# Kevin Ford (mathematician)

Kevin B. Ford
Born22 December 1967 (age 54)
NationalityAmerican
Alma materCalifornia State University, Chico
University of Illinois at Urbana-Champaign
Known for
Scientific career
FieldsMathematics
InstitutionsUniversity of Illinois at Urbana-Champaign
University of South Carolina

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 ${\displaystyle 10^{10^{10}}}$. [2] In 1999, he settled Sierpinski’s conjecture. [3]

In August 2014, Kevin Ford, in collaboration with Green, Konyagin and Tao, .[4] resolved a longstanding conjecture of Erdős on large gaps between primes, also proven independently by James Maynard .[5] The five mathematicians were awarded for their work the largest Erdős prize (\$10,000) ever offered. [6] In 2017, they improved their results in a joint paper. [7]

He is one of the namesakes of the Erdős–Tenenbaum–Ford constant,[8] named for his work using it in estimating the number of small integers that have divisors in a given interval.[9]

## Recognition

In 2013, he became a fellow of the American Mathematical Society.[10]

## References

1. ^
2. ^ Ford, Kevin (1998). "The distribution of totients". Ramanujan Journal. 2 (1–2): 67–151. arXiv:1104.3264. doi:10.1023/A:1009761909132. S2CID 6232638.
3. ^ Ford, Kevin (1999). "The number of solutions of φ(x) = m". Annals of Mathematics. Princeton University and the Institute for Advanced Study. 150 (1): 283–311. doi:10.2307/121103. JSTOR 121103.
4. ^ Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016). "Large gaps between consecutive primes". Annals of Mathematics. 183 (3): 935–974. arXiv:1408.4505. doi:10.4007/annals.2016.183.3.4. S2CID 16336889.
5. ^ Maynard, James (2016). "Large gaps between primes". Annals of Mathematics. Princeton University and the Institute for Advanced Study. 183 (3): 915–933. arXiv:1408.5110. doi:10.4007/annals.2016.183.3.3. S2CID 119247836.
6. ^ Klarreich, Erica (22 December 2014). "Mathematicians Make a Major Discovery About Prime Numbers". Wired. Retrieved 27 July 2015.
7. ^ Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence (2018). "Long gaps between primes". Journal of the American Mathematical Society. 31: 65–105. doi:10.1090/jams/876.
8. ^ Luca, Florian; Pomerance, Carl (2014). "On the range of Carmichael's universal-exponent function" (PDF). Acta Arithmetica. 162 (3): 289–308. doi:10.4064/aa162-3-6. MR 3173026.
9. ^ Koukoulopoulos, Dimitris (2010). "Divisors of shifted primes". International Mathematics Research Notices. 2010 (24): 4585–4627. arXiv:0905.0163. doi:10.1093/imrn/rnq045. MR 2739805. S2CID 7503281.
10. ^ List of Fellows of the American Mathematical Society, retrieved 2017-11-03.