**Gertrude Blanch**was named Gittel Kaimowitz when she was born in Kolno, about 140 km north of Warsaw. Although we have given her place of birth as being in Poland, in fact at the time the country was partitioned and Gittel Kaimowitz was born in a part which was in the Russian Empire. Her parents were Wolfe Kaimowitz and Dora Blanc, and she was the youngest of their seven children. Her father emigrated to the United States with the intention of having his wife and the younger children follow him in due course. In 1907, Dora with Gittel and one other daughter, joined Wolfe Kaimowitz in New York. Gittel was ten years old when she arrived in New York and she first attended elementary school, followed by secondary school, in Brooklyn, New York. She graduated from Eastern District High School in 1914 but later in that year her father died so Gittel, who by this time was known by the Americanised version of Gertrude, decided that she would take a job so that she could support her mother.

Gertrude Kaimowitz, as she was then called, took a job as a clerk. She took American citizenship in 1921 and continued to work until her mother died in 1927. By this time she was thirty years old, but she had always wanted to further her education and so she took evening classes at Washington Square College, part of New York University. Gertrude decided to give up her job working for a hat dealer so that she could concentrate on her studies but her employer, not wishing to lose such a valuable employee, offered to pay her tuition fees if she continued to work for him. This was an attractive offer, so Gertrude continued to work for the hat dealer while studying mathematics. She graduated with a B.S. (major in mathematics, minor in physics) from New York University in 1932 and, in February of that year, legally changed her name from Kaimowitz to Blanch. She chose this name as an Americanised version of her mother's name Blanc.

Blanch had been awarded her B.S. with distinction and decided to continue to graduate study. She entered Cornell University in September 1932 and was awarded a Master's Degree in February 1934. Continuing to undertake research supervised by Virgil Snyder, she submitted her doctoral thesis *Properties of the Veneroni transformation in S_4* and was awarded a Ph.D. by Cornell University in 1935. Her thesis on algebraic geometry considered a transformation which first appeared in a paper by Veneroni in 1901. These transformations had, prior to Blanch's thesis, been studied by a number of mathematicians including J A Todd, Virgil Snyder and H F Baker. Blanch published the main results of her thesis in 1937 in the *American Journal of Mathematics* in a paper with the same title as her thesis.

After the award of her doctorate, Blanch returned to New York City where she worked for a year as a tutor in Hunter College, replacing a member of the faculty who was on leave. After this she was employed as a bookkeeper with a firm in Manhattan who were manufacturing cameras for colour photography. In [4] she explained how she moved from being a bookkeeper to working in the Mathematical Tables Project:-

Blanch worked on the Mathematical Tables Project from the beginning of 1938 until 1942. She published several papers, most jointly with Arnold N Lowan, such as:Since I didn't want to lose my knowledge of mathematics I decided to take[Arnold N]Lowan's course in relativity[at Brooklyn College]. Well actually, of course you know how evening sessions are. Most students are very tired when they come there and they don't have time to do their homework. I had the time to, and what is more I had the basic knowledge; so of course when I handed in a paper it was a paper that was fairly well written. Lowan used to take the same bus home that I did, and one day on the bus he told me that he was very pleased with the sort of papers I handed in, even though I didn't attend every night, and I told him that I did have a Ph.D. in mathematics at that time. So that's how he knew that I was a mathematician and he told me the next night on the bus that he had been selected to head this Mathematical Tables Project and wouldn't I join it?

*Tables of Planck's radiation and photon functions*(1940),

*Errors in Hayashi's table of Bessel functions for complex arguments*(1941) and

*On the inversion of the q-series associated with Jacobian elliptic functions*(1942). The last two mentioned papers were published in the

*Bulletin*of the American Mathematical Society. She was also employed as a tutor for evening courses at Brooklyn College from 1940 to 1942. In December 1941 the Japanese attacked the US navy in Pearl harbour and the United States entered World War II. The National Bureau of Standards took over most of the staff of the Mathematical Tables Project in 1942 for their work with the Applied Mathematics Panel of the National Defense Research Committee. Blanch said that after that [4]:-

Up to 1948 the Mathematical Tables Project continued in New York but it was then moved to Washington. Blanch did not go to Washington, however [4]:-We had a much smaller group, but we had equipment. We even had IBM equipment in those days. That was during the war when some of our things that we had worked on were flown to Los Alamos because they were needed. Some material we happened to have had it in our files. ... At that time we knew how to do things. We had expertise.

The McCarthy era to which Blanch refers in this quote began in February 1950 when the United States Senator Joseph R McCarthy made unsubstantiated claims that Communists had infiltrated high government circles [1]:-... at that time I was asked to go to the West Coast to the Institute for Numerical Analysis to start the laboratory there and I was tickled pink to go. I had never been to the West Coast, so for me California was a revelation. ... Now I stayed in California up to the McCarthy era when the Institute folded.

[As well as her sister being a member of the Communist Party, other evidence against Blanch was the ridiculous claim that she was likely to be a Communist because she had never married or had children. Blanch got a job with the Electrodata Corporation in Pasadena but only worked for them for a year before she became a senior mathematician at the Aerospace Research Laboratories at the Wright Patterson Air Force Base in Dayton, Ohio. She already had connections to the Wright Patterson Air Force Base having worked on Mathieu functions for Henry Fettis who worked there [4]:-Blanch]was one of the professional staff of the Institute who were investigated by a loyalty board of the Department of Commerce, which oversaw the National Bureau of Standards. Although previously Blanch had been denied security clearance, presumably because her sister was a member of the Communist Party, she was allowed to continue her job with the Institute. Nonetheless, the Institute was under attack and it closed in June1954.

Blanch's first published paper on Mathieu functions was published in 1946, before she went to California. This was the paper... on Mathieu functions I was probably the only one who had any experience with them, and I helped Fettis out in some things that had given him a lot of trouble. He couldn't get anybody to help him with[it]. So apparently when they realized that I might be available, the one in charge of the mathematics group at Wright-Patterson Air Force Base was Dr Millsaps, a real Southern gentleman who got his degree with Von Karman in mathematics. ... Millsaps tried to get me to come to Wright Field. Every time he came to California he would invite me to have dinner with him. ... I realized that the firm I was with would not be in business very long before it would be sold to somebody, and Millsaps had asked me three times. I didn't want to leave California, but then I decided maybe I'd better, and I took the job. In many ways it was the best thing I ever did. ... I left at the right time and I was never happier anywhere - I was never as happy in any other place as I was at Wright Field. I had complete freedom to do exactly what I wanted the way I wanted to do it and, I think, my best work was done there.

*On the computation of Mathieu functions*which was reviewed by L J Comrie who begins his review as follows:-

However, in 1945 the National Bureau of Standards had produced a volume ofFor the Mathieu equationy" + (a- 2qcos 2x)y= 0, it is well known that certain values of a, described as characteristic values, lead to periodic solutions. Ince, Goldstein and, more recently, McLachlan have developed methods of obtaining these characteristic values from a continued fraction. The author remarks, "there does not seem to appear in the literature any method for improving the accuracy of the characteristic values, except by cumbersome iteration." She then develops a method which corrects not only an approximate characteristic value, but also the coefficients in the series for the periodic solutions.

*Tables relating to Mathieu functions*which had included work by Blanch.

Among other papers that Blanch wrote before moving to Wright Patterson Air Force Base were: (with Roselyn Siegel) *Table of modified Bernoulli polynomials* (1950), *On the numerical solution of equations involving differential operators with constant coefficients* (1952), *On the numerical solution of parabolic partial differential equations* (1953) and (with Henry E Fettis) *Subsonic oscillatory aerodynamic coefficients computed by the method of Reissner and Haskind* (1953).

In [4] she describes her work at the Wright Patterson Air Force Base:-

Examples of her work on Mathieu functions during her time at Wright Field is the paperPrimarily I was working on Mathieu functions. We did Mathieu functions in a complex plane and it is published. We didn't do very much routine computing there.[Carl Gottfried]Guderley used to have some very interesting special problems in connection with some thermodynamic theory. We'd help with those. People from here, there, and other laboratories at Wright Field would come for advice, and if we had the knowledge we were very glad to share it. We would have lectures on modern mathematics and so on. We all participated in them. It was a college atmosphere. They had a graduate institute ... They teach aerodynamics primarily to those officers who needed training.

*The asymptotic expansions for the odd periodic Mathieu functions*(1960) published in the

*Transactions*of the American Mathematical Society and the paper

*Numerical aspects of Mathieu eigenvalues*(1966). She also published a two-volume book with D S Clemm

*Tables relating to the radial Mathieu functions*. The first volume subtitled

*Functions of the first kind*appeared in 1962 and the second volume

*Functions of the second kind*was published three years later.

In 1967 Blanch retired from her job at Wright Patterson Air Force Base and was honoured with the publication of *Blanch anniversary volume *(1967), which contained a series of papers by her friends. She continued to publish on Mathieu functions with D S Clemm after retiring, publishing the paper *The double points of Mathieu's differential equation* (1969) and the book *Mathieu's equation for complex parameters. Tables of characteristic values* (1969). Until 1970 she was employed by Ohio State University as an Air Force consultant. After 1970 she returned to California where she lived a long retirement, dying just a month before her ninety-ninth birthday.

Let us end this biography by quoting David Grier [3]:-

Gertrude Blanch can be viewed as either the last and most important leader of human computers or one of the first numerical analysts for electronic computers.

**Article by:** *J J O'Connor* and *E F Robertson*

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