# Edmund Landau

> German Jewish mathematician (1877–1938)

**Wikidata**: [Q58750](https://www.wikidata.org/wiki/Q58750)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Edmund_Landau)  
**Source**: https://4ort.xyz/entity/edmund-landau

## Summary
Edmund Landau was a German Jewish mathematician (1877–1938) renowned for his foundational work in number theory and complex analysis. He is particularly known for his rigorous approach to mathematical analysis and his formulation of Landau's problems, which remain central to modern number theory.

## Biography
- Born: 14 February 1877, Berlin, German Reich
- Nationality: German
- Education: Educated at the University of Berlin and the University of Göttingen
- Known for: Contributions to number theory, complex analysis, and the formulation of unsolved prime number problems
- Employer(s): Humboldt University of Berlin, University of Göttingen, Hebrew University of Jerusalem
- Field(s): Number theory, complex analysis, mathematical analysis

## Contributions
Edmund Landau made several significant contributions to mathematics:
- **Landau's problems**: A set of four unsolved problems about prime numbers, including Goldbach’s conjecture, the twin prime conjecture, Legendre’s conjecture, and the question of infinitely many primes of the form 𝑛²+1.
- **Landau's function**: A function that returns the largest least common multiple of any partition of its input.
- **Landau–Ramanujan constant**: A constant in number theory that he studied in collaboration with Srinivasa Ramanujan.
- **Big O notation**: Landau introduced and popularized the use of Big O notation, a fundamental tool in the analysis of algorithms and asymptotic behavior.
- **Publications**: Authored numerous papers and texts in number theory and complex analysis, including foundational work that influenced generations of mathematicians.

## FAQs
### Where did Edmund Landau work?
Edmund Landau worked at several academic institutions, including the University of Göttingen, Humboldt University of Berlin, and the Hebrew University of Jerusalem. He was also affiliated with the Royal Prussian Academy of Sciences and the German Academy of Sciences Leopoldina.

### What is Edmund Landau's contribution to mathematics?
Landau's contributions include foundational work in number theory, particularly his formulation of Landau's problems, his development of the Big O notation, and his study of the Landau–Ramanujan constant. He also contributed to complex analysis and was known for his rigorous approach to mathematical proofs.

### What are Landau's problems?
Landau's problems consist of four unsolved problems about prime numbers: Goldbach’s conjecture, the twin prime conjecture, Legendre’s conjecture, and the question of whether there are infinitely many primes of the form 𝑛²+1.

### What is the Landau–Ramanujan constant?
The Landau–Ramanujan constant is a number theory constant that arises in the study of the representation of integers as sums of squares. It is named after Landau and Srinivasa Ramanujan, who both contributed to its development.

### What is the significance of Big O notation in Landau's work?
Big O notation, introduced by Landau, is used to describe the asymptotic behavior of functions. It is a fundamental tool in computer science and mathematics for analyzing the efficiency of algorithms and the growth rates of functions.

## Why They Matter
Edmund Landau's rigorous approach to number theory and analysis laid the groundwork for many modern mathematical concepts. His formulation of Landau's problems continues to challenge and inspire mathematicians. His work in defining and popularizing Big O notation has had a lasting impact on computer science and algorithm analysis. Landau's contributions to the field of mathematics remain foundational, influencing both theoretical developments and practical applications.

## Notable For
- Formulating Landau's problems, four unsolved problems in number theory
- Introducing and popularizing Big O notation
- Developing the Landau–Ramanujan constant
- Establishing the Landau's function
- Affiliation with the University of Göttingen, Humboldt University of Berlin, and the Hebrew University of Jerusalem
- Membership in the Royal Prussian Academy of Sciences, German Academy of Sciences Leopoldina, and the Accademia Nazionale dei Lincei
- Educated at the University of Berlin and the University of Göttingen
- Contributions to number theory, complex analysis, and mathematical analysis

## Body
### Early Life and Education
Edmund Landau was born on 14 February 1877 in Berlin, German Reich. He was a German Jewish mathematician who became one of the most prominent figures in number theory and complex analysis. Landau was educated at the University of Berlin and the University of Göttingen, where he was influenced by leading mathematicians of the time.

### Career
Landau's career was marked by his association with several prestigious institutions:
- **University of Göttingen**: Landau was a professor here and conducted significant research in number theory.
- **Humboldt University of Berlin**: He was a faculty member and made substantial contributions to mathematical analysis.
- **Hebrew University of Jerusalem**: Landau was involved in the early development of the university and contributed to its academic reputation.

### Mathematical Contributions
Landau's work spanned several areas of mathematics:
- **Number Theory**: He made significant contributions to the study of prime numbers, including formulating Landau's problems.
- **Complex Analysis**: His work in this field included the study of the distribution of prime numbers and the Riemann zeta function.
- **Mathematical Analysis**: Landau's rigorous approach to analysis influenced the field significantly.

### Affiliations and Memberships
Landau was a member of several prestigious academies and societies:
- **Royal Prussian Academy of Sciences**
- **German Academy of Sciences Leopoldina**
- **Accademia Nazionale dei Lincei**
- **Russian Academy of Sciences**

### Publications and Works
Landau published numerous papers and books that have had a lasting impact:
- **Foundational Texts**: He authored texts on number theory and complex analysis that are still referenced today.
- **Landau's Problems**: These four unsolved problems in number theory continue to be a major area of research.
- **Big O Notation**: His work in formalizing this notation has been crucial in the development of computer science.

### Legacy
Landau's legacy includes his rigorous mathematical proofs and the formulation of problems that remain unsolved. His influence on number theory and complex analysis is still felt today, with his work forming the basis for ongoing research. The concepts he introduced, such as Big O notation, are fundamental to modern computational theory and algorithm design.

### Influence on Modern Mathematics
Landau's influence extends beyond his direct contributions:
- **Algorithm Analysis**: The Big O notation is essential in computer science for analyzing the efficiency of algorithms.
- **Number Theory Research**: His problems continue to drive research in prime number theory.
- **Educational Impact**: Landau's rigorous approach to mathematics education has influenced generations of mathematicians.

### Personal Life and Death
Edmund Landau passed away on 19 February 1938. His work continues to be celebrated for its precision and depth, and his contributions to mathematics remain foundational.

## References

1. Integrated Authority File
2. Great Soviet Encyclopedia (1969–1978)
3. BnF authorities
4. Czech National Authority Database
5. Find a Grave
6. [Q52239587. 2014](https://books.google.fr/books?id=GC7aBAAAQBAJ&pg=PAPR454)
7. MacTutor History of Mathematics archive
8. Mathematics Genealogy Project
9. International Standard Name Identifier
10. Virtual International Authority File
11. CiNii Research
12. SNAC
13. Brockhaus Enzyklopädie
14. Freebase Data Dumps. 2013
15. [Source](https://cyberleninka.ru/article/n/viktor-iosifovich-levin-vydayuschiysya-pedagog-i-uchenyy/pdf)
16. CONOR.SI
17. LIBRIS. 2007