CHAPTER SEVENTEEN

The Victor’s Share

SOMETIME IN 1944, computers became “girls.” The University of Pennsylvania hired “girl computers”; Warren Weaver started calling Applied Mathematics Panel computers “girls”; Oswald Veblen, who had once led a team of computing men, used the term “girls”; George Stibitz began ranking calculating projects in “girl-years” of effort.¹ One member of the Applied Mathematics Panel defined the unit “kilogirl,” a term that presumably referred to a thousand hours of computing labor, though in at least one letter it suggested an Amazonian team of computers.² L. J. Comrie, in an article entitled “Careers for Girls,” stated that girls “can be made proficient and give good service [as scientific computers] in the year before they (or many of them) graduate to married life and become experts with the housekeeping accounts.”³ Even at this date, computing was not the sole domain of women. It was really the job of the dispossessed, the opportunity granted to those who lacked the financial or societal standing to pursue a scientific career. Women probably constituted the largest number of computers, but they were joined by African Americans, Jews, the Irish, the handicapped, and the merely poor. The Mathematical Tables Project employed several polio victims as computers, while the Langley research center kept an office of twelve African American computers carefully segregated from the rest of the staff.⁴

For all of the Applied Mathematics Panel computers, female and male, the end of the war was first glimpsed on September 25, 1944, when Warren Weaver received a letter reminding him that the National Defense Research Committee was “a war time agency which will go out of existence at the end of the war.” The letter informed the panel that they needed to prepare their plans for demobilizing the organization.⁵ There was scant military news to support the idea that the war was nearly over and that research was no longer needed. Germany, though in retreat, still commanded a strong military that could inflict substantial injury on Allied forces. Japan promised a long and bloody fight for the control of its home islands. Still, the senior leadership of American science felt that the last months of the war “would involve almost no research and very little development work.”⁶ They viewed the National Defense Research Committee as “an emergency organization” that “deserved to die a dignified death.”⁷

“For planning purposes,” Weaver told the members of the Applied Mathematics Panel, “we are assuming that Germany will fall by November 15, 1944.”⁸ Shortly after the end of the European war, the panel would start terminating research programs and liquidating contracts. The panel would have to provide guidelines on how project records should be preserved, which materials could be published, and when computing groups could be disbanded.⁹ As the panel developed its demobilization plans, Warren Weaver recorded that the members were “becoming deeply interested in the post-war possibility of the important new computing techniques, which are being developed during this war.” They discussed computing machines over an eight-month period, sometimes reviewing their progress as part of a formal meeting, at other times sharing speculations about Stibitz or Aiken or the Aberdeen Proving Ground over lunch. “Quite outside of the mere furnishing of labor-saving assistance,” Weaver explained, these machines “may, in fact, have theoretical consequences of very great significance.”¹⁰

In its discussions, the panel was beginning to recognize that there might be a substantial demand for computing services after the war. Weaver observed that the navy was using Aiken’s Harvard machine for three shifts a day, seven days a week. From this, he concluded that “two machines could be kept busy on [naval] Ordnance work alone” and that the navy should consider building “a central machine … under a broad agency in Washington.”¹¹ He argued that the navy should make this last machine available to both military and civilian researchers, as it might “take care of a variety of problems.”¹²

All of the major computing laboratories had a full load of requests that winter. The New York Hydrographic Office was completing LORAN tables for the Pacific Ocean. The group’s leader, Milton Abramowitz, had lost almost half of his staff, yet he had reduced the computing time from six weeks per table to four. He had received some help from the Mathematical Tables Project staff, to be sure, but he had achieved much of this improvement by developing a new method of preparing the tables.¹³

The Mathematical Tables Project found that it could add only a few numbers each week to the unfinished WPA volumes. It was handling about two dozen calculations at once. A computer might work on two or three or four assignments, advancing each a little each day. That winter, the big calculation was a rather gruesome optimization problem. It attempted to determine the “combination of [high explosive] and [incendiary bombs] that should be used for specific Japanese targets.” High explosives would shatter Japanese buildings but not set them on fire. Incendiaries would light fires, but the damage would be limited if the buildings remained intact. A well-planned combination of the two kinds of bomb would create firestorms that would destroy Japanese cities.¹⁴ The mathematical analysis of this problem had been assigned to Jerzy Neyman, who, again, had failed to meet his deadlines and keep his expenditures on budget. The Mathematical Tables Project computers had to work at a stiff pace in order to complete the work before the start of the Pacific bombing campaign in March 1945.¹⁵

With two years of experience, the Applied Mathematics Panel was becoming reluctant to label every computing problem as essential to the war effort. When General Electric requested thirty computers, the panel demurred. General Electric wanted these computers to prepare tables for the antiaircraft systems of the B-29 bombers, the planes that would lead the bombing campaign against Japan and would carry the atomic bomb. The work was important, but Warren Weaver informed General Electric that the Applied Mathematics Panel had no computers to spare and “suggested that [the company] use the computation facilities of some insurance company.”¹⁶

General Electric was not alone in its rejection. The Applied Mathematics Panel accepted few new problems that winter. Those that went from the panel to the Mathematical Tables Project or the Thomas J. Watson Astronomical Computing Bureau tended to be expansions of old calculations. The work was becoming routine, and hence it is probably not surprising that Warren Weaver became interested in an unusual problem that had no obvious mathematical solution. In March, he told the panel of an issue that was “being held very secret.” The secret would not last long, he informed them, because “all Police Departments in the US have been informed about it.” Nevertheless, the panel should treat the request as confidential, for any public discussion of the problem might incite panic among American citizens. Large balloons had been discovered across the country. They were constructed out of rice paper and were about thirty feet in diameter. Most had landed in Oregon and California, but several had made it over the Rocky Mountains and landed as far east as Michigan. They apparently came from Japan, but no one knew where they were launched or what they were designed to accomplish. Some members of the National Defense Research Committee believed that the Japanese planned “to use bombs in dry weather to start large scale forest or crop fires.” Others suggested that the balloons might be intended to carry poisonous gas or deadly viruses. Weaver could offer no theory of his own, though he argued that they must be weapons of last resort, as any damage to the United States mainland would be “a poor bargain in view of our demonstrated ability to put bombs on Japan.”¹⁷

Weaver asked the panel members to estimate the number of balloons that had reached North America, given “the number of recoveries which have been made and of the tolerable assumptions concerning the probability of recovery.” It seemed likely that most of the balloons were lost at sea and that many of the remainder had landed in remote sections of the coastal mountains or in the deserts of the western states. He also asked the mathematicians to consider “what other questions related to the problem can have rough numerical answers.”¹⁸ With hindsight, it is difficult to understand how Weaver’s announcement could have been anything more than a reaction to an unsettling piece of news. Given how little the military knew about the balloons, the Applied Mathematics Panel would have found it difficult to prepare a mathematical analysis of the attacks. Weaver’s response may have also been shaped by a growing anxiety among the members of the panel that “mathematics is not adequately represented” in the country’s plans for postwar science.¹⁹ President Roosevelt had recently announced a new organization, the Research Board for National Security, to coordinate scientific research after the war. Only a single mathematician, Oswald Veblen, had been appointed to this committee.

As a whole, the members of the Applied Mathematics Panel had no coherent vision for postwar mathematics. Few of their number showed any interest in building a new institution for postwar mathematical research. John von Neumann argued that mathematics should have no organizational hierarchy, as “decentralization would be the more efficient manner of organization.”²⁰ Richard Courant, from New York University, wanted a small executive body to coordinate research but warned that “the enthusiasm among capable scientists for war research will abate after a short time.” Organized mathematics research would have “no attraction whatsoever for scientists of high quality unless research can be conducted with as few strings attached as possible.”²¹ Only Warren Weaver seemed interested in promoting a government office for mathematical research, yet he described such an office only in terms of the way that it would operate. The American government should “set up laboratories in a place where scientific people like to be,” he stated. It would also have to “pay high salaries” and would need to “provide better materials and greater leisure than are commonly provided in government service.”²²

The death of Franklin Roosevelt in April introduced new uncertainty into the discussions of the Applied Mathematics Panel. “To many,” wrote historian David McCullough, “it was not just that the greatest of men had fallen, but that the least of men—or at any rate the least likely of men—had assumed his place.”²³ The mathematicians knew little about his successor, Harry Truman. No one knew how the new president felt about government sponsorship of science or whether he would be able to get the approval of Congress for any ambitious scientific program. The members of the Applied Mathematics Panel were somber when they convened their first meeting after Roosevelt’s death. Warren Weaver was ill, and Thorton Fry held the meeting at Bell Telephone Laboratories. They heard reports from several projects, approved a few minor actions, and accepted a request for calculations from New York University. They assigned the work to the Mathematical Tables Project but asked that Arnold Lowan “secure some time estimate” before starting the work. Just as the meeting broke up, the panel agreed that “meetings in the future [will] be held at intervals of 3 to 4 weeks until further notice.”²⁴

The mathematical work for the Second World War was coming to an end, but the future of the computing staffs remained undecided. The Applied Mathematics Panel did not even raise the issue until June, when Oswald Veblen suggested that the staff of the Mathematical Tables Project might be useful to the Research Board for National Security. Thornton Fry, still acting as chair, showed no enthusiasm for the idea, noting that there were many new computing machines, and “presumably after the war [they will] not be fully used.” He acknowledged “that if this group is broken up, it cannot be put together again,” but the only employment that he foresaw for Arnold Lowan, Gertrude Blanch, and the others was the preparation of “out of hour uses for these machines,” computations on the second or third shift.²⁵ Fundamentally, the panel did not give the computers the same professional status that they accorded mathematicians. When appointing a mathematician “to keep track of the types of analytical problems arising at Aberdeen; of the computing problems which are involved in these; and of their relations to modern computation devices,” they wanted the appointment to have a government rank of at least P-6, more than halfway up the professional appointment scale, and even a P-7 or “a P-8 is not absolutely excluded.”²⁶ When they dealt with the senior computers, who did the same kind of work, they had no such scruples. At the Mathematical Tables Project, Arnold Lowan held the highest rank at a P-5. Gertrude Blanch, who had already done the tasks required by the Aberdeen position, was a P-3. The rest of the Mathematical Tables Project planning committee held a P-2 or even a lowly P-1 ranking.²⁷

The first months of summer brought the initial skirmishes for the spoils of war, and when the fights were over, the results remained inconclusive for the Applied Mathematics Panel computers. The first trophies of the conflict were visits to the German scientific institutions, the rocket development center at Peenemünde, the large industrial laboratories along the Rhine, Werner Heisenberg’s nuclear research facilities. A select cadre of British, French, and American scientists followed the advancing Allied troops, seizing scientific documents, confiscating equipment, and interrogating research personnel. Often, these visits were an opportunity to greet old friends, to become reacquainted with a familiar scientific colleague who had been isolated from Allied researchers by the war. It was also a chance to look into the enemy’s lair and to evaluate the science that had been used against the conquering troops, the convoys of the North Atlantic, and the civilians of Europe.

The Allied generals did not consider computational laboratories to be of much importance until the British army mistakenly seized the German mathematician Alwin Walther. The British had confused Walther with a senior rocket engineer who had the nearly identical name of Helmuth Walter. When they took Alwin Walther to London for interrogation, the mathematician protested that he had nothing to do with the rocket program but actually operated a computing facility at the Technische Hochschule in the town of Darmstadt. To prove his claim, he produced a battered photograph, which he had been carrying for just such a situation. The picture showed him walking arm in arm with another man, who he claimed was the mathematician Richard Courant of the Applied Mathematics Panel.²⁸ The British military, looking for a mathematician to confirm or deny the story, turned to Olga Taussky, the consultant working with the Ministry of Aircraft Production.

Taussky interviewed Walther and concluded that he was telling the truth. Before Walther was released, she returned with her husband, John Todd of the Admiralty Computing Service, for a second interview. Walther told his interrogators that the Darmstadt facility was the largest computing office in Germany and that there was a second mathematical laboratory, the Mathematisches Reichsinstitut, or National Mathematics Laboratory, in Oberwolfach. He explained that the Oberwolfach offices had done mathematical analyses for aircraft design, ballistics trajectories, and the guidance systems of the V-2 missile. The Technische Hochschule at Darmstadt had served as a “calculating workshop” for the German military. Its researchers had developed a number of computing machines, including a differential analyzer, extensions to punched card tabulators, and a device that could solve systems of linear equations, though it was a very different machine from the one created by John Atanasoff. The Technische Hochschule also had a substantial computer staff and had produced a number of tables.²⁹ These stories intrigued Taussky and her husband. “Business was not as brisk at the Admiralty then as it had been earlier,” Todd reported, and hence he was free to travel. When he returned to the Admiralty offices, he discussed the German institute with his colleagues. Together, they “conceived an intelligence mission to investigate mathematics in Germany.”³⁰

From his work with the Admiralty Computing Service, Todd was familiar enough with the British war ministries that he could identify the individuals who might support a trip to the defeated Germany and could present the idea in a way that would gain their support. “Before the week was out we were officers in the Royal Navy Volunteer Reserve,” he reported, “with open orders and maps of all Germany.” They were instructed to visit “targets of opportunity,” which included the Mathematisches Reichsinstitut, the Technische Hochschule, and the University at Göttingen, long the premier training facility for mathematicians. Outfitted with naval commando uniforms and given a fresh round of inoculations, Todd and five colleagues from the Admiralty flew to Brussels and went in search of German mathematics.³¹

“Before the group had spent a week in Germany, its numbers began to dwindle. One member fell ill and returned to London. A second was reassigned to an expedition that was preparing to visit the north magnetic pole. A third mathematician accepted an invitation to view a solar eclipse and was killed in a plane crash. The remaining three, Todd, a second mathematician, and a translator, crossed a devastated landscape as they continued without their colleagues. They had to be alert for unexploded ordnance, German deserters, booby traps, and the final defenders, the Volksstrum, or provincial volunteers. A member of the Mathematisches Reichsinstitut stated that “a feeling of anxious suspense hung in the air” during the first weeks after the surrender. To protect themselves, they destroyed items that would connect the mathematics institute with the Nazi regime. “The meadow behind the house saw dozens of copies of the Hitler bible, ‘Mein Kampf,’ go up in flames and vanish,” she wrote. Though they gladly sacrificed the most common totem of the Nazi regime, they spared copies of another volume of propaganda, The National Socialist View of History. In these volumes, “a wide margin had been left for notes,” she explained, and the staff was willing to risk incrimination in order to have the scrap paper. In the end, the gamble was rewarded, for the books were never used as evidence against the institute, and the pages “proved to be most advantageous in many ways during the coming period of extreme need.”³²

By the time Todd arrived at Darmstadt, Alwin Walther had returned to the organization and resumed his work. The Technische Hochschule had a staff of about ninety. Twelve of them were PhD mathematicians; the rest were young women, “some quite young,” according to Todd. A staff member at the facility identified the computers as “female university entrants with a flair for mathematics whom the state compulsorily assigned” to the Technische Hochschule and who were known as “Walther’s harem.”³³ The largest section of the institute, consisting of about thirty computers, worked for the V-2 missile program calculating ballistics trajectories. Two smaller groups of computers processed wind tunnel data and calculated the propagation of electromagnetic waves, the kind of work that was needed for radar research. The institute had two other computing offices. One operated a differential analyzer; the other used adding machines and punched card tabulators to do miscellaneous calculations, the sort of work that was handled by the Mathematical Tables Project in the United States.³⁴ The tabulators had been seized by the German army from the occupied states. The Darmstadt staff claimed that it accepted the machines reluctantly, “hoping it might benefit from the machines for its research activities—a hope that proved to be false.”³⁵

During June and July 1945, Todd spent six weeks in Germany and visited eight centers of mathematical research. He moved methodically from institute to institute, collecting papers, seizing books, interviewing mathematicians, and occasionally finding old friends. From the experience, he concluded that “German mathematical research was not centralized until the very end of the war.”³⁶ From what he saw, he felt that the Admiralty Computing Service had done a better job of organizing mathematicians and solving problems for the military. Still, he was impressed with the quality of German mathematical research and returned home with a substantial collection of texts, tables, and reports of computation. Traveling with restrictions on military luggage, he stuffed his trophies into pockets and jackets, shirt sleeves and trouser legs. When he stepped on a scale to be weighed for the flight home, the diminutive mathematician registered 300 pounds.³⁷

Before Todd returned to London, a British scientific officer notified the Applied Mathematics Panel of the mathematical mission to Germany and asked whether the Americans wanted to send a representative. The request reached the desk of Thornton Fry, who was still running the panel in the absence of Warren Weaver. Fry knew that it would be easy to add an American to the party, as several Applied Mathematics Panel researchers were already working in London on field projects. However, he concluded that Todd would do an adequate job and declined the offer.³⁸ Arnold Lowan reached a different conclusion when he learned of Todd’s trip. “Imperative that a representative of MTP should go to Darmstadt,”³⁹ he wrote to the Applied Mathematics Panel. Lowan had read a preliminary report from the Technische Hochschule and had concluded, correctly, that the group was similar to his own. He hoped that a visit to the enemy’s computing center might give added importance to his group. It might show that Germany profited from organized calculation and that the United States would strengthen its defenses by expanding the Mathematical Tables Project. Thornton Fry received this request coolly. “I can find nothing in the report of the Darmstadt activities to justify sending anyone to Darmstadt on AMP account,” he concluded. In what Todd had found there were not “any strong indications that they were much ahead of us. In the matter of methods of computation and especially in the development of computing machines, they seem to be far behind us.” Even if the Germans had achieved some interesting results, he was not prepared to let Arnold Lowan investigate. “I do not know what future Dr. Briggs has in mind for the Lowan group,” Fry wrote, “and therefore cannot guess how he would feel about sending Lowan over as a Bureau of Standards representative.”⁴⁰

Lowan undoubtably appreciated that the denial from Fry suggested an uncertain future for the Mathematical Tables Project. However, this news was accompanied by a special request for calculation, a request that must have reminded Lowan how far the group had come. This request came from Richard Courant at New York University for some unnamed third party and was marked as top secret. Even though no one in the group had received a security clearance, they had occasionally handled sensitive calculations. The calculations would be passed to Warren Weaver at the Applied Mathematics Panel, who would strip the mathematics of every reference to the physical setting, including the units of all quantities involved in the work. Though the members of the planning committee could usually grasp the general nature of the application, they were rarely able to piece together the full problem. During the winter and spring of 1945, the Mathematical Tables Project had handled classified computations for microwave radar and the targeting of depth charges.⁴¹ “I did not completely understand what we were doing,” said one committee member, “until I read [the official history] after the war.”⁴²

This new request was an explosion problem. It traced shock waves through different materials. Superficial evidence suggests that the request came from the Manhattan Project and may have been a duplicate or more refined calculation for the Fat Man bomb. The memo was passed through the explosives division of the National Defense Research Committee, which was helping the scientists at Los Alamos design the mechanism for detonating the plutonium bomb. The Los Alamos scientists requested duplicate calculations of many key elements in order to verify their work. The first test of the plutonium bomb was only a few weeks away, and engineers were already assembling the test equipment at Alamogordo. Even if the calculation did not come from the Manhattan Project, it was still important evidence that the group, once judged impossible to secure, had gained some measure of trust and prestige among the wartime scientists, for it came with a stern warning:

With the surrender of Japan on August 16, 1945, the contractors of the Applied Mathematics Panel dropped their tools in the field and returned to their homes. The final demobilization began quickly, as the mathematical contractors released workers, declassified results, published significant discoveries, and recorded the history of their organizations. By the end of September, the bulk of the projects were liquidated, including the statistical studies at Columbia, the remaining work of Jerzy Neyman, the explosion analyses at New York University, and the bombing mathematics at the Institute for Advanced Study. The rest of the contractors, save the Mathematical Tables Project, had scheduled their final dates of operation. Most would finish their work in October. Only the mathematicians of Brown University would operate through the month of November.⁴⁴

In this final flurry of activity, the Applied Mathematics Panel had arranged for the navy to fund the Mathematical Tables Project as a special-purpose computing laboratory. This arrangement would reunite the two divisions, joining the New York Hydrographic Office computers, who were already under navy authority, to those who had been directed by the panel. The navy, viewing the project as the seed of a larger computing laboratory, agreed to provide Arnold Lowan with IBM punched card tabulators. Naval officers would take no role in the daily operation of the center and stated that they would support “special computations for various navy bureaus, [and] also the work on basic tables.”⁴⁵ The consolidation required one final move. The computers of the Mathematical Tables Project had to pull their mathematical books off the shelves, pack their notes, box their adding machines, and join the New York Hydrographic Office staff in the Hudson Terminal Building. The combined facility was the best office that had ever been given to the group. It had separate space for the punched card equipment, a room for the planning committee, and a view of New York Harbor.⁴⁶

As the computers prepared to move to their new offices, Arnold Lowan, accompanied by Milton Abramowitz, traveled north to attend a conference on computation. The conference was sponsored by the Subcommittee on the Bibliography of Mathematical Tables and Other Aids to Computation and was the evidence of R. C. Archibald’s faith and efforts. After a dozen years of uncertain fortune, the committee was able to organize a weekend discussion of computation for eighty-four researchers, “those chiefly active in connection with mechanical computation on both sides of the Atlantic,” according to Archibald.⁴⁷ Much of this new authority came from the success of the committee’s journal, Mathematical Tables and Other Aids to Computation. In a little more than three years, the journal’s subscription list had grown to nearly three hundred. The periodical could be found with every contractor for the Applied Mathematics Panel and was generally accepted as the scholarly record of human computers.⁴⁸

41. Hudson Terminal Building, last home of the Mathematical Tables Project

The meeting, held at the Massachusetts Institute of Technology, was a mixture of the old and the new, Depression-era methods and wartime accomplishments. L. J. Comrie mingled with John von Neumann. Arnold Lowan watched Howard Aiken operate his Mark I. From the same stage, speakers talked about difference engines and differential analyzers, the punched card machines of the Nautical Almanac and the relay computers of Bell Laboratories. “The conference was most notably successful,” Archibald reported, “and one heard on every side expressions of the hope that such a conference might become an annual event.”⁴⁹ Yet this meeting was the only time that the war computers gathered as equals, the one moment when mathematicians and human computers, punched card clerks and differential analyzer operators, electrical and mechanical engineers came together and talked about their experiences with equations and numbers. A second meeting, held just three months later, gave clear signs that machine designers were starting to outpace human computers. This meeting was a press conference, held at the University of Pennsylvania, that announced the age of electronic computation. In the building that held the old differential analyzer, university officials unveiled its replacement, the ENIAC. The machine had been proposed in 1943, but it had not been finished by the end of the war. It had done its first complete calculations in November, just at the time of the MIT conference.⁵⁰

Like the meeting that had been organized by MTAC, the ENIAC announcement pointed toward the future while not letting go of the past. The machine was fast because it was entirely electronic. The calculations did not have to pause for a gear to turn or a telephone relay to click. It was more precise than older machines because it computed digitally. Each number was represented as a series of electrical pulses rather than as the turn of a wheel or the level of a voltage. The output was more useful than that of the differential analyzer because it came as numbers, not as an ambiguous graph. Yet for all of its benefits, the ENIAC was not quite a modern computer. It was really a collection of electronic calculators. Most of these devices were nothing more than adding machines, a few did multiplication, and one took square roots. The engineers prepared for a calculation by connecting these units with large, black cables. Following the computing plan, they arranged the cables so that they took a number from a punched card, passed it to an adder, sent it to the square root unit, returned it to the adder, and finally left it on the multiplying unit. The staff called this cabling process “programming,” but only the word, not the actions, would be the legacy of the machine.⁵¹

The press conference was a time of great pride and accomplishment, but it was also marked with a bit of impatience. As the ENIAC became operational, the University of Pennsylvania researchers had come to appreciate the limitations of their machine. “We designed [the ENIAC],” recounted Adele Goldstine’s husband, Herman, “and immediately lost interest in it.”⁵² In building this machine, they had recognized that they could design a more flexible machine that was controlled by a special list of electronic instructions rather than by the bulky cables. These lists would inherit the name “program.” The design team had conceived a way to modify the ENIAC so that they could control it with a primitive program, but they were more interested in building a new machine that would be entirely programmable.⁵³

The new, programmable machines were at least two years away, and in the interim, the University of Pennsylvania had to live with the ENIAC. The press conference generated a tremendous interest in computing devices. In response to requests to study and use their machine, the school organized a seven-week course on computing machinery, a conference that would be called the Moore School Lectures. When the course convened in July 1946, the list of lecturers constituted “a Who’s Who of computing of the day.” Most of the speakers came from the ENIAC project, though George Stibitz, Howard Aiken, and John von Neumann also conducted sessions. The talks had little in common with the discussions at Archibald’s conference three months before. The Moore lectures dealt with circuit design and the preparation of problems for machine computation. The students were not human computers but “a select group of seasoned professional engineers and mathematicians.”⁵⁴ The discussions made little reference to human computing groups, and few in attendance had any experience with organized calculation. No one from the Mathematical Tables Project was invited to attend. L. J. Comrie was not chosen as a representative of Great Britain. There were no computers from any Nautical Almanac Office, the Manhattan Project, or any of the projects of the Applied Mathematics Panel.⁵⁵

Had any human computers been at the Moore School Lectures, they would have heard a somewhat fanciful history of calculating devices that ignored the contributions of workers like themselves. This history, the first of the lectures, also overlooked the punched card machines of Herman Hollerith and described the difference engine of Charles Babbage as “a special purpose [device] developed for the satisfaction of personal curiosity or as an intellectual stunt.”⁵⁶ Historians of the conference claim that the talk was meant to “entertain and inspire,”⁵⁷ but a close examination of the text suggests that it was an attempt to build a distinguished lineage for the electronic computing machine, a pedigree that ignored the influence of commerce and the hard labor of human computers. To many at the talk, the human computer was already starting to fade from memory. Most of the wartime computing groups had been shut down, reduced to a small remnant, or replaced by punched card equipment. The major employer of human computers, the Applied Mathematics Panel, had finally ceased operations after one last meeting. Led by Warren Weaver, the mathematicians had gathered in their old conference room to celebrate their accomplishments. There would be those who would criticize the panel and argue that it missed an opportunity to advance the cause of mathematics, but this was not the time for such discussions.⁵⁸ The members of the panel spoke their praise to mathematics, to science, and to their accomplishments, though no one felt it necessary to express gratitude toward the workers who had undertaken the calculations.⁵⁹

Even though Arnold Lowan and Gertrude Blanch were not invited to the Moore School Lectures in the summer of 1946 or to the final meeting of the Applied Mathematics Panel, they were confident about the future. The navy and the Army Air Corps had guaranteed funds to sustain the operations of the Mathematical Tables Project for two more years, and the military services seemed likely to continue providing that money for a subsequent period, at least until they were in possession of a comprehensive facility with electronic computers. Even then, they seemed likely to retain the members of the Mathematical Tables Project as the support staff for the new computing machines.⁶⁰ For the moment, the military provided the project with new and interesting computations, work beyond the traditional labor of preparing mathematical function and LORAN tables. The services asked for guided missile trajectories, radar wave deflections, and shock wave propagations. In addition to this work, the Mathematical Tables Project was now receiving requests for calculations relating to the development of atomic energy, such as problems that described the interactions of particles or analyzed reactor designs.⁶¹

The only worrisome development for the project was a change of leadership at the National Bureau of Standards. The bureau had been the fixed point of the Mathematical Tables Project through the fluctuations of the Depression and the war. Lyman Briggs, director of the bureau, had been the champion of the project, sponsoring it for the WPA, serving as the executive manager under the Applied Mathematics Panel, and helping to obtain the postwar funding from the military.⁶² The planning committee of the project viewed him as the “Beloved Boss” who had supported Arnold Lowan, corrected his mistakes, both gently and not so gently, and spoken for him in the high councils of science.⁶³ Briggs had retired in the fall of 1945 and had been succeeded by the physicist Edward Condon (1902–1974). When he first arrived at the Bureau of Standards, Condon had questioned the value of the group. He had changed his mind after a visit to the project’s offices, when he met Lowan, talked with the planning committee, and observed the computing staff. Condon concluded that the Mathematical Tables Project might be able to contribute to the National Bureau of Standards, though he also observed that there was no reason for Lowan to report directly to the bureau director. After returning to New York, he informed Lowan that the project would be guided by his new assistant, John Curtiss.⁶⁴

Curtiss was familiar with the work of the project and sympathetic to the group. Back in 1940, he had reviewed the first volumes from the Mathematical Tables Project in the American Mathematical Monthly and found them quite acceptable. By training, he was a statistician, but he came from a mathematical family and was well connected in the mathematical community. His father had been a professor at Northwestern University and had served as president of the Mathematical Association of America, the professional society devoted to mathematical instruction. Curtiss had studied at the University of Iowa and at Harvard. His rise to prominence had come during the war, when he had taken a naval commission and served as a statistician for the Bureau of Ships. Most of his work concerned quality control, the statistical methods that tested batches of manufactured products to ensure that all of them operated properly or met basic standards. At the end of the war, he was recommended to Condon as a mathematician who understood the nature of organizational politics.⁶⁵

Perhaps remembering Curtiss’s review, one of the few favorable signs in the early days of the Mathematical Tables Project, Arnold Lowan welcomed the arrival of John Curtiss and invited the statistician to visit New York. Curtiss accepted the offer and, like Condon before him, came away from the project offices with a favorable impression. He decided that the group should be a key part of a new mathematical research organization that he hoped to create within the National Bureau of Standards. For the moment, he was using the name “National Applied Mathematics Laboratories” to describe his idea. In his plan, the laboratories would have four distinct units. The first would research the methods of applied mathematics, the second would consider problems of applied statistics, and the third would develop new computing machines. The Mathematical Tables Project would be the fourth and final laboratory within the group. Renamed the Computation Laboratory, it would provide “a general computing service of high quality and large capacity, for use by private industry, Government agencies, educational institutions, etc.”⁶⁶

In Curtiss’s plan, the Computation Laboratory would be larger and better equipped than the old Mathematical Tables Project. It would have desk calculators, difference engines, punched card tabulators, “special analogue equipment for the solution of algebraic equations,” and finally “two general purpose automatic electronic digital computing machines of large capacity.”⁶⁷ Arnold Lowan was delighted with this idea and immediately started referring to the Mathematical Tables Project as the Computation Laboratory, even though the new title would not become official for another eighteen months and the old name would stick to the group as if there was no other way to describe the former WPA project. There were many details to complete before Curtiss’s plan could be implemented. Curtiss and his boss, Edward Condon, had to obtain funding from Congress and explain how the National Applied Mathematics Laboratories would work with other government agencies. One minor point to resolve was the location of the new Computation Laboratory. Curtiss had stated that the laboratory might be located in either New York or Washington, D.C., but Lowan wanted the laboratory to remain in New York. New York was the nation’s financial capital, headquarters to much of its industry, close to the bulk of its major universities, and the home of the American Mathematical Society. It was also the city in which Arnold Lowan lived and the place where he held a second job, his professorship at Yeshiva University.

In the summer of 1947, Curtiss announced that the Mathematical Tables Project would have to move to Washington, D.C., as it was “an integral part of the National Bureau of Standards, rather than a field office.”⁶⁸ Arnold Lowan immediately protested the decision and claimed that it would cause “complete demoralization of our personnel.”⁶⁹ Indeed, outside observers could detect that something was wrong that summer, even though the staff kept to their tasks. The computers were “so upset that they didn’t know what to do,” reported Everett Yowell of the Thomas J. Watson Computing Bureau.⁷⁰ Yowell’s presence at the project offices was the first cooperation between the two New York computing institutions, and it should have been another sign that the Mathematical Tables Project was finally becoming part of the scientific community. With so many staff members preoccupied with the potential move, it was an opportunity lost. Yowell largely interacted only with Milton Abramowitz, teaching him some punched card techniques to earn “a little extra money.”⁷¹

Believing that he was fighting one more time for the survival of the Mathematical Tables Project, Arnold Lowan again turned to his scientific allies: Philip Morse, John von Neumann, Julius Stratton, and R. C. Archibald. Letters came from Lowan’s home in Brooklyn, marked “Personal” and bearing the now familiar tag line, “For obvious reasons I would appreciate your keeping this letter in strict confidence.”⁷² With Phil Morse, he explored the possibility of bringing the Mathematical Tables Project under the authority of the Atomic Energy Commission and moving the group to the new Brookhaven Laboratory on Long Island. After discussing the idea with friends on the Atomic Energy Commission, Morse reported that Brookhaven would not accept the computing group. He never mentioned whether the Atomic Energy Commission was at all interested in the Mathematical Tables Project but instead reported that the new laboratory, which was located in an area then considered quite isolated, could not provide housing for the computers.⁷³ Turning next to John von Neumann, Lowan suggested that the staff of the Mathematical Tables Project might work as a computing office for the Institute for Advanced Study, though of course they would remain in New York. Von Neumann, who was already planning to build his own electronic computer, never raised the issue with his colleagues at the institute, writing that “my own impression is that the Institute is not a suitable vehicle for such a function.”⁷⁴

As rejection followed rejection, Lowan’s letters became more frequent, more urgent, more desperate. Through the winter of 1947–48, Morse was the recipient of four letters, each more anxious than the last. Lowan described his problems yet again, asked why he had received no reply, requested a meeting with his supporter, and finally begged for any contact.⁷⁵ “I have reason to believe that Dr. Curtiss intends to proceed with his plan of either transferring the [Computation Laboratory] to Washington even at the risk of wrecking it,” he wrote, “or to curtail it considerably by even abolishing some of the jobs of the mathematicians.”⁷⁶ His writing became tinged with self-pity, as the legacy of the Mathematical Tables Project became intertwined with every little slight that he had felt as its leader. He complained that he had been denied a promotion, that Curtiss had already appointed his successor, that his accomplishments were being ignored.⁷⁷

Finding no aid from his traditional supporters, Lowan looked outside the scientific community for any assistance that might be offered. He turned first to the New York City congressional delegation and asked for help from Representatives Emmanuel Cellars of Brooklyn and Jacob Javits of Manhattan. The two congressmen wrote to the leaders of the National Bureau of Standards, presented Lowan’s arguments, and asked for an explanation. Both congressmen got polite responses from John Curtiss that offered no compromise on his plan to move the Mathematical Tables Project to Washington.⁷⁸

As the date for the move approached, Arnold Lowan asked for the assistance of the union that represented his human computers, the United Public Workers of America. The United Public Workers had organized the Mathematical Tables Project computers in 1938 as part of a broader effort to represent the clerical workers of the WPA. The union was on the more radical side of 1930s labor organizations. It was a member of the CIO, the Congress of Industrial Organizations, and kept its offices in the same building that housed the American Communist Party. It had mounted at least one strike against the WPA, in 1939, though the correspondence of Arnold Lowan suggests that the labor action spared the Mathematical Tables Project.⁷⁹

The United Public Workers followed the lead of Arnold Lowan in pressing its case. They contacted Cellars and Javits in Congress, R. C. Archibald and Phil Morse in the scientific community, John Curtiss and the senior scientists of the National Bureau of Standards. The union’s first letters were polite and deferential. “The employees of the Computation Laboratory appreciate the interest you have shown in the problem of its location,” the union president wrote to Phil Morse. “May we take the liberty of writing to you once more on the subject.”⁸⁰ The union argued that the planned move would destroy jobs and damage the legacy of the Mathematical Tables Project. “It may never be possible,” wrote the president, “to fully make up for the loss of skilled personnel that the move would entail.”⁸¹

42. Phil Morse in his computing laboratory after the war

Subsequent letters were not so deferential to the authority of the scientists. The union attacked John Curtiss and portrayed him as naive, opportunistic, and prejudiced. Quoting a memo that had been supplied by Lowan, the union president charged that “twenty per cent of the present employees of the [Mathematical Tables Project] who are Negroes are not expected to go to Washington because of the Jim Crow conditions existing there.” Furthermore, “fifty percent of the employees are Jewish and fear increased discrimination in Washington.”⁸² The charges had more than a grain of truth, for Washington was a segregated city. “White-collar work and employment in skilled trades dominated in Washington,” wrote one historian of the city, “but access to such jobs was anything but equal racially.”⁸³ The letter stirred only one scientist to action, the volatile R. C. Archibald. Archibald, who had praised the Mathematical Tables Project in the pages of Mathematical Tables and Other Aids to Computation and in Science, took up his pen to rail against “the attempted transfer of the [Mathematical Tables Project] from New York to Washington” and the “brutal treatment of Lowan” at the hands of John Curtiss, whom he characterized as “not even a second rate mathematician.”⁸⁴

Neither the United Public Workers nor R. C. Archibald could keep the Mathematical Tables Project in New York City. The death blow for the group was delivered by John von Neumann, who wrote one final letter at the request of Arnold Lowan. In the letter, von Neumann told John Curtiss that he had “always had a great admiration for the work of the Mathematical Tables Project–Computation Laboratory” and added, “I think that this organization constituted and still constitutes an ideal computing group on the non-automatic level.” He felt that the project had done “very excellent and valuable work in the past, and is likely to do so in the future.” The strong tone of the letter began to waver when von Neumann suggested “that a group of this type will become obsolescent when automatic devices become widely distributed,” and it collapsed in the last paragraph, when he deferred to Curtiss’s judgment. “If you are satisfied that [it is impossible to fund the group in New York], then I concur with you that a gradual transfer to Washington is the only possible solution.”⁸⁵

Arnold Lowan probably never read von Neumann’s letter, but he knew that its effect was “extremely unfavorable.” After receiving the letter and meeting with the members of the Mathematical Tables Project, John Curtiss announced that the move would begin immediately and that the punched card unit would be the first group transferred to Washington. He offered jobs to most members of the planning committee and to eighteen of the human computers, about half of a staff working in New York.⁸⁶ In order to limit Arnold Lowan’s ability to thwart the move, Curtiss offered two alternatives to the project leader. Lowan could come to Washington, take charge of the new Computation Laboratory, and receive a promotion. If he did not wish to do that, Lowan could remain in New York as the director of a fifteen-person computing office. The Bureau of Standards would provide funds for exactly one year. After that, Lowan would have to finance the group himself.⁸⁷

In the history of human computers, this is the one moment that might have provoked a labor action, a strike by those who worked with numbers, but the computers were unwilling to back Arnold Lowan. The United Public Workers made one final attempt to start a protest by charging that Curtiss’s plan “would certainly lead to the Bureau’s having two relatively inefficient computing groups,” but they found that there was no support for their position among either the computers or the scientists.⁸⁸ By midsummer, they had abandoned their efforts on behalf of the Mathematical Tables Project. That July, the new Computation Laboratory opened its doors in downtown Washington, and simultaneously, Arnold Lowan changed the name of his office to “Computation Laboratory, New York.”

During the ten-year history of the Mathematical Tables Project, John von Neumann was a distant figure whose letters offered nothing but vague encouragement and deferred hope. He never visited the project offices, though he made time to visit the Admiralty Computing Service in England, and he never offered an unconditional blessing to Arnold Lowan. Only in the final days of the Mathematical Tables Project, just as his letter was sealing the project’s fate, did von Neuman ask Arnold Lowan for computational assistance. He asked whether the computers would test a new technique called “linear programming.” Von Neumann was not really interested in the results of the test computation, just as he was not especially interested in the future of the Mathematical Tables Project. He requested the calculation because he wanted to use the human computers as surrogates for computing machines, as a means of projecting the operation of a programmable electronic computer.

John von Neumann may have initiated the request, but he did not invent the method of linear programming. The technique was developed by a student of Jerzy Neyman named George Dantzig (1914–). Dantzig had spent much of the war analyzing operational problems for the Army Air Corps. A typical problem looked for the best way of storing spare parts for aircraft. The idea was to find the number of storehouses that would provide the best access to parts yet at the same time minimize the expense of keeping a large inventory.⁸⁹ Such problems had posed serious difficulties for the air corps, according to one of Dantzig’s contemporaries, and had “required the labors of hundreds of highly trained staff officers.”⁹⁰

Dantzig had been able to test his method of linear programming only on small, simple problems, as the work had the same kind of demands as least squares or simultaneous equations. A small problem, such as the task of locating two or three storehouses, was simple and straightforward. As problems grew, the amount of calculation expanded rapidly. If the problem was doubled to six storehouses, then the calculations would require eight times the effort. Dantzig would have been restricted to these simple problems had he not been given the opportunity to present his method to von Neumann. He visited von Neumann at the Institute for Advanced Study and encountered an impatient mathematician. “In under one minute, I slapped the geometric and the algebraic version of the problem on the [black]board,” he recalled. Von Neumann quickly grasped the nature of the problem, took the chalk, and “then proceeded for the next hour and a half to lecture me on the mathematical theory of linear programs.”⁹¹ As it happened, Dantzig’s work was related to research that von Neumann had already completed. Von Neumann wanted to see Dantzig’s method tested on a large problem, one that had a classic standing in the economics literature. This problem attempted to identify the cheapest possible diet from among seventy-seven different foods. The list of foods began with wheat flour and ended with strawberry preserves. The diet had to provide 3,000 calories and minimum amounts of eight different nutrients.⁹² The calculations for this problem included 29,856 additions, 15,315 multiplications, and 1,243 divisions.⁹³ Von Neumann had hoped that the Aberdeen Proving Ground might agree to do this calculation on the ENIAC, but the ballistics researchers refused the request, so he turned to Arnold Lowan and the Mathematical Tables Project.⁹⁴

The calculations began in mid-April, just as Arnold Lowan was preparing for his meeting with John Curtiss. The work required twenty-five computers and was overseen by a junior member of the planning committee. It was a somber time in the office, but the work progressed steadily. Dantzig monitored the efforts of the computers and kept von Neumann informed of their progress. Von Neumann would take the letters from Dantzig, turn them over, and calculate the amount of time that the ENIAC would spend on the same work. Dantzig’s last letter reported that twenty-five computers had completed the work in twenty-one days. In half a page of pencil scratching and little diagrams, von Neumann concluded that the ENIAC could do the same work in about nine hours.⁹⁵ This was the only number that he would ever use from the Mathematical Tables Project. He never saw the final calculations. “The setting up of a computational procedure for this type of problem is the main objective,” acknowledged the final report on the work, “rather than the solution of this specific diet problem.”⁹⁶

The computers began to disperse almost as soon as Dantzig’s calculations came to an end. Some went to Washington; a few, including Ida Rhodes, started to learn about the new electronic computers;⁹⁷ most started looking for jobs in New York City. By January 1949, Lowan had fewer than fifteen computers working for him, and they were all assigned to old problems that had been started under the authority of the WPA. Struggling to keep his facility operating, he still hoped that Philip Morse would be the savior of his New York office this final time, but he was coming to accept that there would be no future for his organization. “The fact that you have not replied to my [last letter],” he wrote to Morse, “would seem to substantiate my feeling that you are seemingly unable to do anything which would change the trend of events.”⁹⁸ The return mail brought the news he had dreaded. “I very much fear you are right,” Morse had written. “It seems that the situation you are up against is well nigh unbreakable. I don’t like it but there it is.”⁹⁹ Having served, in its last moment of public glory, as a proxy for the digital electronic computer, the Mathematical Tables Project closed its doors for the final time on Friday, September 30, 1949.