Top Ten Mathematicians

Top Ten Mathematicians


  1. Pythagoras

           Pythagoras of Samos (570 – 495 BC) was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and might have traveled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy, and there set up a religious sect. His followers pursued the religious rites and practices developed by Pythagoras, and studied his philosophical theories. The society took an active role in the politics of Croton, but this eventually led to their downfall. The Pythagorean meeting-places were burned, and Pythagoras was forced to flee the city. He is said to have ended his days in Metapontum. Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. He is often revered as a great mathematician, mystic and scientist, but he is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than that of the other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics and natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Whether or not his disciples believed that everything was related to mathematics and that numbers were the ultimate reality is unknown. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.
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  2. Hypatia
          Hypatia (ca. AD 350–370–March 415) was a Greek Neoplatonist philosopher in Roman Egypt who was the first well-documented woman in mathematics. As head of the Platonist school at Alexandria, she also taught philosophy and astronomy. As a Neoplatonist philosopher, she belonged to the mathematic tradition of the Academy of Athens, as represented by Eudoxus of Cnidus; she was of the intellectual school of the 3rd century thinker Plotinus, which encouraged logic and mathematical study in place of empirical enquiry and strongly encouraged law in place of nature. According to the only contemporary source, Hypatia was murdered by a Christian mob after being accused of exacerbating a conflict between two prominent figures in Alexandria: the governor Orestes and the Bishop of Alexandria. Kathleen Wider proposes that the murder of Hypatia marked the end of Classical antiquity, and Stephen Greenblatt observes that her murder “effectively marked the downfall of Alexandrian intellectual life.” On the other hand, Maria Dzielska and Christian Wildberg note that Hellenistic philosophy continued to flourish in the 5th and 6th centuries, and perhaps until the age of Justinian.
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  3. Girolamo Cardano
    Gerolamo (or Girolamo, or Geronimo) Cardano (24 September 1501 – 21 September 1576) was an Italian Renaissance mathematician, physician, astrologer and gambler. He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion and music. His gambling led him to formulate elementary rules in probability, making him one of the founders of the field.
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  4. Leonhard Euler (15 April 1707 – 18 September 1783)

    Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler’s influence on mathematics: “Read Euler, read Euler, he is our teacher in all things,” which has also been translated as “Read Euler, read Euler, he is the master of us all.” Euler was featured on the sixth series of the Swiss 10-franc banknote and on numerous Swiss, German, and Russian postage stamps. The asteroid 2002 Euler was named in his honor. He is also commemorated by the Lutheran Church on their Calendar of Saints on 24 May, he was a devout Christian (and believer in biblical inerrancy) who wrote apologetics and argued forcefully against the prominent atheists of his time.
  5. Johann Gauss (30 April 1777 – 23 February 1855)
           Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. Sometimes referred to as the Princeps mathematicorum (Latin, “the Prince of Mathematicians” or “the foremost of mathematicians”) and “greatest mathematician since antiquity,” Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians. He referred to mathematics as “the queen of sciences.” Gauss was a child prodigy. There are many anecdotes pertaining to his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it was not published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.
  6. Emmy Noether (23 March 1882 – 14 April 1935)
    Emmy Noether was an influential German mathematician known for her contributions to abstract algebra and theoretical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed the theories of rings, fields, and algebras. Noether’s mathematical work has been divided into three “epochs.” In the first (1908–19), she made significant contributions to the theories of algebraic invariants and number fields. Her work on differential invariants in the calculus of variations, Noether’s theorem, has been called “one of the most important mathematical theorems ever proved in guiding the development of modern physics.” In the second epoch (1920–26), she began work that “changed the face of [abstract] algebra.” In her classic paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921) Noether developed the theory of ideals in commutative rings into a powerful tool with wide-ranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor. In the third epoch (1927–35), she published major works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.
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  7. Georg Cantor (1845 – January 6, 1918)

    Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are “more numerous” than the natural numbers. In fact, Cantor’s theorem implies the existence of an “infinity of infinities.” He defined the cardinal and ordinal numbers and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware. Cantor’s theory of transfinite numbers was originally regarded as so counter-intuitive, even shocking, that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Some Christian theologians (particularly neo-Scholastics) saw Cantor’s work as a challenge to the uniqueness of the absolute infinity in the nature of God, on one occasion equating the theory of transfinite numbers with pantheism. The objections to his work were occasionally fierce: Poincaré referred to Cantor’s ideas as a “grave disease” infecting the discipline of mathematics, and Kronecker’s public opposition and personal attacks included describing Cantor as a “scientific charlatan,” a “renegade” and a “corrupter of youth.” Writing decades after Cantor’s death, Wittgenstein lamented that mathematics is “ridden through and through with the pernicious idioms of set theory,” which he dismissed as “utter nonsense” that is “laughable” and “wrong.” Cantor’s recurring bouts of depression from 1884 to the end of his life were once blamed on the hostile attitude of many of his contemporaries, but these episodes can now be seen as probable manifestations of a bipolar disorder. The harsh criticism has been matched by later accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics. Cantor believed his theory of transfinite numbers had been communicated to him by God. David Hilbert defended it from its critics by famously declaring: “No one shall expel us from the Paradise that Cantor has created.”
  8. Paul Erdös
           Paul Erdős (26 March 1913 – 20 September 1996) was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory. He is also known for his “legendarily eccentric” personality.
  9. John Horton Conway

           John Horton Conway (born 26 December 1937) is a British mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971), was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.
  10. Grigori Perelman

           Grigori Yakovlevich Perelman (born 13 June 1966) is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology. In 1994, Perelman proved the soul conjecture. In 2003, he proved Thurston’s geometrization conjecture. This consequently solved in the affirmative the Poincaré conjecture, posed in 1904, which before its solution was viewed as one of the most important and difficult open problems in topology. In August 2006, Perelman was awarded the Fields Medal for “his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow.” Perelman declined to accept the award or to appear at the congress, stating: “I’m not interested in money or fame, I don’t want to be on display like an animal in a zoo.” On 22 December 2006, the journal Science recognized Perelman’s proof of the Poincaré conjecture as the scientific “Breakthrough of the Year,” the first such recognition in the area of mathematics. On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture.
  11. Terry Tao
    Terence “Terry” Chi-Shen Tao FRS (born 17 July 1975, Adelaide), is an Australian mathematician working in harmonic analysis, partial differential equations, additive combinatorics, ergodic Ramsey theory, random matrix theory and analytic number theory. He currently holds the James and Carol Collins chair in mathematics at the University of California, Los Aangeles. He was one of the recipients of the 2006 Fields Medal.
  12. Kurt Godel

           Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian American logician, mathematician and philosopher. After WWII, he emigrated to the US. Considered among the most significant logicians in human history—at the level of Aristotle and Frege—Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics. Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers. He also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent. The former result opened the door for “working mathematicians” to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic and modal logic.
  13. Jean Fourier (21 March 1768 – 16 May 1830)

           Jean Baptiste Joseph Fourier was a French mathematician and physicist best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier’s Law are also named in his honor. Fourier is also generally credited with the discovery of the greenhouse effect.
  14. Georg Riemann (September 17, 1826 – July 20, 1866)

           Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity.
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