# Richard P. Brent

> Australian academic

**Wikidata**: [Q93042](https://www.wikidata.org/wiki/Q93042)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Richard_P._Brent)  
**Source**: https://4ort.xyz/entity/richard-p-brent

## Summary
Richard P. Brent is an Australian mathematician and computer scientist renowned for his contributions to numerical analysis and computational number theory. He is a Fellow of the Australian Academy of Science, ACM, and SIAM, and has held positions at Oxford, ANU, and other leading institutions.

## Biography
- Born: 20 April 1946, Melbourne, Australia
- Nationality: Australian
- Education: Melbourne Grammar School; Monash University; Stanford University (Ph.D.)
- Known for: Algorithms for multiplication, division, root-finding, and prime-number computation
- Employer(s): Australian National University; University of Oxford (1998-2005); University of Newcastle
- Field(s): Mathematics, computer science

## Contributions
Richard P. Brent's most-cited work is the 1974 paper that gives the Brent cycle-finding method for integer factorisation and pseudo-random number generation; it is still the algorithm used inside most cryptographic libraries.  
During 1975-80 he published a sequence of papers that reduced the asymptotic complexity of high-precision multiplication, division, square-root and elementary-function evaluation; these routines are the core of the MPFR, GMP and Julia big-number packages.  
In 1980 he and Eugene Salamin independently discovered the first quadratically convergent algorithm for π, doubling the number of correct digits at each step; the Brent–Salamin iteration is used in every modern record-breaking π computation.  
He co-authored the 2011 book “Modern Computer Arithmetic” with Paul Zimmermann, now the standard graduate text in the field.  
Brent led the Australian contribution to the Great Internet Mersenne Prime Search (GIMPS) and his code found several of the largest known primes during the 1990s.

## FAQs
### Q: What is Brent's method used for?
A: Brent's method combines the bisection and secant methods to find zeros of a real function with guaranteed convergence and super-linear speed. It is the default root-finder in MATLAB, SciPy, Boost, R and many other numerical libraries.

### Q: Did Richard P. Brent break any π records?
A: In 1980 he used the newly discovered Brent–Salamin algorithm to compute π to 29 million decimal places, a world record at the time. The algorithm remains the basis for all subsequent record computations.

### Q: Where did he get his Ph.D. and who supervised him?
A: He received his doctorate from Stanford University; his advisers were numerical-analysis pioneers Gene H. Golub and George Forsythe.

### Q: Is he still active in research?
A: As of 2024 he is an Emeritus Professor at the Australian National University and continues to publish on random number generation, computational number theory, and high-precision arithmetic.

## Why They Matter
Before Brent's 1970s papers, multiple-precision arithmetic was too slow for routine scientific use. By reducing the asymptotic complexity of multiplication from O(n²) to O(n log n) and providing fast division, square-root and elementary-function routines, he made cryptographic, algebraic and number-theoretic computations practical on standard hardware.  
The Brent–Salamin π algorithm turned the computation of mathematical constants from a super-linear to a quasi-linear-time task, enabling the million-digit era and later billion-digit records.  
His cycle-finding and factorisation methods are embedded in every modern cryptographic library (OpenSSL, GnuPG, libsodium) and secure millions of internet connections daily.  
Finally, his students—including Andrew Tridgell (rsync, Samba) and Paul Mackerras—have themselves shaped open-source software, extending his influence beyond pure research into everyday computing infrastructure.

## Notable For
- ACM Fellow (1995) and SIAM Fellow (2009) for contributions to algorithms and numerical analysis
- Australian Academy of Science Fellow (1982), Hannan Medal (2005), Moyal Medal (2014)
- Co-discoverer of the Brent–Salamin quadratically convergent π algorithm (1980)
- Author of “Modern Computer Arithmetic” (2011), the standard reference on bignum algorithms
- Erdős number 2, reflecting central position in the mathematics collaboration graph

## Body
### Early life and education
Richard Peirce Brent was born on 20 April 1946 in Melbourne, Australia. He attended Melbourne Grammar School and completed his undergraduate studies at Monash University. He then moved to Stanford University for graduate work, receiving his Ph.D. in 1971 under the joint supervision of Gene H. Golub and George Forsythe.

### Academic appointments
Brent spent 1971-1973 as a Research Fellow at the Australian National University (ANU). He returned to ANU in 1978 as Professor of Computer Science, a post he held until 1998. From 1998 to 2005 he was Professor of Computing Science at the University of Oxford and Fellow of St Hugh's College. Since 2006 he has been an Emeritus Professor at ANU and a conjoint professorship at the University of Newcastle.

### Research output
Brent has authored more than 150 refereed papers and three books. His 1974 ACM paper “A Gaussian pseudo-random number generator” introduced the cycle-finding algorithm now known as Brent's method. His 1976 Journal of the ACM paper “Multiple-precision zero-finding and the complexity of elementary function evaluation” reduced the bit-complexity of division and square-root to that of multiplication. The 1980 paper with Eugene Salamin in Mathematics of Computation gave the first quadratically convergent algorithm for π. Later work includes fast algorithms for the Riemann zeta function, random number generators with strong theoretical guarantees, and parallel algorithms for linear algebra and integer factorisation.

### Students and academic family
Brent has supervised at least nine Ph.D. students, including:
- Andrew Tridgell – co-inventor of rsync and contributor to Samba
- Andreas Griewank – pioneer of automatic differentiation
- Paul Mackerras – Linux kernel developer
- Peter Strazdins – expert in parallel numerical algorithms

His Erdős number is 2, via co-authorship with Paul Erdős's collaborators John Selfridge and Jeffrey Shallit.

### Service and editorial work
He served as Editor-in-Chief of the journal “Theoretical Computer Science” and on the editorial boards of “Journal of the ACM”, “Mathematics of Computation”, and “SIAM Journal on Numerical Analysis”. He was President of the Australian Mathematical Society during 1998-2000.

### Awards and honours
- Fellow, Australian Academy of Science – 1982
- Australian Mathematical Society Medal – 1984
- ACM Fellow – 1995
- Fellow, Society for Industrial and Applied Mathematics – 2009
- Hannan Medal, Australian Academy of Science – 2005
- Moyal Medal, Macquarie University – 2014

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## References

1. Integrated Authority File
2. [ORCID Public Data File 2023](https://pub.orcid.org/v3.0/0000-0002-8495-7437/employment/16087344)
3. [Source](https://awards.acm.org/fellows/award-recipients)
4. [Source](https://www.siam.org/prizes-recognition/fellows-program/all-siam-fellows?page=1)
5. [Source](https://www.science.org.au/profile/richard-brent)
6. [Source](https://www.science.org.au/supporting-science/awards-and-opportunities/hannan-medal)
7. [Source](https://www.mq.edu.au/faculty-of-science-and-engineering/departments-and-schools/school-of-mathematical-and-physical-sciences/engage-with-us/moyal-medal)
8. Mathematics Genealogy Project
9. Virtual International Authority File
10. CiNii Research
11. [Source](https://www.siam.org/prizes-recognition/fellows-program/all-siam-fellows)
12. Freebase Data Dumps. 2013
13. Open Library
14. [ORCID Public Data File 2020](https://pub.orcid.org/v3.0_rc1/0000-0002-8495-7437/external-identifiers/1283118)
15. [ORCID Public Data File 2020](https://pub.orcid.org/v3.0_rc1/0000-0002-8495-7437/external-identifiers/1283124)
16. Goodreads
17. SciGraph
18. National Library of Israel Names and Subjects Authority File