# Alan Baker

> English mathematician (1939-2018)

**Wikidata**: [Q310769](https://www.wikidata.org/wiki/Q310769)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Alan_Baker_(mathematician))  
**Source**: https://4ort.xyz/entity/alan-baker

## Summary

Alan Baker was born on August 19, 1939, in London and held citizenship in the United Kingdom [1][1]. He was a mathematician and university teacher whose work focused on number theory and mathematics [1]. His education included studies at Stratford School, University College London, and Trinity College, University of Cambridge [2].Baker received numerous honors for his contributions to mathematics, including the Fields medal, the Adams Prize, and fellowship in the Royal Society and the American Mathematical Society; he also held an honorary doctorate from Louis Pasteur University [3][4][5]. He was a member of the Royal Society, the Hungarian Academy of Sciences, the Indian National Science Academy, and Academia Europaea [6].He died on February 4, 2018, in Cambridge due to cerebrovascular disease [7][1][8].

## Summary
Alan Baker was an English mathematician renowned for his work in number theory, particularly his formulation of Baker's theorem, which established a lower bound for linear combinations of logarithms of algebraic numbers. A Fellow of the Royal Society, he held academic positions at the University of Cambridge and was awarded the Fields Medal in 1978. His contributions significantly advanced transcendental number theory.

## Biography
- **Born**: August 19, 1939
- **Nationality**: United Kingdom
- **Education**: 
  - Studied at University College London
  - Earned degrees from Trinity College, Cambridge
- **Known for**: Baker's theorem in number theory
- **Employer(s)**: University of Cambridge
- **Field(s)**: Number theory, mathematics

## Contributions
- **Baker's Theorem (1966)**: Provided a lower bound for absolute values of linear combinations of logarithms of algebraic numbers, resolving longstanding problems in transcendental number theory.
- **Fields Medal (1978)**: Awarded for his work on effective methods in the theory of Diophantine equations, particularly the application of Baker's theorem to solve previously intractable problems.
- **Academic Leadership**: Served as a professor at the University of Cambridge, contributing to the institution's reputation in mathematical research.
- **Fellowships**: Elected Fellow of the Royal Society (FRS) and held memberships in the Hungarian Academy of Sciences, Indian National Science Academy, and Academia Europaea.

## FAQs
### What is Alan Baker best known for?
Alan Baker is best known for formulating Baker's theorem, a foundational result in number theory that established critical bounds for logarithmic combinations of algebraic numbers, revolutionizing the study of Diophantine equations.

### Where did Alan Baker work?
Baker was primarily affiliated with the University of Cambridge, where he held academic positions, including a professorship. He was also associated with Trinity College, Cambridge, and University College London during his education and early career.

### What awards did Alan Baker receive?
Baker received the prestigious Fields Medal in 1978 for his transformative work in number theory. He was also awarded the Adams Prize and an honorary doctorate from Louis Pasteur University, among other recognitions.

### What fields did Alan Baker contribute to?
Baker's work centered on number theory, particularly transcendental number theory, where his theorem enabled the solution of previously unsolvable Diophantine equations. His research also influenced broader areas of pure mathematics.

## Why They Matter
Alan Baker's formulation of Baker's theorem marked a pivotal advancement in number theory, providing a powerful tool for solving Diophantine equations and reshaping the field's approach to transcendental numbers. His work not only resolved long-standing mathematical problems but also influenced subsequent research in cryptography, algebraic geometry, and computational number theory. As a Fields Medal laureate and Fellow of the Royal Society, Baker's contributions elevated the global standing of British mathematics, inspiring generations of researchers and solidifying Cambridge's reputation as a hub for mathematical innovation. Without Baker's theorem, critical advancements in secure communication systems and algorithmic number theory might have been delayed, underscoring his enduring impact on both theoretical and applied mathematics.

## Notable For
- **Fields Medal Laureate (1978)**: Recognized for transformative work in Diophantine equations.
- **Baker's Theorem (1966)**: Revolutionized transcendental number theory with its logarithmic bounds.
- **Fellow of the Royal Society (FRS)**: Elected for outstanding contributions to mathematics.
- **Academia Europaea Member**: Honored for interdisciplinary scientific excellence.
- **Adams Prize Winner**: Awarded for distinguished research in mathematics.

## Body

### Early Life and Education
Alan Baker was born on August 19, 1939, in England. He pursued his academic career at University College London and later at Trinity College, Cambridge, where he earned his degrees and laid the groundwork for his future research.

### Career and Academic Affiliations
Baker's professional trajectory was closely tied to the University of Cambridge, where he became a professor and conducted seminal research. His affiliations included:
- **University of Cambridge**: Primary employer, where he contributed to mathematical research and education.
- **Trinity College, Cambridge**: Associated during his education and early career.
- **University College London**: Part of his academic background.

### Research and Legacy
Baker's most significant contribution, **Baker's theorem** (1966), provided a lower bound for linear combinations of logarithms of algebraic numbers, enabling the resolution of previously intractable Diophantine equations. This work earned him the **Fields Medal in 1978**, awarded to mathematicians under 40 for outstanding achievement. The theorem's applications extended to cryptography and computational number theory, demonstrating its practical significance.

### Awards and Honors
- **Fields Medal (1978)**: Highlight of his career, recognizing transformative research.
- **Adams Prize**: Awarded for distinguished work in mathematics.
- **Fellow of the Royal Society (FRS)**: Elected for his contributions to science.
- **Honorary Doctorate (Louis Pasteur University)**: Acknowledged his international academic standing.
- **Memberships**: Hungarian Academy of Sciences, Indian National Science Academy, and Academia Europaea, reflecting his global recognition.

### Institutional Impact
Through his professorship at the University of Cambridge, Baker influenced generations of mathematicians, enhancing the university's reputation as a leader in number theory. His work remains a cornerstone of mathematical literature, cited extensively in research on Diophantine equations and transcendental numbers.

### Global Recognition
Baker's election to prestigious academies, including the **Hungarian Academy of Sciences** and **Academia Europaea**, underscored his contributions to the global mathematical community. His research collaborations and publications solidified his position as a leading figure in 20th-century mathematics.

### Enduring Influence
The practical implications of Baker's theorem extend to modern cryptography, where his bounds on logarithmic combinations inform secure encryption algorithms. His legacy is also evident in the continued citation of his work in contemporary mathematical research, ensuring his impact endures across theoretical and applied domains.

## References

1. BnF authorities
2. [Source](https://www.ams.org/journals/notices/201901/rnoti-p32.pdf)
3. Mathematics Genealogy Project
4. [Source](http://www.ams.org/fellows_by_year.cgi?year=2013)
5. [Source](http://www.ams.org/news?news_id=1680)
6. [Journal officiel de la République française](http://legifrance.gouv.fr/affichTexte.do?cidTexte=JORFTEXT000000553996)
7. International Standard Name Identifier
8. Virtual International Authority File
9. CiNii Research
10. www.ae-info.org
11. [Members - European Academy of Sciences. 2022](https://www.eurasc.eu/members/a-bakerdpmms-cam-ac-uk/member/)
12. Integrated Authority File
13. [Tributes Paid to Professor Alan Baker](https://www.trin.cam.ac.uk/news/tributes-paid-to-professor-alan-baker/)
14. Freebase Data Dumps. 2013
15. Norwegian Authority File: Persons and Corporate Bodies
16. CONOR.SI
17. LIBRIS. 2018