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, structure, space, models, and change. History On ...

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 Diric ...

Career

Schoenfeld received his Ph.D. in 1944 from

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

under the direction of

Hans Rademacher Hans Adolph Rademacher (; 3 April 1892, Wandsbeck, now Hamburg-Wandsbek – 7 February 1969, Haverford, Pennsylvania, USA) was a German-born American mathematician, known for work in mathematical analysis and number theory. Biography Rademacher r ...

. In 1953, as an assistant professor at the

University of Illinois Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...

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

tenured Tenure is a category of academic appointment existing in some countries. A tenured post is an indefinite academic appointment that can be terminated only for cause or under extraordinary circumstances, such as financial exigency or program disco ...

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 Pennsylvan ...

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 called the University at Buffalo (UB) and sometimes called SUNY Buffalo, is a public research university with campuses in Buffalo and Amherst, New York. The university was founded in 1846 ...

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 ...

: :

, \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 ''x''. It is denoted by (''x'') (unrelated to the number ). History Of great interest in number theory is t ...

''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 theoretic significance. In particular, according to the prime number theorem, it is a ...

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 Number theorists University of Pennsylvania alumni University of Illinois Urbana-Champaign faculty Pennsylvania State University faculty University at Buffalo faculty {{US-mathematician-stub