Philip Gibbs

Philip Gibbs
Philip Gibbs
Born	20 February 1960; England
Education	University of Cambridge; University of Glasgow
Occupation	Mathematician, Software Engineer
Known for	viXra; Research on Jeanne Louise Calment

Philip Gibbs (born 20 February 1960) is a British independent mathematician known for contributions to geometric optimisation, number theory, and preprint archiving.[1][2]

Early life and career[edit]

Gibbs earned a BA in mathematics from the University of Cambridge and a PhD in theoretical physics from the University of Glasgow. He worked as a software engineer in sectors including ship design, air traffic control, and finance before retiring in 2006.[3]

viXra[edit]

In 2009, Gibbs founded viXra, an open e-print archive reversing arXiv's name and moderation policies to allow unrestricted submissions, amid criticisms of arXiv's alleged "blacklisting."[4][5]

Lebesgue universal covering problem[edit]

In 2015 and 2018, Gibbs published improvements to the smallest known universal cover for unit-diameter sets, reducing the conjectured area from 0.8441377 to 0.84409359 using computer simulations and Euclidean geometry proofs. His work was assisted by mathematician John Baez.[3][6][7]

Diophantine m-tuples[edit]

In 1999, Gibbs discovered the first known rational Diophantine sextuple, where the product of any two distinct elements plus one is a perfect square. The set is {11/192, 35/192, 155/27, 512/27, 1235/48, 180873/16}.[8] This extended classical results by Diophantus (quadruples) and Leonhard Euler (quintuples), and has inspired constructions of infinite families of sextuples, though no rational septuple is known.[9][10] The discovery has been cited over 100 times in scholarly literature.[11]

Other contributions[edit]

Gibbs has made further contributions to recreational and computational mathematics:

Co-authored computational studies on Ulam sequences, including numbers up to 10¹² and density conjectures.[12][13]
Developed numerical methods for the moving sofa problem, aligning with Joseph Gerver's conjectured optimal shape.[14]
Co-investigated perfect cuboids with efficient search algorithms.[15]
Analyzed Jeanne Calment's longevity claim using Bayesian methods, suggesting a 99.99% probability of an identity switch.[16]

References[edit]

↑ Kevin Hartnett (2018-11-15). "Amateur Mathematician Finds Smallest Universal Cover". Quanta Magazine. Retrieved 2025-10-04.
↑ "Fledgling site challenges arXiv server". Physics World. 2009-07-15. Retrieved 2025-10-04.
↑ ^3.0 ^3.1 Kevin Hartnett (2018-11-15). "Amateur Mathematician Finds Smallest Universal Cover". Quanta Magazine. Retrieved 2025-10-04.
↑ Hamish Johnston (2009-07-09). "Blacklisted?". Physics World. Retrieved 2025-10-04.
↑ "Fledgling site challenges arXiv server". Physics World. 2009-07-15. Retrieved 2025-10-04.
↑ Philip Gibbs (2015-10-12). "Further Improvement to Lebesgue's Universal Covering Problem". arXiv:1510.03377 [math.MG].
↑ Philip Gibbs (2018-05-18). "Another Improvement to Lebesgue's Universal Covering Problem". arXiv:1805.07349 [math.MG].
↑ Philip Gibbs (1999-02-13). "Some Rational Diophantine Sextuples". arXiv:math/9902081 |class= ignored (help).
↑ Dujella, A.; et al. (2019-10). "Rational Diophantine sextuples with square denominators". Journal of Number Theory. 202: 255–270. doi:10.1016/j.jnt.2019.05.023. PMID 31303758. Explicit use of et al. in: |author= (help); Check date values in: |date= (help)
↑ Dujella, A. (2004). "Diophantine m-tuples". In Thangadurai, R.; et al. (eds.). Diophantine m-tuples. De Gruyter. pp. 111–128. doi:10.1515/9783110256239.111. ISBN 978-3-11-025623-9. Explicit use of et al. in: |editor= (help)
↑ Philip Gibbs (1999). "Some Rational Diophantine Sextuples". Google Scholar. Retrieved 2025-10-04.
↑ Gibbs, P.; McCranie, J. (2017-01-13). "The Ulam Numbers up to One Trillion". arXiv:1701.03597 [math.NT].CS1 maint: multiple names: authors list (link)
↑ "Ulam sequence". OEIS. Retrieved 2025-10-04.
↑ Philip Gibbs (2014-11-02). "A Computational Study of Sofas and Cars". arXiv:1411.0038 [math.MG].
↑ de Grey, A.; Gibbs, P.; et al. (2024-01-06). "Novel required properties of, and efficient algorithms to seek, perfect cuboids". arXiv:2401.06784 [math.NT]. Explicit use of et al. in: |author= (help)CS1 maint: multiple names: authors list (link)
↑ Zak, N.; Gibbs, P. (2019-10). "A Bayesian Assessment of the Longevity of Jeanne Calment". Rejuvenation Research. 22 (5): 546–554. doi:10.1089/rej.2019.2227. PMID 31092043. Check date values in: |date= (help)CS1 maint: multiple names: authors list (link)

[1] Kevin Hartnett (2018-11-15). "Amateur Mathematician Finds Smallest Universal Cover". Quanta Magazine. Retrieved 2025-10-04.

[2] "Fledgling site challenges arXiv server". Physics World. 2009-07-15. Retrieved 2025-10-04.

[quanta-3] 3.0 ^3.1 Kevin Hartnett (2018-11-15). "Amateur Mathematician Finds Smallest Universal Cover". Quanta Magazine. Retrieved 2025-10-04.

[4] Hamish Johnston (2009-07-09). "Blacklisted?". Physics World. Retrieved 2025-10-04.

[5] "Fledgling site challenges arXiv server". Physics World. 2009-07-15. Retrieved 2025-10-04.

[6] Philip Gibbs (2015-10-12). "Further Improvement to Lebesgue's Universal Covering Problem". arXiv:1510.03377 [math.MG].

[7] Philip Gibbs (2018-05-18). "Another Improvement to Lebesgue's Universal Covering Problem". arXiv:1805.07349 [math.MG].

[8] Philip Gibbs (1999-02-13). "Some Rational Diophantine Sextuples". arXiv:math/9902081 |class= ignored (help).

[9] Dujella, A.; et al. (2019-10). "Rational Diophantine sextuples with square denominators". Journal of Number Theory. 202: 255–270. doi:10.1016/j.jnt.2019.05.023. PMID 31303758. Explicit use of et al. in: |author= (help); Check date values in: |date= (help)

[10] Dujella, A. (2004). "Diophantine m-tuples". In Thangadurai, R.; et al. (eds.). Diophantine m-tuples. De Gruyter. pp. 111–128. doi:10.1515/9783110256239.111. ISBN 978-3-11-025623-9. Explicit use of et al. in: |editor= (help)

[11] Philip Gibbs (1999). "Some Rational Diophantine Sextuples". Google Scholar. Retrieved 2025-10-04.

[12] Gibbs, P.; McCranie, J. (2017-01-13). "The Ulam Numbers up to One Trillion". arXiv:1701.03597 [math.NT].CS1 maint: multiple names: authors list (link)

[13] "Ulam sequence". OEIS. Retrieved 2025-10-04.

[14] Philip Gibbs (2014-11-02). "A Computational Study of Sofas and Cars". arXiv:1411.0038 [math.MG].

[15] Grey, A.; Gibbs, P.; et al. (2024-01-06). "Novel required properties of, and efficient algorithms to seek, perfect cuboids". arXiv:2401.06784 [math.NT]. Explicit use of et al. in: |author= (help)CS1 maint: multiple names: authors list (link)

[16] Zak, N.; Gibbs, P. (2019-10). "A Bayesian Assessment of the Longevity of Jeanne Calment". Rejuvenation Research. 22 (5): 546–554. doi:10.1089/rej.2019.2227. PMID 31092043. Check date values in: |date= (help)CS1 maint: multiple names: authors list (link)