Timothy Trudgian is an Australian

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, mathematical structure, structure, space, Mathematica ...

specializing in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and related fields. He is known for his work on

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic c ...

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 Dir ...

, and distribution of primes. He currently is a

Professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

at the University of New South Wales (Canberra).

Education and Career

Trudgian completed his BSc (Hons) at the

Australian National University The Australian National University (ANU) is a public university, public research university and member of the Group of Eight (Australian universities), Group of Eight, located in Canberra, the capital of Australia. Its main campus in Acton, A ...

in December 2005, then his Ph.D. from the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

in June 2010 under the supervision of

Roger Heath-Brown David Rodney "Roger" Heath-Brown is a British mathematician working in the field of analytic number theory. Education He was an undergraduate and graduate student of Trinity College, Cambridge; his research supervisor was Alan Baker. Career ...

. His dissertation was titled ''Further results on Gram's Law''.

Research

Trudgian has made significant contributions to the field of (analytic) number theory. His research includes work on

, distribution of primes, and

primitive root modulo n In modular arithmetic, a number is a primitive root modulo if every number coprime to is congruent to a power of modulo . That is, is a ''primitive root modulo'' if for every integer coprime to , there is some integer for which ...

. One of his notable achievements is proving that 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 pure ...

is true up to 3 trillion. In 2024, together with

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the Co ...

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.

Recognition

Trudgian is a Fellow of the

Australian Mathematical Society The Australian Mathematical Society (AustMS) was founded in 1956 and is the national society of the mathematics profession in Australia. One of the society's listed purposes is to promote the cause of mathematics in the community by representing ...

, elected in 2023.

Personal life

Trudgian is married and he has two sons.

References

{{DEFAULTSORT:Trudgian, Timothy Australian mathematicians Number theorists Living people Year of birth missing (living people)