# Nicolaas Govert de Bruijn

> Dutch mathematician (1918–2012)

**Wikidata**: [Q1078285](https://www.wikidata.org/wiki/Q1078285)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Nicolaas_Govert_de_Bruijn)  
**Source**: https://4ort.xyz/entity/nicolaas-govert-de-bruijn

## Summary
Nicolaas Govert de Bruijn was a distinguished Dutch mathematician and computer scientist recognized for his foundational contributions to combinatorics, graph theory, and theoretical computer science. He served as a professor at the University of Amsterdam and Eindhoven University of Technology, where he developed influential concepts such as the De Bruijn sequence and De Bruijn graph. His work spans number theory, geometry, and the formalization of mathematical language.

## Biography
- **Born:** July 9, 1918, in The Hague, Netherlands
- **Died:** February 17, 2012, in Nuenen, Netherlands
- **Nationality:** Kingdom of the Netherlands
- **Education:**
    - Leiden University (1936–1941)
    - Vrije Universiteit Amsterdam (Ph.D., 1943; Thesis: *Over modulaire vormen van meer veranderlijken*)
    - Doctoral Advisor: Jurjen Ferdinand Koksma
- **Employer(s):**
    - Delft University of Technology (Assistant Professor 1939–1944; Ordinary Professor 1946–1952)
    - Philips Natuurkundig Laboratorium (1944–1946)
    - University of Amsterdam (Ordinary Professor 1952–1960)
    - Eindhoven University of Technology (Professor 1960–1984; Professor Emeritus)
- **Field(s):** Combinatorics, Graph Theory, Theoretical Computer Science
- **Known for:** De Bruijn sequence, De Bruijn graph, BEST theorem, De Bruijn notation

## Contributions
Nicolaas Govert de Bruijn made extensive contributions to mathematics and computer science, with numerous concepts named in his honor. He is perhaps best known for the **De Bruijn sequence**, a cyclic sequence of a given alphabet size in which every possible length-*n* substring appears exactly once, a concept widely applied in cryptography and bioinformatics. In graph theory, he developed the **De Bruijn graph**, a directed graph representing overlaps between sequences, which became fundamental in genome assembly algorithms.

He also co-authored the **BEST theorem** (with van Aardenne-Ehrenfest, Smith, and Tutte), which gives the number of Eulerian circuits in a directed graph. In the realm of geometry and number theory, he contributed to the **Moser–De Bruijn sequence** (sums of distinct powers of 4) and the **de Bruijn-Newman constant** related to the Riemann hypothesis.

Later in his career, he focused on theoretical computer science and mathematical language. He developed **De Bruijn notation** and the **De Bruijn index**, a method for representing lambda calculus terms without naming bound variables, which is crucial for programming language implementation and automated theorem proving. He also defined the **De Bruijn factor**, a measure of the redundancy in formal mathematical proofs compared to their informal counterparts.

## FAQs

### Q: What is the De Bruijn sequence?
A: The De Bruijn sequence is a cyclic string of a given alphabet size in which every possible substring of length *n* appears exactly once. It is a key concept in combinatorics used in coding theory and cryptography.

### Q: What was Nicolaas Govert de Bruijn's role in academia?
A: He was a university teacher and professor who served at Delft University of Technology, the University of Amsterdam, and Eindhoven University of Technology, where he was a professor in the Faculty of Mathematics and Computer Science until his retirement in 1984.

### Q: Did Nicolaas Govert de Bruijn collaborate with Paul Erdős?
A: Yes, he co-authored the **De Bruijn–Erdős theorem** with Paul Erdős. His **Erdős number** was 1, indicating a direct collaboration with the prolific mathematician.

### Q: What award did he receive from the Dutch government?
A: In 1981, he was awarded the title of Knight of the Order of the Netherlands Lion.

## Why They Matter
Nicolaas Govert de Bruijn's work fundamentally shaped the intersection of discrete mathematics and computer science. His invention of the De Bruijn graph and sequence provided essential tools for modern genomics and digital communications, allowing researchers to manage and analyze complex sequential data. His theoretical work on the formalization of mathematics, particularly the De Bruijn index, remains a cornerstone in the design of programming languages and proof assistants (such as the Automath system he influenced), ensuring that mathematical proofs can be verified by computers. His ability to bridge pure mathematics—such as number theory and combinatorics—with practical computing challenges left a permanent legacy in both fields.

## Notable For
- **De Bruijn Sequence & Graph:** Foundational structures in combinatorics and bioinformatics.
- **BEST Theorem:** A significant result in graph theory regarding Eulerian circuits.
- **Theoretical Computer Science:** Development of De Bruijn indices and notation for lambda calculus.
- **Erdős Number 1:** Direct collaborator with Paul Erdős on the De Bruijn–Erdős theorem.
- **Academic Leadership:** Mentored numerous doctoral students who became prominent mathematicians and computer scientists.

## Body

### Early Life and Education
Nicolaas Govert de Bruijn was born on July 9, 1918, in The Hague, Netherlands. He pursued his higher education at Leiden University from 1936 to 1941. He completed his Doctor of Philosophy at the Vrije Universiteit Amsterdam in 1943 under the supervision of Jurjen Ferdinand Koksma. His dissertation was titled *Over modulaire vormen van meer veranderlijken* (On modular forms of several variables).

### Academic and Professional Career
De Bruijn began his academic career early, serving as an assistant professor at the Delft University of Technology from 1939 to 1944. During the latter part of World War II, he worked at the Philips Natuurkundig Laboratorium (Philips Physics Laboratory) from 1944 to 1946. He returned to Delft as a Dutch ordinary professor from 1946 to 1952.

In 1952, he moved to the University of Amsterdam, serving as an ordinary professor in the Faculty of Mathematics and Physics until September 1960. He concluded his active career at the Eindhoven University of Technology, where he served as a professor in the Faculty of Mathematics and Computer Science starting in 1960. He became a professor emeritus in 1984.

### Mathematical and Scientific Contributions
De Bruijn's research output was prolific and diverse:
*   **Combinatorics & Graph Theory:** He is famous for the **De Bruijn sequence**, **De Bruijn graph**, and the **BEST theorem** (N.G. de Bruijn, T. van Aardenne-Ehrenfest, C.A.B. Smith, and W.T. Tutte). He also worked on the **De Bruijn–Erdős theorem** in incidence geometry.
*   **Number Theory:** He contributed to the **Moser–De Bruijn sequence** (sequences of sums of distinct powers of 4) and the **de Bruijn-Newman constant**, a parameter related to the Riemann hypothesis.
*   **Computing:** In computer science, he introduced **De Bruijn notation**, **De Bruijn indices**, and the **De Bruijn factor**, influencing how mathematical expressions are processed and verified by computers.

### Recognition and Memberships
De Bruijn was a member of the **Royal Netherlands Academy of Arts and Sciences**. In 1981, he was recognized as a Knight of the Order of the Netherlands Lion.

Throughout his career, he supervised at least 10 doctoral students, including Johannes Runnenburg (1960), Antonius Henricus Maria Levelt (1961), Stan Ackermans (1964), and Lambert S. van Benthem Jutting (1977).

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## References

1. MacTutor History of Mathematics archive
2. dataset Library TU Delft
3. [Source](https://www.tue.nl/universiteit/alumni/emeriti/album-academicum/)
4. Album Academicum
5. Integrated Authority File
6. Mathematics Genealogy Project
7. International Standard Name Identifier
8. Virtual International Authority File
9. CiNii Research
10. KNAW Past Members
11. [Korteweg-de Vries Institute for Mathematics](http://www.science.uva.nl/math/#item1329781416)
12. Freebase Data Dumps. 2013