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:
You will not show this paper to any member of your group.
You will make no reference to this paper in any of your own work.
No copies of the paper will be made.
The paper will be returned as soon as it has served its purpose.43
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
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