What is the scope of the 'List of Russian mathematicians' article?

The 'List of Russian mathematicians' article compiles famous mathematicians who originated from the Russian Empire, the Soviet Union, and the Russian Federation. This list serves as a comprehensive record of significant mathematical figures from these historical and contemporary Russian entities.

What does the 1961 Soviet stamp referenced in the article depict?

The 1961 Soviet stamp referenced in the article illustrates 'Workers studying mathematics,' publicizing communist labor teams and their efforts in labor, education, and relaxation. This image highlights the Soviet Union's emphasis on education and the importance of mathematics in its society.

What were Georgy Adelson-Velsky's notable contributions to computer science and algorithms?

Georgy Adelson-Velsky is recognized for inventing the AVL tree algorithm, a self-balancing binary search tree, and for his role as a developer of Kaissa, which was the first computer chess program to win a World Computer Chess Championship.

In which area of mathematics did Sergei Adian make significant contributions?

Sergei Adian is primarily known for his extensive work in group theory, particularly his contributions to solving the Burnside problem, which concerns the properties of groups where every element has a finite order.

What geometric concepts are attributed to Aleksandr Aleksandrov?

Aleksandr Aleksandrov is credited with developing the concept of CAT(k) space and formulating Alexandrov's uniqueness theorem, both of which are significant contributions to the field of geometry.

Which topological concepts were authored by Pavel Alexandrov?

Pavel Alexandrov is the author of the Alexandroff compactification, a method for adding a single point to a topological space to make it compact, and the Alexandrov topology, a specific type of topology defined by open sets that are closed under arbitrary unions and finite intersections.

What is Dmitri Anosov known for in dynamical systems?

Dmitri Anosov developed the Anosov diffeomorphism, a type of dynamical system characterized by strong chaotic behavior, where nearby points diverge exponentially fast.

What were some of Vladimir Arnold's major achievements in mathematics?

Vladimir Arnold was a highly influential mathematician who co-authored the Kolmogorov–Arnold–Moser theorem in dynamical systems, successfully solved Hilbert's 13th problem, and introduced the ADE classification and Arnold's rouble problems, demonstrating his broad impact across various mathematical disciplines.

What areas of mathematics and physics did Alexander Beilinson influence?

Alexander Beilinson is an influential mathematician known for his significant work in representation theory, algebraic geometry, and mathematical physics, contributing to the theoretical foundations of these fields.

What mathematical concepts did Sergey Bernstein develop?

Sergey Bernstein developed the Bernstein polynomial, a fundamental tool in approximation theory, Bernstein's theorem on monotone functions, and Bernstein inequalities in probability theory, which provide bounds on the deviation of sums of random variables.

What were Nikolay Bogolyubov's contributions as a mathematician and theoretical physicist?

Nikolay Bogolyubov, a distinguished mathematician and theoretical physicist, authored the edge-of-the-wedge theorem, the Krylov–Bogolyubov theorem, and the describing function, while also making multiple important contributions to quantum mechanics, a branch of physics dealing with the behavior of matter and light at the atomic and subatomic level.

What mathematical spaces did Vladimir Berkovich develop?

Vladimir Berkovich is known for developing Berkovich spaces, which are analytic spaces over non-Archimedean fields, providing a framework for non-Archimedean geometry.

For what work is Viktor Bunyakovsky noted, and what discovery is he credited with?

Viktor Bunyakovsky is noted for his significant work in theoretical mechanics and number theory, and he is credited with an early discovery of the Cauchy–Schwarz inequality, a fundamental inequality in mathematics that relates the inner product of two vectors to their norms.

What is Leonid Berlyand's area of expertise and what award did he receive?

Leonid Berlyand is a PDE (Partial Differential Equation) theorist who has worked on asymptotic homogenization methods, which are techniques used to analyze the behavior of materials with rapidly varying properties. He is also a recipient of the Humboldt Prize, an award given to internationally recognized scientists and scholars.

What is Georg Cantor known for, and what is his connection to the Russian Empire?

Georg Cantor is renowned as the inventor of set theory, a foundational branch of mathematics dealing with collections of objects. He was born into the Russian Empire, although he later moved to Saxony with his family at age 11.

What are Sergey Chaplygin's key contributions to aerodynamics?

Sergey Chaplygin is the author of Chaplygin's equation, which is important in aerodynamics for describing gas flow, and he also introduced the notion of Chaplygin gas, a theoretical gas model used in cosmology.

What significant theorem is attributed to Nikolai Chebotaryov?

Nikolai Chebotaryov is the author of Chebotarev's density theorem, a fundamental result in algebraic number theory that describes the distribution of prime ideals in number fields.

What were Sergei Chernikov's contributions to group theory and linear programming?

Sergei Chernikov made significant contributions to both infinite group theory, where he developed Chernikov groups, and linear programming, a mathematical method for determining a way to achieve the best outcome in a given mathematical model.

What did Boris Delaunay invent, and what event did he organize?

Boris Delaunay is known for inventing Delaunay triangulation, a fundamental concept in computational geometry, and he organized the first Soviet Student Olympiad in mathematics, promoting mathematical talent among students.

What were Vladimir Drinfeld's key introductions in mathematics and physics, and what award did he receive?

Vladimir Drinfeld, a mathematician and theoretical physicist, introduced quantum groups and the ADHM construction. His significant work was recognized with a Fields Medal, one of the highest honors in mathematics.

What concepts did Eugene Dynkin develop in algebra and probability?

Eugene Dynkin developed the Dynkin diagram, used in the classification of Lie algebras and other algebraic structures, the Doob–Dynkin lemma in probability theory, and the Dynkin system, a type of collection of sets used in measure theory.

What areas did Dmitri Egorov contribute to in mathematics?

Dmitri Egorov is known for his significant contributions to the areas of differential geometry, which studies geometric properties of curves, surfaces, and their higher-dimensional analogs using calculus, and mathematical analysis, a broad area of mathematics that includes calculus and its generalizations.

Who is considered a preeminent 18th-century mathematician, and what were his contributions, despite his Swiss origin?

Leonhard Euler, a Swiss-born mathematician, is considered a preeminent 18th-century mathematician and arguably one of the greatest of all time. He made important discoveries in mathematical analysis, graph theory, and number theory, and introduced much of the modern mathematical terminology and notation, including Euler's number (e) and Euler circles, having spent most of his life in St. Petersburg, Russia.

What is Ivan Fesenko's area of mathematical specialization?

Ivan Fesenko is a number theorist, a mathematician who specializes in the study of integers and their properties.

What controversial theory did Anatoly Fomenko propose?

Anatoly Fomenko, a topologist and chronologist, put forth a controversial theory known as the New Chronology, which reinterprets historical events and timelines.

What pioneering theory did Alexander Alexandrovich Friedmann originate?

Alexander Alexandrovich Friedmann, a Russian and Soviet physicist and mathematician, originated the pioneering theory that the universe is expanding, which is governed by a set of equations he developed known as the Friedmann equations. He is also known for the Friedmann–Lemaître–Robertson–Walker metric, a fundamental solution to Einstein's field equations of general relativity.

What were Yevgraf Fyodorov's contributions to geometry and crystallography?

Yevgraf Fyodorov, a mathematician and crystallographer, identified the Periodic graph in geometry and was the first to systematically catalogue all 230 space groups of crystals, which describe the symmetry of crystal structures.

What method in numerical analysis did Boris Galerkin develop?

Boris Galerkin developed the Galerkin method, a numerical technique used to convert a continuous operator problem into a discrete problem, often employed for solving differential equations.

What are some of Israel Gelfand's major contributions across various mathematical fields?

Israel Gelfand was a major contributor to numerous areas of mathematics, including group theory, representation theory, and linear algebra. He is known for concepts such as the Gelfand representation, Gelfand pair, Gelfand triple, and integral geometry, which have had a profound impact on functional analysis and other fields.

What significant theorem is associated with Alexander Gelfond, and what award did he receive?

Alexander Gelfond is the author of Gelfond's theorem, which provided a means to obtain an infinite number of transcendentals, including the Gelfond–Schneider constant and Gelfond's constant. He was also a recipient of the Wolf Prize in Mathematics, an international award recognizing outstanding achievements in the field.

What theorem is Semyon Aranovich Gershgorin famous for?

Semyon Aranovich Gershgorin is famous for the Gerschgorin circle theorem, which provides bounds for the eigenvalues of a matrix, a crucial tool in numerical linear algebra.

What mathematical concepts did Sergei Godunov develop in differential equations?

Sergei Godunov developed Godunov's theorem and Godunov's scheme, both of which are important contributions to the field of differential equations, particularly in numerical methods for solving hyperbolic partial differential equations.

What types of codes did Valery Goppa invent in algebraic geometry?

Valery Goppa is recognized as the inventor of Goppa codes and algebraic geometry codes, which are types of error-correcting codes used in information theory and cryptography, based on principles from algebraic geometry.

What are Mikhail Gromov's significant contributions and the awards he received?

Mikhail Gromov is a prominent developer of geometric group theory and the inventor of the homotopy principle. He introduced concepts such as Gromov's compactness theorem, Gromov norm, and Gromov product, and his work was recognized with the Wolf Prize, an international award for achievements in science and art.

What were Leonid Kantorovich's contributions to mathematics and economics, and what prestigious award did he win?

Leonid Kantorovich, a mathematician and economist, founded linear programming, a method for optimizing a linear objective function subject to linear equality and inequality constraints. He introduced the Kantorovich inequality and Kantorovich metric, and developed the theory of optimal allocation of resources, for which he was awarded the Nobel Prize in Economics.

What algorithm did Anatoly Karatsuba develop?

Anatoly Karatsuba developed the Karatsuba algorithm, which was the first fast multiplication algorithm, significantly improving the efficiency of multiplying large numbers compared to traditional methods.

What are some of David Kazhdan's key contributions and the honors he received?

David Kazhdan, a Soviet, American, and Israeli mathematician, made significant contributions to Representation theory and Category theory. He is known for the Kazhdan-Lusztig conjecture, Kazhdan-Margulis theorem, and Kazhdan property (T). He held a MacArthur Fellowship, received the Israel Prize, and the Shaw Prize in Mathematics, and was the doctoral adviser to Fields Medal recipient Vladimir Voevodsky.

What algorithm for linear programming did Leonid Khachiyan develop?

Leonid Khachiyan developed the Ellipsoid algorithm, a polynomial-time algorithm for linear programming, which was a significant breakthrough in optimization theory.

What formulas and inequalities did Aleksandr Khinchin develop in probability theory?

Aleksandr Khinchin developed the Pollaczek-Khinchine formula, the Wiener–Khinchin theorem, and the Khinchin inequality, all of which are important concepts in probability theory and stochastic processes.

What theories and contributions did Askold Khovanskii make in mathematics?

Askold Khovanskii is the inventor of the theory of Fewnomials, which deals with polynomials having a small number of terms, and he made contributions to the theory of toric varieties in algebraic geometry. He is also a recipient of the Jeffery–Williams Prize.

Who is considered a preeminent 20th-century mathematician, and what are some of his diverse contributions?

Andrey Kolmogorov is regarded as a preeminent 20th-century mathematician and a Wolf Prize winner. His multiple contributions to mathematics include the probability axioms, the Chapman–Kolmogorov equation, and the Kolmogorov extension theorem in probability theory, as well as Kolmogorov complexity in information theory, demonstrating his wide-ranging impact.

What integral and formula are attributed to Maxim Kontsevich, and what award did he receive?

Maxim Kontsevich is the author of the Kontsevich integral and the Kontsevich quantization formula. His groundbreaking work in mathematics earned him a Fields Medal, one of the most prestigious awards in the field.

What fundamental theorem in information theory is Vladimir Kotelnikov associated with?

Vladimir Kotelnikov was a pioneer in information theory and is recognized as an author of the fundamental sampling theorem, which states that a continuous-time signal can be perfectly reconstructed from its samples if the sampling rate exceeds twice the highest frequency of the signal.

What polynomials and matrix did Mikhail Kravchuk develop?

Mikhail Kravchuk developed the Kravchuk polynomials, a family of orthogonal polynomials, and the Kravchuk matrix, which are used in various areas of mathematics and engineering, including coding theory.

What duality, theorem, and space are associated with Mark Krein, and what award did he receive?

Mark Krein developed the Tannaka–Krein duality, the Krein–Milman theorem, and the Krein space. His significant contributions to functional analysis and other areas of mathematics were recognized with a Wolf Prize.

What formula and computer chess program did Alexander Kronrod develop?

Alexander Kronrod is known for developing the Gauss–Kronrod quadrature formula, a method for numerical integration, and for his role in creating Kaissa, which became the first world computer chess champion.

What numerical method for linear problems did Aleksey Nikolaevich Krylov first develop?

Aleksey Nikolaevich Krylov first developed the method of Krylov subspace, which is still a widely used numerical method for solving linear problems, particularly large systems of linear equations.

What theorems and functions are attributed to Nikolay Krylov?

Nikolay Krylov is the author of the edge-of-the-wedge theorem, the Krylov–Bogolyubov theorem, and the describing function, all of which are important in mathematical analysis and dynamical systems.

What theorems and problems in group theory are associated with Aleksandr Kurosh?

Aleksandr Kurosh is the author of the Kurosh subgroup theorem and the Kurosh problem in group theory, which are fundamental results concerning the structure of subgroups in free products of groups.

List Of Russian Mathematicians Wiki: Mathematical Luminaries: A Pantheon of Russian Genius

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Introduction

A Rich Mathematical Heritage

The landscape of mathematics has been profoundly shaped by scholars from the Russian Empire, the Soviet Union, and the modern Russian Federation. This compilation highlights the eminent mathematicians whose innovative work has led to fundamental theorems, novel algorithms, and entirely new branches of mathematical thought.

From the foundational principles of analysis and geometry to the complexities of probability theory and computational science, Russian mathematicians have consistently pushed the boundaries of knowledge, leaving an indelible mark on the global scientific community.

Spanning Eras and Disciplines

This list encompasses a vast chronological and thematic range, featuring figures who contributed to diverse fields such as group theory, algebraic geometry, dynamical systems, information theory, and numerical analysis. Many of these individuals are recognized with prestigious international awards, underscoring the universal impact of their intellectual endeavors.

Their work often involved solving long-standing problems, introducing revolutionary concepts, and developing practical applications that continue to influence modern technology and scientific research.

Pioneers: A to D

Algorithms and Topology

**Georgy Adelson-Velsky** is celebrated for co-inventing the AVL tree algorithm (opens in new tab), a self-balancing binary search tree crucial in computer science, and for his role in developing Kaissa, the first world computer chess champion. **Pavel Alexandrov** made significant contributions to topology, notably with the Alexandroff compactification (opens in new tab) and the Alexandrov topology (opens in new tab).

**Sergei Adian** advanced group theory (opens in new tab), particularly in his work on the Burnside problem (opens in new tab).
**Aleksandr Aleksandrov** developed the CAT(k) space (opens in new tab) and Alexandrov's uniqueness theorem (opens in new tab) in geometry.
**Dmitri Anosov** is known for the Anosov diffeomorphism (opens in new tab) in dynamical systems.

Dynamical Systems and Geometry

**Vladimir Arnold** stands as a towering figure, co-authoring the Kolmogorov–Arnold–Moser theorem (opens in new tab) in dynamical systems, solving Hilbert's 13th problem (opens in new tab), and posing the ADE classification (opens in new tab) and Arnold's rouble problems (opens in new tab).

**Alexander Beilinson** has been highly influential in representation theory (opens in new tab), algebraic geometry (opens in new tab), and mathematical physics.

Probability and Analysis

**Sergey Bernstein** developed the eponymous Bernstein polynomial (opens in new tab), Bernstein's theorem (opens in new tab), and Bernstein inequalities (opens in new tab) in probability theory. **Nikolay Bogolyubov**, a versatile mathematician and theoretical physicist, contributed the edge-of-the-wedge theorem (opens in new tab) and the Krylov–Bogolyubov theorem (opens in new tab).

**Viktor Bunyakovsky** is recognized for his work in theoretical mechanics and number theory, and an early discovery of the Cauchy–Schwarz inequality (opens in new tab).
**Boris Delaunay** invented Delaunay triangulation (opens in new tab), a fundamental concept in computational geometry.
**Vladimir Drinfeld** introduced quantum groups (opens in new tab) and the ADHM construction (opens in new tab), earning him a Fields Medal (opens in new tab).
**Eugene Dynkin** developed the Dynkin diagram (opens in new tab), Doob–Dynkin lemma (opens in new tab), and Dynkin system (opens in new tab) in algebra and probability.

Foundational Figures

**Pafnuti Chebyshev** is revered as a founding father of Russian mathematics, with extensive contributions to probability, statistics, and number theory. His legacy includes Chebyshev's inequality (opens in new tab), Chebyshev distance (opens in new tab), and the Chebyshev function (opens in new tab).

While **Georg Cantor** (inventor of set theory (opens in new tab)) was born in the Russian Empire, his later work was primarily in Saxony. **Sergey Chaplygin** contributed to aerodynamics with Chaplygin's equation (opens in new tab) and the notion of Chaplygin gas (opens in new tab).

Influencers: E to H

The Universal Mathematician

Though Swiss-born, **Leonhard Euler** spent a significant portion of his life in St. Petersburg and is arguably one of the greatest mathematicians of all time. His monumental discoveries span mathematical analysis (opens in new tab), graph theory (opens in new tab), and number theory (opens in new tab). Euler introduced much of the modern mathematical terminology and notation, including the concept of a mathematical function (opens in new tab), Euler's number (e) (opens in new tab), and Euler circles (opens in new tab).

Cosmology and Crystallography

**Alexander Alexandrovich Friedmann** (also known as Friedman or Fridman) was a Russian and Soviet physicist and mathematician who originated the pioneering theory that the universe is expanding. He developed the foundational Friedmann equations (opens in new tab) and contributed to the Friedmann–Lemaître–Robertson–Walker metric (opens in new tab).

**Yevgraf Fyodorov**, a mathematician and crystallographer, was the first to catalogue all 230 space groups (opens in new tab) of crystals and identified periodic graphs (opens in new tab) in geometry.

Geometry and Analysis

**Mikhail Gromov** is a prominent developer of geometric group theory (opens in new tab) and the inventor of the homotopy principle (opens in new tab). His contributions include Gromov's compactness theorem (opens in new tab), Gromov norm (opens in new tab), and (opens in new tab)">Gromov product, earning him a Wolf Prize (opens in new tab).

**Dmitri Egorov** made significant contributions to differential geometry and mathematical analysis, notably Egorov's Theorem (opens in new tab).
**Boris Galerkin** developed the Galerkin method (opens in new tab), a widely used technique in numerical analysis for solving differential equations.
**Israel Gelfand** was a major contributor to numerous areas, including group theory (opens in new tab), representation theory (opens in new tab), and linear algebra (opens in new tab), with concepts like the Gelfand representation (opens in new tab).
**Alexander Gelfond** authored Gelfond's theorem (opens in new tab), providing a means to obtain an infinite number of transcendentals (opens in new tab), including the Gelfond–Schneider constant (opens in new tab).

Innovators: K to M

Algorithms and Optimization

**Leonid Kantorovich**, a mathematician and economist, is recognized as a founder of linear programming (opens in new tab). He introduced the Kantorovich inequality (opens in new tab) and Kantorovich metric (opens in new tab), and developed the theory of optimal allocation of resources, which earned him a Nobel Prize in Economics (opens in new tab).

**Anatoly Karatsuba** developed the Karatsuba algorithm (opens in new tab), the first fast multiplication algorithm, significantly impacting computational efficiency.

Universal Contributions

**Andrey Kolmogorov** is one of the preeminent mathematicians of the 20th century, a Wolf Prize (opens in new tab) winner, with multiple profound contributions. His work includes the probability axioms (opens in new tab), the Chapman–Kolmogorov equation (opens in new tab), and the Kolmogorov extension theorem (opens in new tab) in probability, as well as Kolmogorov complexity (opens in new tab).

**Sofia Kovalevskaya** holds the distinction of being the first woman professor in Northern Europe and Russia, and the first female professor of mathematics. She discovered the Kovalevskaya top (opens in new tab), a significant contribution to classical mechanics.

Chains and Spaces

**Andrey Markov, Sr.** is renowned for inventing Markov chains (opens in new tab), a fundamental concept in stochastic processes. His extensive work includes the Markov brothers' inequality (opens in new tab), the hidden Markov model (opens in new tab), and various other Markov-related concepts that permeate probability theory and statistics.

**David Kazhdan** is a highly influential mathematician in representation theory and category theory, known for the Kazhdan-Lusztig conjecture (opens in new tab) and Kazhdan property (T) (opens in new tab).
**Leonid Khachiyan** developed the Ellipsoid algorithm (opens in new tab) for linear programming.
**Maxim Kontsevich** is a Fields Medal (opens in new tab) winner, known for the Kontsevich integral (opens in new tab) and Kontsevich quantization formula (opens in new tab).
**Mark Krein** contributed significantly to functional analysis, developing the Tannaka–Krein duality (opens in new tab) and the Krein–Milman theorem (opens in new tab).
**Yuri Matiyasevich** provided a negative solution for Hilbert's tenth problem (opens in new tab) with Matiyasevich's theorem (opens in new tab).

Geometry and Stability

**Nikolai Lobachevsky** is celebrated as a "Copernicus of Geometry" for creating the first non-Euclidean geometry (opens in new tab), specifically hyperbolic geometry (opens in new tab), which revolutionized mathematical thought.

**Aleksandr Lyapunov** founded stability theory (opens in new tab), a cornerstone of control theory and dynamical systems. His work includes Lyapunov's central limit theorem (opens in new tab), the Lyapunov equation (opens in new tab), and the concept of Lyapunov time (opens in new tab).

Modern Masters: N to P

Topology and Problem Solving

**Sergei Novikov** is a Wolf Prize (opens in new tab) and Fields Medal (opens in new tab) winner, known for his work in algebraic topology (opens in new tab) and soliton theory (opens in new tab). He developed the Adams–Novikov spectral sequence (opens in new tab) and the Novikov conjecture (opens in new tab).

**Pyotr Novikov** famously solved the word problem for groups (opens in new tab) and Burnside's problem (opens in new tab), demonstrating profound insights into group theory.

Conjectures and Prizes

**Grigori Perelman** made landmark contributions to Riemannian geometry (opens in new tab) and topology (opens in new tab). He famously proved the Geometrization conjecture (opens in new tab) and the Poincaré conjecture (opens in new tab), for which he was awarded a Fields Medal (opens in new tab) and the first Clay Millennium Prize Problems (opens in new tab) Award, both of which he declined.

**Andrei Okounkov** is a Fields Medal (opens in new tab) winner, known for his research on infinite symmetric groups (opens in new tab) and the Hilbert scheme (opens in new tab).
**Mikhail Ostrogradsky** was a mathematician and physicist, author of the divergence theorem (opens in new tab) and contributions to partial fractions in integration (opens in new tab).
**Lev Pontryagin**, a blind mathematician, developed Pontryagin duality (opens in new tab) and Pontryagin classes (opens in new tab) in topology, and Pontryagin's minimum principle (opens in new tab) in optimal control.

Contemporary Giants: R to Z

Computational Theory and Logic

**Alexander Razborov** is a mathematician and computational theorist who won the Nevanlinna Prize (opens in new tab) in 1990 and the Gödel Prize (opens in new tab) for his contributions to computer sciences, particularly in complexity theory.

**Moses Schönfinkel** is recognized as the inventor of combinatory logic (opens in new tab), a foundational system in mathematical logic and theoretical computer science.

Analysis and Probability

**Sergei Sobolev** introduced the influential Sobolev spaces (opens in new tab) and mathematical distributions (opens in new tab), which are indispensable tools in the study of partial differential equations. He also co-developed the first ternary computer (opens in new tab), Setun (opens in new tab).

**Yakov Sinai** is a Wolf Prize (opens in new tab) winner, known for developing the Kolmogorov–Sinai entropy (opens in new tab) and the Sinai billiard (opens in new tab) in dynamical systems.

Fields Medalists and Visionaries

**Vladimir Voevodsky**, a Fields Medalist (opens in new tab), introduced a homotopy theory (opens in new tab) for schemes and modern motivic cohomology (opens in new tab), profoundly influencing algebraic geometry and topology.

**Efim Zelmanov**, also a Fields Medal (opens in new tab) winner, solved the challenging restricted Burnside problem (opens in new tab) in group theory.

**Lev Schnirelmann** developed the Lusternik–Schnirelmann category (opens in new tab) in topology and Schnirelmann density (opens in new tab) of numbers.
**Igor Shafarevich** introduced the Shafarevich–Weil theorem (opens in new tab) and proved the Golod–Shafarevich theorem (opens in new tab).
**Stanislav Smirnov** is a Fields Medalist (opens in new tab) for his research on the triangular lattice (opens in new tab).
**Andrey Tikhonov** is known for the Tikhonov space (opens in new tab) and Tikhonov's theorem (opens in new tab) in general topology, and Tikhonov regularization (opens in new tab) for ill-posed problems.
**Pavel Urysohn** developed topological dimension theory (opens in new tab) and metrization theorems (opens in new tab), including Urysohn's Lemma (opens in new tab).
**Vladimir Vapnik** developed the Vapnik–Chervonenkis theory (opens in new tab) of statistical learning and co-invented the support-vector machine (opens in new tab).
**Georgy Voronoy** invented the widely used Voronoi diagram (opens in new tab).

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Mathematical Luminaries

💡 Dive in with Flashcard Learning! 💡

Introduction 📚

🇷🇺 A Rich Mathematical Heritage

🕰️ Spanning Eras and Disciplines

Pioneers: A to D 💡

🌳 Algorithms and Topology

🌌 Dynamical Systems and Geometry

📊 Probability and Analysis

🔢 Foundational Figures

Influencers: E to H ✨

♾️ The Universal Mathematician

🔭 Cosmology and Crystallography

📐 Geometry and Analysis

Innovators: K to M 🧠

💡 Algorithms and Optimization

🌐 Universal Contributions

🔗 Chains and Spaces

🗺️ Geometry and Stability

Modern Masters: N to P 🔬

🧩 Topology and Problem Solving

🏆 Conjectures and Prizes

Contemporary Giants: R to Z 🚀

💻 Computational Theory and Logic

📊 Analysis and Probability

🌟 Fields Medalists and Visionaries

Teacher's Corner 🧑‍🏫

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📜 References

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To report an issue with this page, or to find out ways to support the mission, please click here.

Disclaimer ⚠️

📜 Important Notice

Dive in with Flashcard Learning!

Introduction

A Rich Mathematical Heritage

Spanning Eras and Disciplines

Pioneers: A to D

Algorithms and Topology

Dynamical Systems and Geometry

Probability and Analysis

Foundational Figures

Influencers: E to H

The Universal Mathematician

Cosmology and Crystallography

Geometry and Analysis

Innovators: K to M

Algorithms and Optimization

Universal Contributions

Chains and Spaces

Geometry and Stability

Modern Masters: N to P

Topology and Problem Solving

Conjectures and Prizes

Contemporary Giants: R to Z

Computational Theory and Logic

Analysis and Probability

Fields Medalists and Visionaries

Teacher's Corner

True or False?

Test Your Knowledge!

Gamer's Corner

Discover other topics to study!

References

Feedback & Support

Disclaimer

Important Notice