# Mikhail Gromov

> Russian and French mathematician and academic

**Wikidata**: [Q353451](https://www.wikidata.org/wiki/Q353451)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Mikhael_Gromov_(mathematician))  
**Source**: https://4ort.xyz/entity/mikhail-gromov

## Summary
Mikhail Gromov is a renowned Russian and French mathematician and academic celebrated for his transformative contributions to geometry and group theory. Recognized with prestigious awards such as the Wolf Prize and the Abel Prize, Gromov's work has profoundly influenced modern mathematics, particularly in the areas of geometric group theory and symplectic geometry.

## Biography
- **Born:** December 23, 1943
- **Nationality:** Russian and French
- **Education:** Graduated from Saint Petersburg State University
- **Known for:** Pioneering work in geometric group theory, Gromov-Hausdorff convergence, and pseudoholomorphic curves
- **Employer(s):** Institut des Hautes Études Scientifiques (IHÉS), New York University, Stony Brook University
- **Field(s):** Mathematics, specifically geometry, group theory, and mathematical analysis

## Contributions
- **Geometric Group Theory:** Developed the theory of hyperbolic groups and introduced the concept of Gromov-Hausdorff convergence, revolutionizing the study of metric spaces.
- **Symplectic Geometry:** Introduced pseudoholomorphic curves, a foundational tool in symplectic topology, which earned him the Wolf Prize in Mathematics (2010).
- **Gromov's Compactness Theorem:** Established criteria for the compactness of sets of Riemannian manifolds, impacting differential geometry.
- **Non-Squeezing Theorem:** Demonstrated the rigidity of symplectic structures, a cornerstone result in symplectic geometry.
- **Polynomial Growth Theorem:** Proved that groups of polynomial growth are virtually nilpotent, bridging group theory and geometry.
- **Publications:** Authored seminal works such as *Metric Structures for Riemannian and Non-Riemannian Spaces* and *Partial Differential Relations*.

## FAQs
### What are Mikhail Gromov's most notable mathematical contributions?
Gromov's key contributions include the development of geometric group theory, the introduction of pseudoholomorphic curves in symplectic geometry, and the Gromov-Hausdorff convergence concept in metric geometry.

### Where has Mikhail Gromov held academic positions?
Gromov has been affiliated with the Institut des Hautes Études Scientifiques (IHÉS), New York University, and Stony Brook University, among other institutions.

### What awards has Mikhail Gromov received?
He has been honored with the Wolf Prize in Mathematics, the Abel Prize, the Balzan Prize, and the Lobachevsky Prize, among others.

### How has Gromov influenced modern mathematics?
Gromov's work has reshaped multiple fields, from geometric group theory to symplectic geometry, introducing foundational concepts and tools that remain central to contemporary research.

## Why They Matter
Mikhail Gromov's influence on mathematics is profound and far-reaching. His introduction of pseudoholomorphic curves transformed symplectic geometry, while his work on geometric group theory and metric spaces has redefined approaches to studying large-scale geometric properties. The Gromov-Hausdorff convergence and compactness theorem have become essential in differential geometry and topology. His polynomial growth theorem resolved long-standing questions in group theory, illustrating the interconnectedness of algebraic and geometric structures. Without Gromov's innovations, modern advancements in these fields would lack critical theoretical underpinnings, impacting areas from theoretical physics to data analysis.

## Notable For
- **Awards:** Wolf Prize in Mathematics (2010), Abel Prize (2022), Balzan Prize (2014), Lobachevsky Prize (2005)
- **Concepts:** Gromov-Hausdorff convergence, pseudoholomorphic curves, non-squeezing theorem, Gromov's compactness theorem
- **Institutions:** Institut des Hautes Études Scientifiques, New York University, Stony Brook University
- **Fields:** Geometric group theory, symplectic geometry, differential geometry
- **Publications:** *Metric Structures for Riemannian and Non-Riemannian Spaces*, *Partial Differential Relations*

## Body

### Early Life and Education
Mikhail Gromov was born on December 23, 1943. He pursued his education at Saint Petersburg State University, where he developed a strong foundation in mathematics, laying the groundwork for his future contributions.

### Career and Academic Affiliations
Gromov's academic career spans multiple prestigious institutions. He has been a key figure at the Institut des Hautes Études Scientifiques (IHÉS) in France, New York University, and Stony Brook University in the United States. These affiliations have provided him with platforms to conduct groundbreaking research and mentor emerging mathematicians.

### Geometric Group Theory and Metric Spaces
Gromov's work in geometric group theory introduced hyperbolic groups and the concept of Gromov-Hausdorff convergence. This convergence notion allows for the comparison of metric spaces, enabling the study of their large-scale geometric properties. His compactness theorem provided criteria for the relative compactness of sets of Riemannian manifolds, a pivotal result in differential geometry.

### Symplectic Geometry and Pseudoholomorphic Curves
In symplectic geometry, Gromov's introduction of pseudoholomorphic curves revolutionized the field. These curves, which satisfy the Cauchy-Riemann equation in an almost complex manifold, became a fundamental tool in symplectic topology. This work earned him the Wolf Prize in Mathematics in 2010 and laid the foundation for modern symplectic geometry.

### Polynomial Growth Theorem
Gromov's theorem on groups of polynomial growth demonstrated that such groups are virtually nilpotent, resolving a major question in geometric group theory. This result highlighted the deep connections between algebraic properties of groups and their geometric manifestations.

### Awards and Recognition
Throughout his career, Gromov has received numerous accolades. Notable awards include the Wolf Prize in Mathematics (2010), the Abel Prize (2022), the Balzan Prize (2014), and the Lobachevsky Prize (2005). These honors reflect the broad and lasting impact of his contributions across multiple mathematical disciplines.

### Institutional Legacy
Gromov's affiliations with leading research institutions have fostered collaborative environments that nurture mathematical innovation. His presence at IHÉS, NYU, and Stony Brook University has attracted scholars worldwide, cementing his role as a central figure in the global mathematical community.

### Publications and Influence
Gromov's seminal publications, such as *Metric Structures for Riemannian and Non-Riemannian Spaces* and *Partial Differential Relations*, have become standard references in their fields. His work continues to influence contemporary research, with applications extending to theoretical physics, data science, and beyond.

### Interdisciplinary Impact
The breadth of Gromov's contributions underscores the interdisciplinary nature of his work. From the rigidity of symplectic structures (non-squeezing theorem) to the study of polynomial growth in groups, his research bridges algebra, geometry, and topology, exemplifying the unity and depth of mathematical inquiry.

### Legacy and Continued Influence
Mikhail Gromov's legacy is marked by the foundational concepts and tools he has introduced, which remain indispensable to modern mathematics. His ability to uncover and articulate deep connections between disparate fields has inspired generations of mathematicians, ensuring his work will continue to shape the trajectory of mathematical research for years to come.

## References

1. Virtual International Authority File
2. BnF authorities
3. [Journal officiel de la République française](https://www.legifrance.gouv.fr/jorf/jo/1992/08/18/0190)
4. Mathematics Genealogy Project
5. Czech National Authority Database
6. [Source](https://math.nyu.edu/people/profiles/GROMOV_Mikhael.html)
7. [Source](https://medal.kpfu.ru/laureatyi-medali/)
8. [Source](https://www.abelprize.no/c53859/seksjon/vis.html?tid=54323)
9. [Source](https://www.kyotoprize.org/en/laureates/)
10. [Source](https://www.unine.ch/unine/home/luniversite/Evenements/dies-academicus/dies-academicus-2009.html)
11. [Source](https://www.ams.org/prizes-awards/pabrowse.cgi?parent_id=27)
12. International Standard Name Identifier
13. Library of Congress Name Authority File
14. CiNii Research
15. www.ae-info.org
16. MacTutor History of Mathematics archive
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19. Munzinger Personen
20. Freebase Data Dumps. 2013
21. French Academy of Sciences
22. LIBRIS. 2018