Kevin Ford (mathematician) explained

Kevin B. Ford
Birth Date:	1967 12, df=y
Nationality:	American
Fields:	Mathematics
Workplaces:	University of Illinois at Urbana-Champaign University of South Carolina
Alma Mater:	California State University, Chico University of Illinois at Urbana-Champaign
Doctoral Advisor:	Heini Halberstam
Known For:	Carmichael's totient function conjecture Sierpinski's conjecture Work on prime gaps

Kevin B. Ford (born 22 December 1967) is an American mathematician working in analytic number theory.

Education and career

He has been a professor in the department of mathematics of the University of Illinois at Urbana-Champaign since 2001. Prior to this appointment, he was a faculty member at the University of South Carolina.

Ford received a Bachelor of Science in Computer Science and Mathematics in 1990 from the California State University, Chico. He then attended the University of Illinois at Urbana-Champaign, where he completed his doctoral studies in 1994 under the supervision of Heini Halberstam.

Research

Ford's early work focused on the distribution of Euler's totient function. In 1998, he published a paper that studied in detail the range of this function and established that Carmichael's totient function conjecture is true for all integers up to

10 ^{10 ^{10}} .^[1] In 1999, he settled Sierpinski’s conjecture on Euler's totient function.^[2]

In August 2014, Kevin Ford, in collaboration with Green, Konyagin and Tao,^[3] resolved a longstanding conjecture of Erdős on large gaps between primes, also proven independently by James Maynard.^[4] The five mathematicians were awarded for their work the largest Erdős prize ($10,000) ever offered.^[5] In 2017, they improved their results in a joint paper.^[6]

He is one of the namesakes of the Erdős–Tenenbaum–Ford constant,^[7] named for his work using it in estimating the number of small integers that have divisors in a given interval.^[8]

Recognition

In 2013, he became a fellow of the American Mathematical Society.^[9]

Notes and References

1. The distribution of totients . Kevin . Ford . Ramanujan Journal . 2 . 1–2 . 67–151 . 10.1023/A:1009761909132. 1998 . 1104.3264 . 6232638.
2. The number of solutions of φ(x) = m . Kevin . Ford . Annals of Mathematics . 150 . 1 . 283–311 . Princeton University and the Institute for Advanced Study . 10.2307/121103 . 1999 . 121103 . 2019-04-19 . 2013-09-24 . https://web.archive.org/web/20130924145941/http://annals.math.princeton.edu/articles/7954 . dead .
3. Large gaps between consecutive primes . Ford. Kevin. Green. Ben. Konyagin. Sergei. Tao. Terence . Annals of Mathematics . 183 . 3 . 935–974 . 10.4007/annals.2016.183.3.4 . 2016 . 1408.4505 . 16336889 .
4. Large gaps between primes . James . Maynard . Annals of Mathematics . 183 . 3 . 915–933 . Princeton University and the Institute for Advanced Study . 10.4007/annals.2016.183.3.3 . 2016 . 1408.5110 . 119247836 .
5. Mathematicians Make a Major Discovery About Prime Numbers. Wired. 27 July 2015. Erica . Klarreich. 22 December 2014.
6. Long gaps between primes . Kevin. Ford . Ben . Green . Sergei . Konyagin . James . Maynard . Terence . Tao. Journal of the American Mathematical Society . 31 . 65–105 . 10.1090/jams/876 . 2018 . free . 1412.5029 .
7. Florian. Luca. Carl. Pomerance. Carl Pomerance. On the range of Carmichael's universal-exponent function. Acta Arithmetica. 162. 2014. 3. 289–308. 3173026. 10.4064/aa162-3-6.
8. Koukoulopoulos. Dimitris. 0905.0163. 10.1093/imrn/rnq045. 24. International Mathematics Research Notices. 2739805. 4585–4627. Divisors of shifted primes. 2010. 2010. 7503281.
9. https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society