Timothy Trudgian
{{short description|Australian number theorist}}
{{Infobox scientist
| name = Timothy Trudgian
| image =
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| birth_name = Timothy Scott Trudgian
| birth_date = {{birth year and age|1984|}}
| birth_place = Brisbane, Australia
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| fields = Mathematics
| workplaces = {{ubl|Merton College, Oxford|Australian National University| University of Lethbridge | University of New South Wales}}
| alma_mater = {{ubl|University of Oxford|Australian National University}}
| thesis_title = Further results on Gram's Law
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| thesis_year = 2010
| doctoral_advisor = Roger Heath-Brown
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Timothy Trudgian is an Australian mathematician specializing in number theory and related fields. He is known for his work on Riemann zeta function, analytic number theory, and distribution of primes. He currently is a Professor at the University of New South Wales (Canberra).{{Cite web|url=https://research.unsw.edu.au/people/professor-timothy-trudgian/|title = Professor Timothy Trudgian|access-date=2025-02-01}}
Education and Career
Trudgian completed his BSc (Hons) at the Australian National University in December 2005, then his Ph.D. from the University of Oxford in June 2010 under the supervision of Roger Heath-Brown. His dissertation was titled Further results on Gram's Law.{{Cite thesis|url=https://ora.ox.ac.uk/objects/uuid:04eeba27-584b-48fe-ae6b-7dc504268209|title = Further results on Gram's Law| date= 2010 | publisher=University of Oxford | author=Timothy Trudgian }}
Research
Trudgian has made significant contributions to the field of (analytic) number theory. His research includes work on Riemann zeta function, distribution of primes, and primitive root modulo n. One of his notable achievements is proving that the Riemann hypothesis is true up to 3 × 1012.{{cite journal |author1=Dave Platt |author2=Timothy Trudgian |title=The Riemann hypothesis is true up to 3 × 1012 |journal=Bulletin of the London Mathematical Society |year=2021 |volume=53 |issue=3 |pages=792–797 |doi=10.1112/blms.12460 |url=https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/blms.12460|arxiv=2004.09765 }} In 2024, together with Terence Tao and Andrew Yang, Trudgian published an on-going database of known theorems for various exponents appearing in analytic number theory, named Analytic Number Theory Exponent Database (ANTEDB), which could be used in the future for Lean formalization.{{Cite web|url=https://github.com/teorth/expdb/|title = Analytic Number Theory Exponent Database|access-date=2025-02-01}}{{cite arxiv |last1=Tao |first1=Terence |last2=Trudgian |first2=Timothy |last3=Yang |first3=Andrew |title=New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach |year=2025 |eprint=2501.16779 |class=math.NT}}
Recognition
Trudgian is a Fellow of the Australian Mathematical Society, elected in 2023.[https://www.unsw.edu.au/content/dam/pdfs/unsw-canberra/2024-05-cv/CVlight2012-08-09.pdf Curriculum vitae]