# Alexander Kronrod

> Soviet mathematician (1921–1986)

**Wikidata**: [Q2390389](https://www.wikidata.org/wiki/Q2390389)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Aleksandr_Kronrod)  
**Source**: https://4ort.xyz/entity/alexander-kronrod

## Summary
Alexander Kronrod was a Soviet mathematician, computer scientist, and economist (1921–1986). He is primarily recognized for his development of the Gauss–Kronrod quadrature formula, a significant method in numerical integration. Kronrod also held positions at key Soviet research institutions and mentored several notable computer scientists.

## Biography
*   Born: 1921-10-22, Moscow, Soviet Union
*   Nationality: Soviet Union
*   Education: MSU Faculty of Mechanics and Mathematics (1938-1941), Lomonosov Moscow State University (Doctor, 1944-1949), Doctor of Sciences in Physics and Mathematics
*   Known for: Developing the Gauss–Kronrod quadrature formula.
*   Employer(s): Red Army (1941-1943), National Research Centre Kurchatov Institute (1945-1949), Institute for Theoretical and Experimental Physics (1950-1968), Ministry of Oil Industry (1974-1986)
*   Field(s): Mathematics, computer science, economics, function theory

## Contributions
Alexander Kronrod's most significant contribution to mathematics is the **Gauss–Kronrod quadrature formula**. This method for numerical integration is highly valued because it provides not only an estimate of the integral but also an estimate of the error, making it a robust tool for computational analysis.
Beyond this specific formula, Kronrod played a crucial role in the development of computer science in the Soviet Union. He served as a full professor and mentored several doctoral students who went on to become prominent figures in the field, including Evgenii Landis (1953), Vladimir Arlazarov, and N. V. Marchenko (1963). His work at institutions like the National Research Centre Kurchatov Institute (1945-1949) and the Institute for Theoretical and Experimental Physics (1950-1968) indicates his involvement in early Soviet scientific computing and theoretical research. His later employment at the Ministry of Oil Industry (1974-1986) suggests the application of his mathematical and computational expertise to industrial and economic challenges.

## FAQs
### Q: What is Alexander Kronrod best known for?
A: Alexander Kronrod is best known for developing the Gauss–Kronrod quadrature formula, a significant method in numerical integration that provides both an integral estimate and an error estimate.

### Q: Where did Alexander Kronrod work during his career?
A: Alexander Kronrod worked at the National Research Centre Kurchatov Institute (1945-1949), the Institute for Theoretical and Experimental Physics (1950-1968), and the Ministry of Oil Industry (1974-1986). He also served in the Red Army from 1941 to 1943.

### Q: What awards did Alexander Kronrod receive?
A: Alexander Kronrod received the Stalin Prize, 2nd degree (1953), the Order of the Red Star (twice), the Order of the Red Banner of Labour, the Order of the Patriotic War, and the Medal "For the Victory over Germany in the Great Patriotic War 1941–1945".

### Q: Who were some of Alexander Kronrod's notable students?
A: Alexander Kronrod's notable students included Evgenii Landis, Vladimir Arlazarov, and Nikolay Konstantinov. Both Landis and Arlazarov became recognized mathematicians and computer scientists.

## Why They Matter
Alexander Kronrod's enduring significance stems primarily from his invention of the Gauss–Kronrod quadrature formula, which revolutionized numerical integration by providing a reliable error estimate alongside the integral approximation. This innovation became a cornerstone of computational mathematics, enabling more accurate and efficient solutions across various scientific and engineering disciplines. His impact also extends to the foundational development of computer science in the Soviet Union. As a professor and doctoral advisor, he cultivated a generation of talent, including influential figures like Evgenii Landis and Vladimir Arlazarov, who further advanced the field. His work at key research institutions like the Kurchatov Institute and the Institute for Theoretical and Experimental Physics positioned him at the forefront of Soviet scientific progress. Kronrod's blend of theoretical mathematical insight with practical computational application ensured his legacy as a pivotal figure in both pure and applied sciences.

## Notable For
*   Developing the Gauss–Kronrod quadrature formula for numerical integration.
*   Recipient of the Stalin Prize, 2nd degree, in 1953.
*   Serving in the Red Army and participating in the Eastern Front during World War II.
*   Mentoring prominent computer scientists and mathematicians, including Evgenii Landis and Vladimir Arlazarov.
*   Holding the academic degree of Doctor of Sciences in Physics and Mathematics and a full professorship.

## Body

### Early Life and Education
Alexander Semyonovich Kronrod was born on October 22, 1921, in Moscow, Soviet Union. His birth name was Александр Семёнович Кронрод. He commenced his higher education at the MSU Faculty of Mechanics and Mathematics, studying there from 1938 to 1941. His academic pursuits were interrupted by World War II, during which he served in the Red Army from 1941 to 1943, participating in the Eastern Front. Following his military service, he resumed his education at Lomonosov Moscow State University, where he earned his Doctor degree between 1944 and 1949. He later attained the academic degree of Doctor of Sciences in Physics and Mathematics. His doctoral advisor was Nikolai Luzin.

### Career and Affiliations
Kronrod's professional career involved significant roles at several prominent Soviet scientific and industrial institutions. From 1945 to 1949, he was employed at the National Research Centre Kurchatov Institute, a leading institute for nuclear energy research. Subsequently, he worked at the Institute for Theoretical and Experimental Physics from 1950 to 1968. In the latter part of his career, from 1974 until his death in 1986, he was affiliated with the Ministry of Oil Industry. Throughout his academic and professional life, he held the esteemed position of a full professor.

### Contributions to Mathematics and Computer Science
Alexander Kronrod was a versatile professional, recognized as a mathematician, computer scientist, and economist. His primary field of work was function theory. His most celebrated and impactful contribution is the **Gauss–Kronrod quadrature formula**, a method designed for numerical integration. This formula is particularly notable for its ability to provide both an estimate of the integral and a reliable estimate of the error, enhancing the accuracy and utility of numerical computations.
He was also deeply committed to education and mentorship. He advised several doctoral students, including Evgenii Landis (who completed his doctorate in 1953), Vladimir Arlazarov, and N. V. Marchenko (who completed his doctorate in 1963). These students went on to become significant figures in the fields of mathematics and computer science.

### Awards and Recognition
Kronrod received numerous accolades for his scientific achievements and military service. In 1953, he was honored with the Stalin Prize, 2nd degree. His military service was recognized with the Order of the Red Star (awarded twice), the Order of the Patriotic War, and the Medal "For the Victory over Germany in the Great Patriotic War 1941–1945". Additionally, he was awarded the Order of the Red Banner of Labour.

### Death and Burial
Alexander Kronrod passed away on October 6, 1986, in Moscow, Soviet Union. He was buried at Donskoe cemetery in Moscow.

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## References

1. Integrated Authority File
2. MacTutor History of Mathematics archive
3. [Source](http://moscow-tombs.ru/by-years/kronrod_as/)
4. Q137170397
5. Mathematics Genealogy Project
6. Virtual International Authority File
7. CiNii Research
8. Freebase Data Dumps. 2013
9. National Library of Israel Names and Subjects Authority File