# David Vernon Widder

### Quick Info

Harrisburg, Pennsylvania, USA

Arlington, Massachusetts, USA

**David Widder**was an American mathematician who worked on integral transforms and partial differential equations.

### Biography

**David Widder**was the son of David Henry Widder (1864-1917) and Edith Drabenstadt (1863-1945). David Henry Widder, born in Montsera, Pennsylvania, was a railway mail clerk who died of myocarditis in Harrisburg. Edith Drabenstadt was born in Maytown, Pennsylvania. David Henry Widder and Edith Drabenstadt were married in 1893. In the 1910 census the family are living in their own home at 1516 Derry Street, Harrisburg, Dauphin, Pennsylvania. David Widder, the subject of this biography, had a sister Freda Bernice Widder (1894-1959) who was four years older than him. We note at this point that Freda B Widder graduated from the Central High School, Harrisburg, and the Pennsylvania Academy of Fine Arts. She became an artist working for J Horace McFarland Company and married Harris A Ledford in Chicago.

There is, however, a rather strange claim which we do not understand. The above information about Widder's family comes various census returns and the details about his parents is confirmed on Widder's 'Certificate of Intention of Marriage'. But he writes in [12]:-

My father was a minister and former high school principal, and I think he would have liked to have me attend a religious college.David Widder, the subject of this biography, like his sister Freda attended Central High School, Harrisburg. In this school he sat beside a student called Rusty who said that Harvard was the best university so Widder applied to Harvard, took the entrance examination, and was accepted to begin his studies in September 1916.

Since David Widder wrote the interesting article

*Some Mathematical Reminiscences*[12] which gives a detailed description of his education and early career we quote freely from that article:-

I arrived at the South Station, Boston, in late September, 1916, asked where Harvard was, took the subway to the last stop and found myself at Harvard Square. Disillusionment! College buildings were separated by two busy highways with stores and business buildings mixed in. True, some of the buildings and a campus, which I learned later to call "The Yard," were enclosed inside walls. But this did not fit my preconceived notions.World War I broke out in 1914 but the United States only entered the war in April 1917. Six months after they entered the war, the United States set up the Aberdeen Proving Ground in Aberdeen, Maryland. Oswald Veblen took up the command of the office of experimental ballistics there in January 1918. Widder became a member of Veblen's team [12]:-

By mail I had been assigned living quarters in Standish Hall, a Freshman dormitory, now part of Winthrop House. I found my room on the top floor, where I had three room mates, each with a separate bedroom. The dining room was on the first floor. I do not remember the charge for board and room, but I think tuition was $200. The food was sumptuous, elegantly served by waiters. These new dormitories on the Charles River were a project of President A L Lowell, who felt that students should be taught a proper life style. In any case I gained weight and almost lost my seat on a Standish crew, until I began reducing!

The two courses that I remember most clearly that year were Analytic Geometry under Bôcher and Inorganic Chemistry under E P Kohler. It was a novel experience and somewhat exciting to be using a text that the professor had written: Bôcher's Analytic Geometry. Perhaps I did not appreciate at the time that a world famous mathematician had condescended to take a Freshman class. But I came to admire him and to become enamoured with the subject. Professor Kohler was also a master expositor who could make his subject live.

In my Sophomore year I was lucky again. I had Modern Geometry under Bôcher. In the first weeks he had us discovering properties of the ellipse from familiar ones for the circle by use of affine transformations. This was just a foretaste of the marvels to come. I think it was the influence of this course by this instructor that determined for me the choice of a career. In any case I determined to take any course Bôcher offered in later years. The same year I studied Calculus under another famous mathematician, teaching from his own text. Professor W F Osgood had a less inspiring style. I recall that he gave us good advice, ignored by most, on how to prepare a paper. You were to fold it down the middle, put a first draft on the right, corrections on the left. He used rubber finger caps to hold chalk. On the whole I would describe him as somewhat imperious.

I became a civilian computer in the range firing section at Aberdeen Proving Grounds. ... I was bunked in barracks with Norbert Wiener and Philip Franklin. I learned a lot from these enthusiasts, but at times they inhibited sleep when they talked mathematics far into the night. On one occasion I hid the light bulb, hoping to induce earlier quiet. One of our jobs was to convert French range tables to American units, using hand operated calculators, which we called "crashers." Armistice enabled me to return to Harvard in the middle of a term. I recall that Wiener was distressed that he could not leave immediately. He was in uniform and subject to army regulations.Back at Harvard, Widder took courses on complex variable from William Caspar Graustein (1888-1941) who, like Widder, had been at the Aberdeen Proving Ground. Graustein had returned to Harvard in 1919 to help the Mathematics Division which had lost three members. Edward B Van Vleck from the University of Wisconsin was visiting Harvard for a term and also taught Widder who graduated in 1920. He was awarded a Sheldon Traveling Fellowship to continue his studies in France.

On 16 September 1920 he was issued a passport to allow him to study in France but when in Paris on 19 January 1921 he applied for an Amendment to his passport to allow him to visit Italy, Switzerland, Belgium and Holland for "travel and study." He writes [12]:-

While in France I did not learn much mathematics. But I did at least come in contact, however remote, with some famous personages. I heard a lecture by Mme Curie and another by Émile Borel. I attended, irregularly, Goursat's 'Cours d'Analyse'. If Osgood was imperious, Goursat was regal. An usher opened the door for his entrance and escorted him out at the close. He lectured in a vast amphitheatre, nearly filled (some said partly by street people who came in for warmth), and had absolutely no contact with his audience. Although I had taken many French courses in college I still had trouble following the lectures. It was only near the end of the year that I became at all at ease with the language.After his year abroad, Widder returned to Harvard for the beginning of the 1921-22 academic year. He was appointed as a half-time teaching fellow while he worked for his Master's degree which he was awarded in 1923. He then became a full-time research student working on his Ph.D. thesis advised by G D Birkhoff. In 1924 he published the paper

*A general mean-value theorem*which begins:-

In a paper published in 1906 [General mean-value and remainder theorems], Professor G D Birkhoff treated the mean-value and remainder theorems belonging to polynomial interpolation, in which the linear differential operator $u^{(n)}$ played a particular role. It is natural to expect that a generalization of many of the ideas of that paper may apply to the general linear differential operator of order $n$, and the author is attempting such a program. This generalization throws fundamentally new light on the theory of trigonometric interpolation.Widder was awarded his Ph.D. in 1924 for his thesis

*Theorems of mean value and trigonometric interpolation*.

After the award of his Ph.D., Widder was appointed to Bryn Mawr College where the head of mathematics was Anna Pell. Anna Pell had been a professor at Bryn Mawr since 1918 but had only become head of mathematics in 1924 when Charlotte Angas Scott retired. Anna Pell married Arthur Leslie Wheeler in July 1925 and she retired from Bryn Mawr. At this time Widder was appointed so succeed her as head of mathematics. He writes [12]:-

During my stay at Bryn Mawr I was granted one year's leave of absence, assisted financially by a National Research Fellowship. The first part of the year was spent at the University of Chicago, where I had contact with G A Bliss and L E Dickson. The latter loved to play bridge at the Faculty Club after lunch, and I often joined the game. Next I went to the Rice Institute to study with S Mandelbrojt, a visiting lecturer. I found him very stimulating, full of ideas. Under his guidance I published two notes, one with J J Gergen, in 'Comptes Rendus'.In 1879 Radcliffe College was set up in Cambridge, Massachusetts, to provide university level education for women who were not admitted to Harvard University. Ada Louise Comstock became the third President of Radcliffe in 1923. In 1930 Widder moved to Cambridge, Massachusetts, when he was given a joint appointment to Radcliffe College and Harvard University. Ada Comstock negotiated a new relationship between Radcliffe College and Harvard University in the 1940s and eventually Widder became a full professor at Harvard. The full merger of Radcliffe College into Harvard University, however, did not happen until 1977.

Widder, in collaboration with Arthur Coble and Joseph Miller Thomas, became a founding managing editor of the

*Duke Mathematical Journal*in 1935. Roland Richardson, the Secretary of the American Mathematical Society, wrote in a letter of 13 January 1936:-

In my dozen years as Secretary of the American Mathematical Society no project has interested me more than the founding of this new mathematical journal. ... It was not thought by anybody that a new journal could start off at such a high level in quality and quantity.In 1935-36 Widder had his first sabbatical leave and, funded by a Guggenheim Fellowship, he spent the year in Cambridge, England, working with G H Hardy [12]:-

That year I wrote the final chapters of my book, 'The Laplace Transform'. At times Hardy would invite me to dine with him at high table in Trinity College, where I met A S Besicovitch, among other notables. I attended his course on Almost Periodic Functions. He was less inspiring than Hardy. Hardy liked bridge, and he often came to my digs for several rubbers with other visiting students.Widder's book

*The Laplace Transform*was published in 1941. Francis Joseph Murray writes in the review [10]:-

The book is certainly enjoyable and interesting. The style is clear, there are few typographical errors and the subject matter is increasingly impressive as one reads on. The applications are particularly striking. In some cases, it is not clear why so many proofs of the same theorem are given and a guide to a reader who might be interested in any one of the many specific results would be valuable. However, it would be quite easy to use various topics treated in the book in a course, whose main interest is not integral operators. One might mention, the Riemann-Stieltjes integral, functions of bounded variation, methods of summation of series, positive definite series, the moment problems, Bernstein's theorem, the Tauberian theorems, the prime number theorem, the Laguerre polynomials, the notion of a positive definite kernel of an integral equation, and the specific integral equations mentioned. Thus the author has presented us with a treatise on a branch of analysis of great importance and whose applications are of wide interest. The book is extremely satisfactory, when concerned with either its principal topics or the other related developments and one is confident that it will have a most valuable effect both on research and graduate study.This book became a classic and there was a Dover unabridged republication of the 1941 edition in 2010. For extracts from other reviews, see THIS LINK.

By the time the book was published, Widder had married. On 12 June 1939 he married Vera Adela Ames (1909-2004), a teacher born in Milestone, Saskatchewan, Canada. They had met at Anna Pell Wheeler's summer cottage in the Adirondacks and were married in Marlboro, New Hampshire. Vera was the daughter of Charles Edgar Ames, a farmer, and Margaret Ophelia Mooney. At the time of the marriage she was Canadian but became a naturalised American in July 1948. She was born on a farm and [13]:-

... attended Milestone School, accumulating 20,000 miles by horse to obtain her early education. She went on to receive a B.A. and M.A. in Mathematics from University of Saskatchewan and a Ph.D. in Mathematics awarded in 1938 from Bryn Mawr College.David and Vera Widder had two children, David Charles Widder (5 August 1940 - 28 December 2010) and Edith Anne Widder (born 11 June 1951). Let us note at this point that David C Widder studied Mechanical Engineering at Northeastern University and Edith Widder studied biology at Tufts University. She became a senior scientist and director of the Bioluminescence Department at the Harbor Branch Oceanographic Institution working there from 1989 to 2005. She then co-founded the Ocean Research & Conservation Association, an organisation whose aim is to protect aquatic ecosystems. She married David Smith, a computer scientist.

Widder attended many conferences, helped to organise some and made research visits. For example he served on the Organising Committee for the International Congress of Mathematicians was held in Cambridge, Massachusetts, from 30 August to 6 September 1950. This Committee was chaired by Garrett Birkhoff. On 2 August 1954 Widder, his wife and children went to France for six weeks. They sailed from Atlantic Seaports, Quebec, Nova Scotia, Canada, on the 'Empress of Australia', arriving in Liverpool, England, before continuing to France. They arrived back in Quebec on 17 September. In March 1955 he attended the 'Conference on Differential Equations' held at the University of Maryland to honour to Alexander Weinstein's 60th birthday on 21 January 1957. He published

*The heat equation and the Weierstrass transform*in the Conference

*Proceedings*.

In 1966 the International Congress of Mathematicians was held in Moscow from 16 August to 26 August. Widder attended this Congress and his wife Vera accompanied him. He wrote [13]:-

I was told that I I Hirschman and I were due royalties on our book, 'The Convolution Transform', which had been translated into Russian (without our permission). We were each given $400 but were not allowed to take it out of Russia. Our train left next day, but we gave a dinner at our hotel for the E R Loves, from Australia, and Lennart Carleson's family, from Uppsala, Sweden. Also Vera bought a silver fox stole and a few nicknacks. It was fun to be forced to spend!In 1967 he attended the conference 'Orthogonal Expansions and their Continuous Analogues' in Edwardsville, Illinois and published the paper

*Expansions in terms of the homogeneous solutions of the heat equation*in the Conference

*Proceedings*.

His wife Vera Widder continued to teach mathematics. She [13]:-

... taught mathematics at Tufts University and University of Massachusetts and did volunteer tutoring as part of the Boston school integration program and in Concord prison.In addition to

*The Laplace transform*(1941) which we mentioned above, Widder wrote several other important books. Thee are:

*Advanced Calculus*(1947); (with Isidore I Hirschman)

*The Convolution Transform*(1955);

*An Introduction to Transform Theory*(1971); and

*The Heat Equation*(1975). For extracts from reviews and Prefaces for these books, see THIS LINK.

David Widder died in Arlington, Massachusetts and was buried in Maytown Union Cemetery in Maytown, Pennsylvania, his mother's home town.

Let us give some details of Widder's wife, following his death [13]:-

After her husband's death in 1990 Vera remained in Boston until 1998 when she moved to Sarasota, Florida. ... She was an extraordinary woman, a loving and thoughtful mother, a patient and kind teacher, a good citizen and human rights activist and above all, a person of exceptional courage.After Vera died in 2004, she was buried with her husband in Maytown Union Cemetery.

### References (show)

- T A A B, Review: The Laplace transform, by David Vernon Widder,
*Science, New Series***95**(2473) (1942), 531-532. - R P Boas, Review: The Laplace transform, by David Vernon Widder, The Mathematical Gazette 27 (273) (1943), 37-39.
- R L Goodstein, Review: Advanced Calculus, by David Vernon Widder,
*The Mathematical Gazette***31**(297) (1947), 298-300. - D T Haimo, Review: The Heat Equation, by D V Widder,
*SIAM Review***19**(2) (1977), 364-365. - I I Hirschman, Jr, Review: An Introduction to Transform Theory, by D V Widder,
*SIAM Review***15**(2.1) (1973), 396-397. - I I Hirschman, Review: An Introduction to Transform Theory, by D V Widder,
*American Scientist***62**(1) (1974), 120. - I I Hirschman, Review: The Heat Equation, by D V Widder,
*American Scientist***65**(3) (1977), 377. - E LaFon, Review: Advanced Calculus, Second Edition, by David Vernon Widder,
*Amer. Math. Monthly***69**(6) (1962), 578. - H S W M, Review: Advanced Calculus, by David Vernon Widder,
*Science Progress*(1933-)**36**(142) (1948), 342. - F J Murray, Review: The Laplace transform, by David Vernon Widder,
*Bull. Amer. Math. Soc.***48**(9.1) (1942), 642-646. - H S Wall, Review: Advanced Calculus, by David Vernon Widder, Mathematics Magazine 22 (3) (1949), 159-161.
- D V Widder, Some Mathematical Reminiscences, in
*P L Duren, R A Askey and U C Merzbach (eds.), A Century of Mathematics in America*(American Mathematical Society, Providence, Rhode Island, 1988), 79-84. - Vera A Widder (1909-2004),
*The Boston Globe*(Sunday, 23 May 2004). - L C Young, Review: The Convolution Transform by I I Hirschman and D V Widder, Science, New Series 123 (3195) (1956), 512-513.

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Written by J J O'Connor and E F Robertson

Last Update November 2019

Last Update November 2019