a fixture in 150,000 American homes. By 1915, the network was a marvel of human engineering, a continent-spanning web that allowed for transcontinental communication at a time when physical travel from coast to coast still took nearly a week.
In 1925, Bell Labs was carved out of the phone company as a stand-alone entity, with custody shared jointly by AT&T and Western Electric. Walter Gifford, the president of AT&T, observed that the Labs, while nominally an arm of the phone company, could “carry on scientific research on a scale that is probably not equaled by any organization in the country, or in the world.” The goal of Bell Labs wasn’t simply clearer and faster phone calls. The Labs were tasked with dreaming up a future in which every form of communication would be a machine-aided endeavor.
So-called basic research became the Labs’ lifeblood. If Google’s “20 percent time”—the practice that frees one-fifth of a Google employee’s schedule to devote to blue-sky projects—seems like a West Coast indulgence, then Bell Labs’ research operation, buoyed by a federally approved monopoly and huge profit margins, would appear gluttonous by comparison. Its employees were given extraordinary freedom. Figure out, a Bell researcher might be told, how “fundamental questions of physics or chemistry might someday affect communications.” Might someday—Bell researchers were encouraged to think decades down the road, to imagine how technology could radically alter the character of everyday life, to wonder how Bell might “connect all of us, and all of our new machines, together.” One Bell employee of a later era summarized it like this: “When I first came there was the philosophy: look, what you’re doing might not be important for ten years or twenty years, but that’s fine, we’ll be there then.”
The extraordinary freedom was a scientist’s dream, and the ability to work as they pleased drew together an astonishing set of minds. Bernard “Barney” Oliver, a Bell Labs researcher who would later head up research for Hewlett-Packard, recalled thinking, “Gee, you know, here I am, I’ve got the world’s knowledge in electrical engineering at my beck and call. All I’ve got to do is pick up the phone or go see somebody and I can get the answer.”
That accumulation of talent paid tremendous dividends. In the span of a few decades, Bell researchers invented the fax machine, touch-tone dialing, and the solar battery cell. They engineered the first-ever long-distance phone call and synchronized the sounds and images in movies. During the war, they improved radar, sonar, and the bazooka, and they created a secure line to allow Franklin Roosevelt to speak to Winston Churchill. And in 1947, Bell researchers John Bardeen, William Shockley, and Walter Brattain created the transistor, the foundation of modern electronics. The trio would earn a Nobel Prize, one of the six Nobels given to Bell scientists during the twentieth century.
It was one thing for an industrial laboratory to hire qualified PhDs and put them to work on various pressing engineering problems. But Nobel Prizes? Pie-in-the-sky projects? Ten or twenty years of leeway? Even accounting for nostalgia, Thornton Fry’s judgment hardly seems out of place; looking back on the Labs, he called it “a fairyland company.”
Consider Clinton Davisson, Nobel laureate and Bell Labs researcher. Known as Davy, he was “wraith-like and slow-moving . . . an almost spectral presence.” A frail, quiet midwesterner who kept largely to himself, Davy was able to write his own ticket at the Labs. As Gertner put it, “he was allowed to carve out a position as a scientist who rejected any kind of management role and instead work as a lone researcher, or sometimes a researcher teamed with one or two other experimentalists, pursuing only projects that aroused his interest.” Importantly, “he seemed to display little concern about how (or whether) such research would assist the phone company.”
Bell Labs was neither a university nor a charity. And yet Davy was allowed to conduct endless experiments on the company dime, many of which had only the most tenuous tie to the bottom line. It’s telling that Davy’s Nobel Prize—awarded for proving that electrons moved in a wave pattern, knowledge gleaned by smashing a piece of crystalline nickel with electrons—won the Labs fame, but no incremental fortune. A mind like his—one that could have navigated its way into the academic career of his choosing—was considered useful to Bell executives, even if the precise use was fuzzy.
A rigorous investment in basic research meant that there were, at any given time, several Davys on the Labs’ payroll. Of course, freedom to research at will could be a burden, a kind of anxiety, in its own right. The thinkers who thrived at the Labs were those who, confronted with a nearly limitless field of questions, chose the “right” ones: the ones most fertile of breakthroughs in technique or theory, the ones that opened on broad vistas rather than dead ends. This choice of questions has always been a matter of intuition as much as erudition, the irreducible kernel of art in science.
Claude Shannon was one of those who thrived. Among the institutions that had dotted the landscape of Shannon’s life, it’s hard to imagine a place better suited to his mix of passions and particular working style than the Bell Laboratories of the 1940s. “I had freedom to do anything I wanted from almost the day I started,” he reflected. “They never told me what to work on.”
Thornton Fry hadn’t simply recruited Shannon to the Labs; he also assigned him to the math group, which Fry had crafted himself to ensure that the talent he recruited wasn’t wasted. Fry held strong views about the role of mathematicians within industry, and depending on one’s perspective, he was either a visionary or a heretic. In a long, thoughtful meditation published in the Bell System Technical Journal, Fry began by pointing out the obvious: there was, for all the enlightened teaching in university math departments, a near-total lack of industrial training for mathematicians who aspired to build things rather than simply think about things. “Though the United States holds a position of outstanding leadership in pure mathematics,” Fry wrote, “there is no school which provides an adequate mathematical training for the student who wishes to use the subject in the field of industrial applications rather than to cultivate it as an end in itself.”
It’s taken as a given in our era that a high-level math mind—a “quant”—can find gainful employment. But that wasn’t always the case, and especially not in the world of elite mathematics in the early twentieth century. What was valued in the highest levels of mathematics had precious little application outside of it. Solutions to abstract problems won glory, and thus whole careers were devoted to chasing solutions to problems like the Riemann hypothesis, the Poincaré and Collatz conjectures, and Fermat’s last theorem. These were the math world’s greatest puzzles, and the fact that decades had passed with no solution made them all the more tantalizing. They were taken dead seriously, and whether or not the solutions had any practical aim or application was an afterthought, if it was a thought at all.
Fry, himself a mathematics PhD, understood this better than most. “The typical mathematician,” Fry observed,
is not the sort of man to carry on an industrial project. He is a dreamer, not much interested in things or the dollars they can be sold for. He is a perfectionist, unwilling to compromise; idealizes to the point of impracticality; is so concerned with the broad horizon that he cannot keep his eye on the ball.
All of which left many a graduate student exceptionally well trained in a style of problem solving that had limited use outside of the mathematical fraternity. An industrial lab, then, had about as much use for a mathematician as a fish had for a bicycle—unless. . . .
Fry’s hunch was that not all mathematicians wanted to write papers and chase tenure. He also guessed that the right environment could play to their strengths and put them to work on practical things, set them on “everyday problems” and “concrete exploitation.” And he was among the few people in a position to make that happen—and to make his case for the “industrial mathematician” as a new breed of thinker-doer.
He baked his philosophy into the heart of the math group. His case was simple: the engineers of Bell Labs were “pathetically ignorant of mathematics,” but math, applied correctly, could help them work out complex problems in telephony. At the same time, the math group served as a catch-all for any gifted member of the Labs staff too odd to play well with others. “Mathematicians are queer people. You are and I am. That’s a fact,” Fry told a mathematically inclined interviewer. “So that anybody who was queer enough that you didn’t know what to do with him, you said, ‘This fellow is a mathematician. Let’s have him transferred over to Fry.’ ”
The math group under Fry’s leadership began as an in-house consulting organization, with mathematicians available as needed to the engineers, physicists, chemists, and others, but free to pick their own internal “clients.” They were there to offer advice and assistance; the management and messy realities of industrial projects could be left to others. As Bell Labs’ Henry Pollak observed, “our principle was that we’ll do anything once, but nothing twice.”
This gave the group a broad mandate, flexible even within the famously loose culture of Bell Labs. As one researcher from that era put it, “Our job was to stick our nose into everybody’s business.” In Fry’s words, “there was nothing that we weren’t entitled to work on if we wanted to.” Or as Shannon himself recalled, “I was in the mathematics research group which was kind of free-wheeling and not so oriented on projects as people trying to do individual research as fast as they could. . . . I enjoyed it more that way, where I was working on my own projects.”
In exchange for its independence, the math group acquainted itself with the phone company’s ways. The earliest members climbed telephone poles and operated switchboards. They mastered the mathematics of switching and solved thorny network problems. Like the rest of the Labs’ employees, they addressed one another exclusively by last names. In time, their hands-on experience combined with their training would enable them to delve deep into the underlying mathematics of communication engineering. The math group would eventually be regarded as a standout within the industry, and Fry’s vision would set the standard for the use of mathematical minds within a large private-sector concern.
Shannon was given a summer’s exposure to Bell Labs—and though few records of his summer there exist, we do know something of his output. Shannon’s work during this period is captured in two technical memoranda, both of which give a sense of how mathematical skills could meet the telephone company’s goals.
Shannon’s first effort was the “Theorem on Color Coding.” In a system as complex as the Bell telephone network, questions about the coloration of wires were a serious business. Shannon was tasked with finding an answer to the following puzzle:
There are a number of relays, switches, and other devices A, B, . . . , K to be interconnected. The connecting wires are first formed in a cable with the leads associated with A coming out at one point those with B at another, etc., and it is necessary, in order to distinguish the different wires, that all those coming out of the cable at the same point be differently colored. There may be any number of leads joining the same two points. We might have, for example, four wires from A to B, two from B to C, three from C to D and one from A to D. The four from A to B must all be of different colors, and all different from those from B to C and A to D, but the three from C to D can be the same as three of those A to B. Also the one from A to D can be the same as one from B to C. If we assume that not more than m leads start at any one point, the question arises as to the least number of different colors that is sufficient to color any network.
If this question has the flavor of “two trains leave the station at the same time . . . ,” it’s because problems like this lend themselves to the search for mathematical shortcuts. That’s what Shannon was after here: a workaround, something that would allow Bell engineers without advanced degrees in mathematics a quick and easy way to arrive at the minimum number of colors they needed for a network. And Shannon’s answer—multiply the number of network lines by 1.5; the greatest integer less than or equal to that value is the number of colors you need—was thorough and thoughtful and well proved. If it wasn’t the stuff of mathematical legend, it was still eminently useful. And unlike, say, an algebra of genetics or a meditation on symbolic logic and circuits, it could be put into immediate practice.
This was significant. The paper illustrates the ways in which the formal education of Claude Shannon the adult had mixed with the informal instruction of Claude Shannon the boy, the one whose childhood was spent happily playing with broken radios and makeshift elevators. And it shows that the part of his nature that was hardheaded and practical had remained firmly intact. It isn’t a stretch to imagine that solving this particular problem—technical and narrow though it may have seemed—gave Shannon a great deal of joy. It was, after all, an intricate puzzle. And it was reminiscent, as well, of a youth spent playing telegraph engineer, a kind of graduated version of building a barbed-wire network.
Shannon’s second effort, “The Use of the Lakatos-Hickman Relay in a Subscriber-Sender Case,” was an attempt to simplify and economize the relays Bell used to connect phone calls. It was the kind of work that called into question whether the Bell network’s system of relays, as currently constituted, was optimal, and whether there wasn’t a better way to make it operate. In other words, it was a kind of tinkering on the very largest scale, on the beating heart of the phone system. It led Shannon to think up two new options for circuits that drew on his master’s thesis work—“designed by a combination of common sense and Boolean algebra methods”—and though he was quick to acknowledge that each of his designs had its own flaws, he also defended them as superior to what was on offer.
When he first arrived at the Labs, Shannon had his doubts: Would an industrial laboratory constrain his ability to think big thoughts and dream up new ideas? After this summer’s work, those concerns were put to bed. The Labs had given him as broad a scope as he might have hoped for in a professional setting.
“I got quite a kick,” Shannon wrote to Vannevar Bush, “when I found out that the Labs are actually using [my] relay algebra in design work and attribute a couple new circuit designs to it.” As with a tinkerer who successfully flips the switch on his latest creation, it isn’t difficult to imagine Bush reading that sentence, sitting back, and smiling with satisfaction.