# John Edensor Littlewood

> English mathematician (1885–1977)

**Wikidata**: [Q353426](https://www.wikidata.org/wiki/Q353426)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/John_Edensor_Littlewood)  
**Source**: https://4ort.xyz/entity/john-edensor-littlewood

## Summary
John Edensor Littlewood was an English mathematician (1885–1977) known for his foundational contributions to mathematical analysis, number theory, and the Hardy–Littlewood circle method. He was a Fellow of the Royal Society and a pioneer in analytic number theory, collaborating with G.H. Hardy on major conjectures and theorems.

## Biography
- Born: 1885
- Nationality: United Kingdom
- Education: Trinity College, University of Cambridge
- Known for: Hardy–Littlewood circle method, conjectures in number theory, and contributions to real analysis
- Employer(s): University of Cambridge, Victoria University of Manchester
- Field(s): Mathematical analysis, number theory, calculus, theory of differential equations

## Contributions
- Developed the Hardy–Littlewood circle method, a technique in analytic number theory.
- Formulated the First and Second Hardy–Littlewood conjectures, which remain influential in number theory.
- Proposed the Hardy–Littlewood inequality and tauberian theorem, advancing real analysis.
- Authored the Hardy–Littlewood maximal function, a key operator in harmonic analysis.
- Published "Littlewood's three principles of real analysis," heuristics in measure theory.
- Co-authored "Littlewood's law," a probabilistic principle about rare events.

## FAQs
- **What was John Edensor Littlewood's primary field of study?**
  Littlewood specialized in mathematical analysis, number theory, and calculus, with significant contributions to the theory of differential equations.

- **Where did John Edensor Littlewood work?**
  He was affiliated with Trinity College, the University of Cambridge, and the Victoria University of Manchester.

- **What major mathematical methods did Littlewood develop?**
  He created the Hardy–Littlewood circle method, inequalities, and tauberian theorems, which are foundational in number theory and analysis.

- **What awards did Littlewood receive?**
  He was elected a Fellow of the Royal Society and received the Copley Medal, Royal Medal, De Morgan Medal, Senior Berwick Prize, Sylvester Medal, and Smith's Prize.

## Why They Matter
Littlewood's work laid the groundwork for modern analytic number theory, influencing generations of mathematicians. His collaboration with G.H. Hardy produced landmark results that shaped the field. The Hardy–Littlewood circle method remains a cornerstone of number theory, and his conjectures continue to inspire research. His principles of real analysis and probabilistic insights, such as Littlewood's law, have broad applications in mathematics and beyond.

## Notable For
- Fellow of the Royal Society (1924)
- Recipient of the Copley Medal (1958)
- Co-developer of the Hardy–Littlewood circle method
- Author of the Hardy–Littlewood maximal function
- Formulator of the First and Second Hardy–Littlewood conjectures
- Pioneer in Tauberian theorems and inequalities

## Body
### Early Life and Education
John Edensor Littlewood was born in 1885. He attended St Paul's School and later studied at Trinity College, University of Cambridge, where he developed a deep interest in mathematics.

### Academic Career
Littlewood began his academic career at the University of Cambridge, where he made groundbreaking contributions to mathematical analysis. He later moved to the Victoria University of Manchester, continuing his research.

### Mathematical Contributions
Littlewood's most significant work was in number theory and analysis. He collaborated extensively with G.H. Hardy, producing the Hardy–Littlewood circle method, a powerful technique in analytic number theory. His conjectures, including the First and Second Hardy–Littlewood conjectures, remain active areas of study. He also developed the Hardy–Littlewood inequality and tauberian theorem, which are fundamental in real analysis. His Hardy–Littlewood maximal function is widely used in harmonic analysis.

### Awards and Recognition
Littlewood's contributions were widely recognized. He was elected a Fellow of the Royal Society in 1924 and received prestigious awards, including the Copley Medal (1958), Royal Medal, De Morgan Medal, Senior Berwick Prize, Sylvester Medal, and Smith's Prize.

### Legacy
Littlewood's work has had a lasting impact on mathematics. His methods and conjectures continue to influence research in number theory and analysis. His principles of real analysis and probabilistic insights, such as Littlewood's law, remain relevant in modern mathematics. Littlewood's collaboration with Hardy set a standard for mathematical collaboration, inspiring future generations of mathematicians.

## References

1. Great Soviet Encyclopedia (1969–1978)
2. BnF authorities
3. [Source](https://royalsocietypublishing.org/doi/abs/10.1098/rsbm.1978.0010)
4. Mathematics Genealogy Project
5. Czech National Authority Database
6. MacTutor History of Mathematics archive
7. [Award winners : Copley Medal. Royal Society](https://docs.google.com/spreadsheets/d/1dsunM9ukGLgaW3HdG9cvJ_QKd7pWjGI0qi_fCb1ROD4/pubhtml?gid=1336391689&single=true)
8. International Standard Name Identifier
9. Virtual International Authority File
10. CiNii Research
11. SNAC
12. KNAW Past Members
13. Freebase Data Dumps. 2013
14. [Source](https://www.ams.org/journals/bull/1933-39-07/S0002-9904-1933-05637-9/)
15. CONOR.SI
16. La France savante
17. LIBRIS. 2004