American mathematician whose major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing.
Worked closely with Norbert Wiener in his early career.
In $1974$ he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.
- Born: 11 August 1912 in Lynn, Massachusetts, USA
- 1929: Entered the Massachusetts Institute of Technology to study electrical engineering
- 1934: Awarded a Bachelor of Science degree and a Master of Science degree, both in electrical engineering
- 1937: Joined the faculty of the Massachusetts Institute of Technology
- 1944: Promoted to Associate Professor in 1944
- 1949: Promoted to full Professor
- 1954: Awarded the Bôcher Memorial Prize of the American Mathematical Society
- 1970: Awarded the Lester R. Ford Award
- 1971: Awarded the Chauvenet Prize
- Died: 10 October 1975 in Boston, Massachusetts, USA of a brain tumour
Theorems and Definitions
- 1935: On the Non-Vanishing of a Function (D.Sc. Thesis)
- 1940: Gap and Density Theorems
- 1947: The Wiener RMS error criterion in filter design and prediction (J. Math. Phys. Vol. 25: 261 – 278)
- 1955: Theory of ordinary differential equations (with Earl A. Coddington)
- 1964: Generalization of an inequality of Ky Fan (J. Math. Anal. Appl. Vol. 8: 133 – 134)
- 1968: Summing certain number theoretic series arising in the sieve (J. Math. Anal. Appl. Vol. 22: 631 – 645)
- 1969: A Motivated Account of an Elementary Proof of the Prime Number Theorem (Amer. Math. Monthly Vol. 76: 225 – 245)
- February 1973: Remarks on a formula of Riemann for his zeta-function (J. Math. Anal. Appl. Vol. 41, no. 2: 345 – 351)
- 1974: Zeros of the Derivatives of the Riemann Zeta Function (Acta Math. Vol. 133: 49 – 65) (with Hugh Lowell Montgomery)
- April 1974: At least one third of the zeros of Riemann's zeta-function are on $\sigma = 1/2$ (Proc. Natl. Acad. Sci. U S A Vol. 71: 1013 – 1015) www.jstor.org/stable/63251
- August 1974: More than one third of zeros of Riemann's zeta-function are on $\sigma = 1/2$ (Advances in Mathematics Vol. 13, no. 4: 383 – 436)
- One day shortly after his paper on the Riemann zeta function appeared, he knocked at the door, came in, and sat down. He looked pale and ill. He complained of a strong headache. ... Shortly afterwards, he entered Massachusetts General Hospital. ... in the August of that summer [I] visited him ... His head was shaven, and red and black lines were drawn on it. ... I never saw him again.