**Norman Levinson** was an American mathematician who worked with Fourier transforms, complex analysis, non-linear differential equations, number theory and signal processing.

- These school years were not easy for Norman but he helped his fellow pupils with their homework which put him on good terms with them.
- These years had a lasting effect on Norman, however.
- Levinson entered the Massachusetts Institute of Technology in 1929 but he did not register for a mathematics degree, rather he studied for a degree in Electrical Engineering.
- The turning point in Levinson's studies had come when he signed up for Wiener's graduate course on Fourier series and integrals in 1933-34.
- After the award of his Master's degree in electrical engineering, Levinson applied to MIT to begin studying for his doctorate in mathematics.
- However the Mathematics Department were convinced that he had already done sufficient for the Ph.D. before starting the course! Instead Wiener together with Phillips, the Head of Mathematics, arranged for Levinson to receive an MIT Redfield Proctor Traveling Fellowship so that he could spend the year at Cambridge in England.
- The attraction of Cambridge for Levinson was the fact the G H Hardy, one of the world's most respected mathematicians, taught there.
- When Levinson returned to MIT in 1935 he was awarded a Doctor of Science degree for a thesis entitled Non-vanishing of a function.
- At the Institute for Advanced Study, Levinson was attached to von Neumann who was to act as a supervisor, but Levinson was a fully independent research worker by this time and certainly did not need a supervisor.
- The Great Depression began in 1929, the year Levinson entered MIT, and by 1932 one quarter of the workers in the United States were unemployed.
- As Levinson undertook his research at Princeton he felt that he had little prospects of gaining a university job, partly because of the high unemployment, but also because anti-Semitism in the United States at this time meant that Jewish mathematicians found it much harder than others to get posts.
- Levinson formed a plan to train as an actuary and try for a job with an insurance company after his Fellowship at Princeton ended.
- If Levinson really had not met Hardy during his year at Cambridge, it was certainly Hardy who fought for Levinson to get a permanent job when he visited the United States.
- Levinson was an obvious person for them to hire and was recommended to them by Wiener but anti-Semitism at MIT tried to prevent such a move.
- The university's provost, Vannevar Bush, turned down Wiener's recommendation that Levinson be offered a position as Instructor but Hardy, on a visit to MIT, went with Wiener to the provost's office to protest against the decision.
- If it isn't, why not hire Levinson.
- Levinson was appointed as an Instructor at MIT in February 1937 having been released from his Fellowship by Princeton before its term was complete.
- In 1940 Levinson published Gap and density theorems in the American Mathematical Society Colloquium Publication Series.
- subsumes much of Levinson's brilliant early research in harmonic and complex analysis.
- By 1954 Levinson had been a professor for five years.
- Levinson believed in employment for all, fighting anti-Semitism, and fighting discrimination against blacks.
- When he learnt of the direction that Stalin had taken Communism in Russia, Levinson left the American Communist Party.
- The Committee demanded that Levinson name other members of the American Communist Party but, although he agreed to talk freely about what he did as a member of the Party, he refused to name others since he knew the consequences that would have.
- Let us return to discuss further Levinson's mathematical contributions.
- Levinson wrote only two papers on time series, but these had a large impact.
- The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifically by his seminal work initiated by Cartwright and Littlewood.
- In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed differential equations.
- Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann hypothesis.
- For a paper on number theory Levinson received the 1971 Chauvenet Prize of the Mathematical Association of America.
- Although Levinson had feared all his life that he would die of a heart attack, and was extremely careful with his diet in an attempt to avoid this fate, it was a brain tumour which lead to his death.
- After his death the MIT Faculty prepared a tribute to Levinson.
- Throughout the mathematical world the name of MIT and the name of Norman Levinson have been synonymous for many years.

Born 11 August 1912, Lynn, Massachusetts, USA. Died 10 October 1975, Boston, Massachusetts, USA.

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Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive