Lowell Schoenfeld (April 1, 1920 – February 6, 2002) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for his work in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

Career

Schoenfeld received his Ph.D. in 1944 from

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

under the direction of

Hans Rademacher Hans Adolph Rademacher (; 3 April 1892 – 7 February 1969) was a German-born American mathematician, known for work in mathematical analysis and number theory. Biography Rademacher received his Ph.D. in 1916 from Georg-August-Universität Göt ...

. In 1953, as an assistant professor at the

University of Illinois Urbana-Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public university, public land-grant university, land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United ...

, he married (as his second wife) associate professor Josephine M. Mitchell, causing the university to fire her from her

tenured Tenure is a type of academic appointment that protects its holder from being fired or laid off except for cause, or under extraordinary circumstances such as financial exigency or program discontinuation. Academic tenure originated in the United ...

position under its anti-nepotism rules while allowing him to keep his more junior tenure-track job. They both resigned in protest, and after several short-term positions they were both able to obtain faculty positions at

Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsyl ...

in 1958. They were both promoted to full professor in 1961, and moved to the

University at Buffalo The State University of New York at Buffalo (commonly referred to as UB, University at Buffalo, and sometimes SUNY Buffalo) is a public university, public research university in Buffalo, New York, Buffalo and Amherst, New York, United States. ...

in 1968.

Contributions

Schoenfeld is known for obtaining the following results in 1976, assuming the

Riemann hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

: :

, \pi(x)-(x), \le\frac

for all ''x'' ≥ 2657, based on the

prime-counting function In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number . It is denoted by (unrelated to the number ). A symmetric variant seen sometimes is , which is equal ...

''π''(''x'') and the

logarithmic integral function In mathematics, the logarithmic integral function or integral logarithm li(''x'') is a special function. It is relevant in problems of physics and has number theory, number theoretic significance. In particular, according to the prime number the ...

li(''x''), and :

, \psi(x)-x, \le\frac

for all ''x'' ≥ 73.2, based on the second Chebyshev function ''ψ''(''x'')..

References

External links

* 1920 births 2002 deaths 20th-century American mathematicians 21st-century American mathematicians American number theorists University of Pennsylvania alumni University of Illinois Urbana-Champaign faculty Pennsylvania State University faculty University at Buffalo faculty {{US-mathematician-stub