Top 10 Mathematicians in 20th Century

In the 20th century, mathematics grew generalized and abstract, largely abandoning the notion of axioms as “self-evident truths.” As a result of it, hundreds of specialized fields and areas of study developed, including group theory, knot theory, topology, graph theory, functional analysis, singularity theory, catastrophe theory, model theory, game theory, complexity theory, and many others.

Thus the mathematics profession became a significant one, attracting thousands of new Ph.D.s annually and jobs in both teaching and industry. But who were the 20th century’s greatest mathematicians? Continue reading our post on the top 10 mathematicians in 20th century.

10. John Horton Conway

John Horton Conway- 10th Top 10 Mathematicians in 20th Century

In 1970, Conway developed the ‘Game of Life’ and its rules, which illustrate automation in which cells develop and expand in a grid. Scientists, particularly computer scientists, are becoming very interested in this “cellular automation.”

Conway, one of the famous mathematicians, also developed ideas such as the great antiprism, surreal numbers, and mathematical games, making significant contributions to group theory, number theory, game theory, and geometry.

The 20th century saw the birth, life, and creation of a sizable number of the greatest brains in mathematics. The world can move quickly and evolve every day because of the advancements in maths and information technology.

9. Alan Turing

Alan Turing- 9th Top 10 Mathematicians in 20th Century

Computer Scientist and Cryptanalyst Alan Turing is one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions.

Undoubtedly affecting the outcome of the war, or at least the time-scale. After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is one of the first true computer scientists.

Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’.

Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.

8. Paul Cohen

Paul Cohen- 8th Top 10 Mathematicians in 20th Century

Paul Cohen resolved one of the 23 difficulties Hilbert posed by demonstrating that the Cantor’s continuum hypothesis, or the conceivable sizes of infinite sets, may both be true and false.

Modern mathematicians now have to determine whether their results depend on this specific premise as a result of this significant discovery, which opened up a whole new universe of mathematics. The name given to the theory is ‘Continuum Hypothesis’.

7. Alexander Grothendieck

Alexander Grothendieck- 7th Top 10 Mathematicians in 20th Century

Weil’s successor, Alexander Grothendieck was an influential and beloved mathematician in the 20th century. He developed a new language in 1950, opening us new perspectives on mathematical structures and allowing us to tackle issues in number theory, basic physics, and geometry.

The “theory of topoi” is of crucial relevance to mathematical logic, while the “theory of schemed” contributed to the resolution of some Weil’s number theory conjectures. In addition, Grothendieck provided an algebraic formulation of the fundamental group of a curve and a demonstration of the Riemann-Roch theorem.

6. Andre Weil

Andre Weil- 6th Top 10 Mathematicians in 20th Century

Another European immigrant who made a significant contribution to modern mathematics is Andre Weil. We were able to connect algebra, topology, number theory, and geometry thanks to his theorems.

Additionally, Weil organised the clandestine group of French mathematicians working under the pen name Nicolas Bourbaki and gave us a great deal of assistance with math problems in the numerous books on mathematics from the 20th century.

Grothendieck succeeded this mathematician as his heir.

5. Claude Shannon

Claude Shannon- 5th Top 10 Mathematicians in 20th Century

Claude Shannon, an American mathematician is the inventor of information theory. He ignited the twentieth-century digital revolution. In 1937, he contributed to the development of the digital circuit and worked on Boolean algebra. In 1948, he created the information theory and the exposition of communication. So he is definitely one of the famous 20th century mathematicians.

4. John von Neumann

John von Neumann- 4th Top 10 Mathematicians in 20th Century

The whole focus of mathematics as a science shifted to America in the 1930s and 1940s when the anti-Jewish Nazi dictatorship came to power. Many of the top mathematicians in Europe at this time, including Einstein and Godel, made the decision to immigrate to the United States. John von Neumann was one of these leading authorities in the field of mathematics.

In addition to mathematics, Neumann also made significant contributions to nuclear physics and quantum theory. One of the most well-liked and brilliant mathematicians of the 20th century, he contributed to the Manhattan Project and the development of the hydrogen bomb.

In the end, he developed a design model for a digital computer that uses a processor unit and a separate storage structure for data and instructions.

3. David Hilbert

David Hilbert- 3rd Top 10 Mathematicians in 20th Century

Hilbert gave one of the most well-known lectures in the history of mathematics in 1900 at the Sorbonne in Paris. The 23 unresolved mathematical puzzles are referred to as the “Hilbert problems” by German mathematician David Hilbert. At this time, the objectives for 20th-century mathematics were established, offering direction to experts in all areas of mathematics.

Currently, 12 out of the 23 issues remain to be worked on, and 10 of them have been completely solved.This mathematician used an axiomatic method but had a very different approach. He was a well-known figure in the society and the originator of many theorems and mathematical ideas.

2. G.H. Hardy

G.H. Hardy- 2nd Top 10 Mathematicians in 20th Century

G.H. Hardy was a mentor to the prominent Indian mathematician Srinivasa Ramanujan. Besides he made contributions to number theory and mathematical analysis. His essay on mathematics, A Mathematician’s Apology, is also popular. He also left his imprint on biology by developing the Hardy-Weinberg principle, a foundational idea in population genetics.

The British mathematician and his Indian protégé, Srinivasa Ramanujan are two of the greatest mathematicians of the 20th century.

1. Srinivasa Ramanujan

Srinivasa Ramanujan- 1st Top 10 Mathematicians in 20th Century

Indian mathematician Srinivasa Ramanujan was born in 1887 and passed away in 1920. Numerous experts regard his work on mathematical analysis, number theory, infinite series, and continued fractions as some of the most outstanding in the field.

The Riemann hypothesis from the previous century was the first problem Ramanujan and G.H. Hardy tried to answer, but they were unsuccessful. Ramanujan is one of the greatest minds of the 20th century, whereas Hardy is famous for modernizing British mathematics.

Conclusion

Some people avoid studying mathematics, yet many well-known mathematicians had a passion for numbers throughout history. They sought ways to comprehend the world through the lens of mathematics, and their discoveries have significantly impacted future generations. Our list of prominent mathematicians and their key findings can encourage many people to explore this logically fascinating subject.

Frequently Asked Questions:

Q1. Who is the Father of Mathematics?

The renowned Greek mathematician and philosopher Archimedes is the “Father of Mathematics.”

Q2. Who is the Founder of Modern Mathematics?

René Descartes, sometimes known as Cartesius, was a well-known French philosopher, mathematician, and physicist who lived from March 31, 1596, to February 11, 1650.

He is one of the most significant and influential intellectuals of modern times, known as the “Founder of Modern Philosophy” and the “Father of Modern Mathematics.”

Q3. Who is the Founder of Mathematics?

We refer to Pythagoras of Samos as the first mathematician. Despite being a pivotal role in the growth of mathematics, we know very little about his mathematical accomplishments.

Top 10 mathematicians in 20th century

http://listverse.com/2010/12/07/top-10-greatest-mathematicians/

10

Pythagoras of Samos

Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.

9

Andrew Wiles

The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat’s Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did ‘invent’ large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).

8

Isaac Newton and Wilhelm Leibniz

I have placed these two together as they are both often given the honor of being the ‘inventor’ of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.

7

Leonardo Pisano Blgollo

Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.

Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.

6

Alan Turing

Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.

After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.

5

René Descartes

French Philosopher, Physicist and Mathematician Rene Descartes is best known for his ‘Cogito Ergo Sum’ philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.

4

Euclid

Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.

3

G. F. Bernhard Riemann

Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use ‘new mathematics’. It would seem that, even in death, Riemann’s work may still pave the way for new contributions to the field, just as he did in life.

2

Carl Friedrich Gauss

Child prodigy Gauss, the ‘Prince of Mathematics’, made his first major discovery whilst still a teenager, and wrote the incredible Disquisitiones Arithmeticae, his magnum opus, by the time he was 21. Many know Gauss for his outstanding mental ability – quoted to have added the numbers 1 to 100 within seconds whilst attending primary school (with the aid of a clever trick). The local Duke, recognizing his talent, sent him to Collegium Carolinum before he left for Gottingen (at the time it was the most prestigious mathematical university in the world, with many of the best attending). After graduating in 1798 (at the age of 22), he began to make several important contributions in major areas of mathematics, most notably number theory (especially on Prime numbers). He went on to prove the fundamental theorem of algebra, and introduced the Gaussian gravitational constant in physics, as well as much more – all this before he was 24! Needless to say, he continued his work up until his death at the age of 77, and had made major advances in the field which have echoed down through time.

1

Leonhard Euler

If Gauss is the Prince, Euler is the King. Living from 1707 to 1783, he is regarded as the greatest mathematician to have ever walked this planet. It is said that all mathematical formulas are named after the next person after Euler to discover them. In his day he was ground breaking and on par with Einstein in genius. His primary (if that’s possible) contribution to the field is with the introduction of mathematical notation including the concept of a function (and how it is written as f(x)), shorthand trigonometric functions, the ‘e’ for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter ‘/i’ for imaginary units, as well as the symbol pi for the ratio of a circles circumference to its diameter. All of which play a huge bearing on modern mathematics, from the every day to the incredibly complex.

As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more – and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.

http://math2033.uark.edu/wiki/index.php/20th_Century_Mathematicians

1 Felix Christian Klein

2 Henri Poincaré

3 David Hilbert

4 Albert Einstein

5 L.E.J. Brouwer

6 Hermann K. H. Weyl

7 Srinivasa Ramanujan

Top 10 mathematicians in 20th century
http://listverse.com/2010/12/07/top-10-greatest-mathematicians/
10
Pythagoras of Samos

Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.
9
Andrew Wiles

The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat’s Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did ‘invent’ large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).
8
Isaac Newton and Wilhelm Leibniz

I have placed these two together as they are both often given the honor of being the ‘inventor’ of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.
7
Leonardo Pisano Blgollo

Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.
Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.
6
Alan Turing

Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.
After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.

5
René Descartes

French Philosopher, Physicist and Mathematician Rene Descartes is best known for his ‘Cogito Ergo Sum’ philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.
4
Euclid

Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.
3
G. F. Bernhard Riemann

Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use ‘new mathematics’. It would seem that, even in death, Riemann’s work may still pave the way for new contributions to the field, just as he did in life.
2
Carl Friedrich Gauss

Child prodigy Gauss, the ‘Prince of Mathematics’, made his first major discovery whilst still a teenager, and wrote the incredible Disquisitiones Arithmeticae, his magnum opus, by the time he was 21. Many know Gauss for his outstanding mental ability – quoted to have added the numbers 1 to 100 within seconds whilst attending primary school (with the aid of a clever trick). The local Duke, recognizing his talent, sent him to Collegium Carolinum before he left for Gottingen (at the time it was the most prestigious mathematical university in the world, with many of the best attending). After graduating in 1798 (at the age of 22), he began to make several important contributions in major areas of mathematics, most notably number theory (especially on Prime numbers). He went on to prove the fundamental theorem of algebra, and introduced the Gaussian gravitational constant in physics, as well as much more – all this before he was 24! Needless to say, he continued his work up until his death at the age of 77, and had made major advances in the field which have echoed down through time.
1
Leonhard Euler

If Gauss is the Prince, Euler is the King. Living from 1707 to 1783, he is regarded as the greatest mathematician to have ever walked this planet. It is said that all mathematical formulas are named after the next person after Euler to discover them. In his day he was ground breaking and on par with Einstein in genius. His primary (if that’s possible) contribution to the field is with the introduction of mathematical notation including the concept of a function (and how it is written as f(x)), shorthand trigonometric functions, the ‘e’ for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter ‘/i’ for imaginary units, as well as the symbol pi for the ratio of a circles circumference to its diameter. All of which play a huge bearing on modern mathematics, from the every day to the incredibly complex.
As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more – and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.
http://math2033.uark.edu/wiki/index.php/20th_Century_Mathematicians
1 Felix Christian Klein
2 Henri Poincaré
3 David Hilbert
4 Albert Einstein
5 L.E.J. Brouwer
6 Hermann K. H. Weyl
7 Srinivasa Ramanujan
8 Amalie Emmy Noether
9 Stefan Banach
10 Andrey N. Kolmogorov

8 Amalie Emmy Noether

9 Stefan Banach

10 Andrey N. Kolmogorov

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