MAA Blog: Mathematics for the Unemployed

“Work relief”

Until she encountered those two words, Gertrude Blanch had few prospects for a conventional career in mathematics. She was one of the very first women to receive a doctorate in mathematics (Cornell University) and she completed her studies in the depths of the Great Depression (1934). Beyond a temporary teaching job at a woman’s college, she had no prospects for employment. When that assignment ended, she took a job keeping books for a hat store on 23rd Street in New York City.

Work Relief came to Blanch almost by happenstance. The Works Progress Administration (WPA), one of the New Deal agencies, was looking to create a large project that would employ the jobless of New York City in an indoor setting. While exploring different ideas, the WPA leadership learned that the U.S. Government had operated a computing and mathematics laboratory during the first world war. That laboratory had done some of the fundamental work to support ballistics research. The WPA leadership thought that it might create a more general-purpose laboratory that would support a wider range of engineering and scientific activities.

As it developed plans for the activity that would come to be known at the Mathematical Tables Project, the WPA faced a potentially insurmountable problem. They were unable to find a mathematician willing to lead the project. WPA projects had acquired the taint of failure. They offered jobs to people who were unable to find any other kind of employment. No successful mathematician was willing to commit their reputation to such a project. Blanch learned of the project only because she was taking a night class at Brooklyn College. With no prospects for mathematical employment before her, she accepted the position as mathematical director of the project and settled into the project offices in an old building a few blocks from Times Square.

The story of Gertrude Blanch and the Mathematical Tables Project is told in a new audio drama that has just been released by the HWMS Audio Theatre. The dramatic nature of the story alone makes it a good play. A woman takes a risk with an unconventional career, builds a computing office with staff of 450 human computers and 12 mathematicians, weathers the Depression, transforms it into the major computing laboratory for the U.S. Government in the second world war, organizes the field of applied mathematics, and lays the foundation for the electronic computer.

The Math Tables Project is best known for the people it trained and the projects it spawned. It is the direct progenitor of the Applied Mathematics and Computing Laboratories at the National Institutes of Standards and Technology, the groups that produced the SEAC and SWAC Computers and did much early research in computer science. It is equally the progenitor of most of the government computing labs of the era, including the computing office of the National Council on Aeronautics at the Langley Laboratory, the lab popularized in the movie Hidden Figures. It trained the editors and most of the authors of the Handbook of Mathematical Functions which is probably the most widely sold mathematics book in history. Many of the book’s authors had learned their skills on the computing floor of the project and in the seminars it offered over the lunch hour.

Yet, as the story of this group unfolds, it quickly reveals how thoroughly the label “Work Relief” clung to it. The Project did not present the ideal that many mathematicians held for their field. A member of the National Academy of Science expressed his reluctance to embrace the organization in a logical syllogism. “Mathematicians,” he claimed, “are successful people. The poor, as evidenced by their poverty, are not successful people.” “Therefore,” he concluded, “the poor are not scientists.” He argued that the government should spend the budget on fellowships. He guessed that the funds that fed the families of 450 workers might provide support for up got 30 students of mathematics.

In spite of its awkward position in the scientific community, the Project had a few strong supporters. Hans Bethe of Cornell, and Phil Morse of MIT used the group to solve problems and promoted the organization to other scientists. The Princeton mathematical community were surprising supporters. Oswald Veblen took an active interest in the group. Einstein recommended one of his assistants, Cornelius Lanczos, to spend a year with the Project as a scientist in residence. John von Neuman, who was just starting to become interested in computing, argued that the mathematical staff of the group had an important set of skills and that they could not be easily replaced. He used the project to test one of the more important mathematical developments of the war, linear programming.

In leading the Mathematical Tables Project, Blanch had to find solutions to problems that were mathematical, organizational, and political. She was responsible for developing calculations for the group and putting them in a form that could be handled by 450 workers with little mathematical training. The literature on applied mathematics was largely unorganized at this point. There was no single journal that captured the major results of the field. Instead, important results and algorithms were scattered over a dozen fields including astronomy, physics, and electrical engineering. She sent her assistants to the libraries of Columbia, New York University, and the United Engineering Society to find methods and results that she could use. She had to convert these methods into worksheets that would guide the computers. She had to devise an industrial process that would keep the computers working and would produce results on a regular schedule.

Finally, she had to create ways of checking the results of the computations. It was not enough to double or even triple compute every number. She quickly learned a truism that had long circulated through the applied mathematics community: Different people, working on common calculations using a common technique, are likely to make the same mistakes. Her approach to this problem was to dissect tables of numbers using finite differences. She would have the computers take differences of numbers on a table and then recursively take differences of those differences. Since the calculations were ultimately done with some form of polynomials, the recursive differences should ultimately produce a function of constant value. Potential errors would appear as spikes or jumps in this function.

In her leadership role, Blanch faced more indifference than outright antagonism. Her letters to outside mathematicians would go unanswered. Requests for reviews of mathematical analyses would garner no response. Perhaps the most galling form of indifference came from the visitors to the project. They would talk with Blanch about how the program developed computing plans, they would observe the floor in operation, and they would review the Project’s output. These visitors would regularly return to their laboratories, establish a similar computing establishment, and never credit the Mathematical Tables Project as the source of their ideas.

By the winter of 1942, the Mathematical Tables Project had become a military research organization for the second world war. In this role, the project faced its greatest challenges. Even before the start of war, the project was producing mathematical work that was deemed to be secret or classified. Blanch quickly became adept at preparing calculations that contained none of the clues that might lead the staff to guess the problem they were solving, clues that included physical descriptions of the problems, the units of various quantities, or the assumptions that had led to a specific analysis.

As the war progressed, secret and classified work became an increasing problem for the project. It placed Blanch and the other leaders under tight scrutiny. Time and again, Blanch applied for government clearances and was told that she simply knew too many people of questionable backgrounds to be awarded a clearance. This scrutiny reached its peak when the U.S. Government began an investigation into Blanch. The investigators felt that she might have ties to a foreign government and that she might be sympathetic to communist ideology.

By the time of this investigation, Blanch established her worth as a government scientist and demonstrated her value to the U.S. Government. She made the point to her investigators that she wanted nothing more than to own her own home, an idea that was not in sympathy with communism. After the charges against her were dismissed, she took a position at the Air Force Research Laboratory in Dayton, Ohio, where she spent the last years of her career doing work on the mathematics of supersonic air flow. The Air Force recognized her contribution by awarding her the rank of Senior Scientist and the U.S. Government gave her a Federal Woman’s Award, an award that President Lyndon Johnson established to honor women who had made long term contributions to the government.

The audio drama covers the period from the conception of the Mathematical Tables Project in 1938 to the end of Blanch’s Loyalty hearing in 1954. The story it tells is taken from the book When Computers Were Human (Princeton University Press, 2005), but it approaches the narrative with the advantages that audio has over print. The printed text is better at conveying the chronology and details of the story. The audio drama is better at conveying how it felt to work on the project and be part of that era. It does these things by asking questions. What was it like to do mathematics on a deadline? What was it like to oversee a shift of computers? What was it like to discuss your ideas and the ideas of your peers in a public setting?

Audio drama is an especially effective tool because it is the drama of the mind. With no cues from sets or costumes or physical actors, the listener is free to imagine the world of the story and respond directly to the emotions of the characters. Blanch lived an unusually dramatic life. Few people have been plucked from obscurity to run a large government program. Yet, all researchers have had to ask questions about the nature of loyalty, the role of friends in professional life, the effect of industrial rules on intellectual activities or simply on how to explain the accomplishments of your career to people who have no grasp of the work that you do. “Add Subtract, Unite, Divide,” attempts to address these issues for Gertrude Blanch. It also attempts to suggest how you might do it in your own career.

David Alan Grier is a Fellow of IEEE, was the Editor-in-chief of IEEE Computer, and is currently the Executive Producer at HWMS Audio Theatre.

For further information:

The Audio Drama “Add, Subtract, Unite, Divide,” can be found on all the major podcast platforms under the name HWMS Audio Theatre or How We Manage Stuff. It can be found on Apple podcasts at apple.HWMSTheatre.com or at its feeder site http://mtp.HWMSTheatre.com.

The book When Computers Were Human can be found at Princeton University Press or on the JSTOR electronic library.