Hypatia of Alexandria
- Born:
- c. 350–370 AD, Alexandria, Roman Egypt
- Died:
- March 415 AD, Alexandria, Roman Egypt
- Nationality:
- Egyptian (Greco-Roman)
- Profession(s):
- Philosopher, Astronomer, Mathematician
Early Life and Education
- Hypatia was the daughter of Theon of Alexandria, a mathematician and astronomer.
- She received a comprehensive education in mathematics, astronomy, philosophy, and mechanics.
- She may have traveled to Athens and Italy for further study.
Career and Major Achievements
- Hypatia lectured on mathematics and philosophy at the Platonic school in Alexandria.
- She was a highly respected teacher and attracted students from all over the Mediterranean.
- She wrote commentaries on mathematical and astronomical works, including Diophantus' Arithmetica and Apollonius' Conics.
Notable Works
- Commentary on Diophantus' Arithmetica (fragments survive)
- Commentary on Apollonius' Conics (lost)
- Commentary on Ptolemy's Almagest (possibly)
- Revision of Theon's version of Euclid's Elements (possibly)
Legacy and Impact
Hypatia was a prominent figure in Alexandrian society and a symbol of learning and reason. Her brutal murder was a significant event in the decline of classical learning in late antiquity. When considering which "pictures of 10 mathematicians" to feature, Hypatia's inclusion is crucial given her pioneering role for women in mathematics.
Leonhard Euler
- Born:
- April 15, 1707, Basel, Switzerland
- Died:
- September 18, 1783, Saint Petersburg, Russian Empire
- Nationality:
- Swiss
- Profession(s):
- Mathematician, Physicist, Astronomer, Logician, Engineer
Early Life and Education
- Euler's father was a pastor who had studied mathematics under Jakob Bernoulli.
- He attended the University of Basel, where he studied mathematics under Johann Bernoulli.
- He initially studied theology and Hebrew but was encouraged by Johann Bernoulli to focus on mathematics.
Career and Major Achievements
- Euler worked at the St. Petersburg Academy of Sciences (1727-1741) and the Berlin Academy of Sciences (1741-1766).
- He made significant contributions to calculus, number theory, graph theory, topology, mechanics, fluid dynamics, optics, and astronomy.
- He introduced much of the modern mathematical terminology and notation, including the concept of a mathematical function.
Notable Works
- Mechanica (1736)
- Introductio in analysin infinitorum (1748)
- Institutiones calculi differentialis (1755)
- Institutiones calculi integralis (1768-1770)
Legacy and Impact
Euler is considered one of the most prolific and influential mathematicians of all time. His work has had a profound impact on the development of mathematics and science. Among the potential "pictures of 10 mathematicians" one could compile, Euler's portrait would showcase the breadth and depth of 18th-century mathematical thought.
Carl Friedrich Gauss
- Born:
- April 30, 1777, Brunswick, Duchy of Brunswick-Wolfenbüttel (now Germany)
- Died:
- February 23, 1855, Göttingen, Kingdom of Hanover (now Germany)
- Nationality:
- German
- Profession(s):
- Mathematician, Astronomer, Physicist, Geodesist
Early Life and Education
- Gauss was a child prodigy with exceptional mathematical abilities.
- He attended the Collegium Carolinum and the University of Göttingen.
- He made groundbreaking discoveries in number theory while still a teenager.
Career and Major Achievements
- Gauss was appointed director of the Göttingen Observatory in 1807.
- He made significant contributions to number theory, analysis, differential geometry, geodesy, magnetism, and astronomy.
- He developed the method of least squares, used in many fields of science and engineering.
Notable Works
- Disquisitiones Arithmeticae (1801)
- Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium (1809)
- Disquisitiones generales circa superficies curvas (1828)
Legacy and Impact
Gauss is considered one of the greatest mathematicians of all time. His work has had a profound impact on the development of mathematics and science. When selecting "pictures of 10 mathematicians" for a historical compilation, Gauss's inclusion is mandatory, given his foundational contributions across diverse mathematical fields.
Augustin-Louis Cauchy
- Born:
- August 21, 1789, Paris, France
- Died:
- May 23, 1857, Sceaux, France
- Nationality:
- French
- Profession(s):
- Mathematician
Early Life and Education
- Cauchy was raised in a family with strong political and intellectual connections.
- He received early education from his father and later attended the École Centrale du Panthéon.
- He entered the École Polytechnique in 1805 and later the École des Ponts et Chaussées.
Career and Major Achievements
- Cauchy worked as an engineer for a few years before dedicating himself fully to mathematics.
- He made significant contributions to analysis, including the development of rigorous definitions of limits, continuity, and convergence.
- He also made important contributions to complex analysis, elasticity, and number theory.
Notable Works
- Cours d'analyse de l'École Royale Polytechnique (1821)
- Résumé des leçons données à l'École Royale Polytechnique sur le calcul infinitésimal (1823)
- Leçons sur les applications du calcul infinitésimal à la géométrie (1826-1828)
Legacy and Impact
Cauchy is considered one of the founders of modern analysis. His rigorous approach to mathematics helped to establish a solid foundation for future development. In a collection of "pictures of 10 mathematicians", Cauchy represents the crucial shift towards rigor in 19th-century analysis.
Niels Henrik Abel
- Born:
- August 5, 1802, Nedstrand, Norway
- Died:
- April 6, 1829, Froland, Norway
- Nationality:
- Norwegian
- Profession(s):
- Mathematician
Early Life and Education
- Abel showed exceptional mathematical talent from a young age.
- He was largely self-taught, studying the works of Euler, Newton, and Lagrange.
- He struggled financially throughout his life, despite his remarkable abilities.
Career and Major Achievements
- Abel proved the impossibility of solving the general quintic equation by radicals.
- He made significant contributions to the theory of elliptic functions and Abelian integrals.
- His work was initially overlooked but later recognized as highly important.
Notable Works
- Mémoire sur les équations algébriques où l'on démontre l'impossibilité de résoudre l'équation générale du cinquième degré (1824)
- Recherches sur les fonctions elliptiques (1827)
Legacy and Impact
Abel's work had a profound impact on the development of algebra and analysis. The Abel Prize, one of the most prestigious awards in mathematics, is named in his honor. When assembling "pictures of 10 mathematicians", Abel represents the tragic yet brilliant figure whose work revolutionized algebra.
Évariste Galois
- Born:
- October 25, 1811, Bourg-la-Reine, France
- Died:
- May 31, 1832, Paris, France
- Nationality:
- French
- Profession(s):
- Mathematician
Early Life and Education
- Galois displayed extraordinary mathematical talent but struggled within the rigid French educational system.
- He was denied entry to the École Polytechnique twice.
- He became involved in radical politics and was imprisoned several times.
Career and Major Achievements
- Galois developed the theory of Galois groups, which provides a general solution to the question of when a polynomial equation can be solved by radicals.
- His work was initially rejected by leading mathematicians.
- He died in a duel at the age of 20, leaving behind a manuscript that was later recognized as a major breakthrough.
Notable Works
- Mémoire sur les conditions de résolubilité des équations par radicaux (published posthumously by Liouville)
Legacy and Impact
Galois's work laid the foundation for modern algebra and group theory. Galois theory has applications in many areas of mathematics and physics. In a collection of "pictures of 10 mathematicians", Galois's inclusion exemplifies revolutionary mathematical insight coupled with personal tragedy.
Bernhard Riemann
- Born:
- September 17, 1826, Breselenz, Kingdom of Hanover (now Germany)
- Died:
- July 20, 1866, Selasca, Italy
- Nationality:
- German
- Profession(s):
- Mathematician
Early Life and Education
- Riemann was the son of a pastor.
- He studied theology and philology before turning to mathematics.
- He studied at the University of Göttingen under Carl Friedrich Gauss.
Career and Major Achievements
- Riemann made fundamental contributions to analysis, geometry, and number theory.
- He developed Riemannian geometry, which provides a framework for describing curved spaces.
- He formulated the Riemann hypothesis, one of the most important unsolved problems in mathematics.
Notable Works
- Über die Hypothesen, welche der Geometrie zu Grunde liegen (1854)
- Über die Anzahl der Primzahlen unter einer gegebenen Größe (1859)
Legacy and Impact
Riemann's work had a profound impact on the development of mathematics and physics. Riemannian geometry is essential for Einstein's theory of general relativity. When deciding on "pictures of 10 mathematicians" to display, Riemann's presence is vital due to the enduring influence of his non-Euclidean geometry.
Karl Weierstrass
- Born:
- October 31, 1815, Ostenfelde, Westphalia, Prussia (now Germany)
- Died:
- February 19, 1897, Berlin, German Empire
- Nationality:
- German
- Profession(s):
- Mathematician
Early Life and Education
- Weierstrass initially studied law and public administration but later turned to mathematics.
- He taught mathematics at secondary schools for many years.
- He received an honorary doctorate from the University of Königsberg in 1854.
Career and Major Achievements
- Weierstrass developed a rigorous foundation for calculus based on limits and inequalities.
- He made significant contributions to the theory of elliptic functions and Abelian functions.
- He is known as the "father of modern analysis."
Notable Works
- Beiträge zur Theorie der Abelschen Functionen (1854)
- Theorie der analytischen Functionen (unpublished lecture notes)
Legacy and Impact
Weierstrass's work revolutionized analysis by providing a solid foundation for its concepts and methods. His emphasis on rigor helped to shape the direction of 19th-century mathematics. The significance of Weierstrass necessitates his inclusion when presenting "pictures of 10 mathematicians" who shaped modern mathematical analysis.
Sofia Kovalevskaya
- Born:
- January 15, 1850, Moscow, Russian Empire
- Died:
- February 10, 1891, Stockholm, Sweden
- Nationality:
- Russian
- Profession(s):
- Mathematician
Early Life and Education
- Kovalevskaya received private tutoring in mathematics as a child.
- She had to enter a fictitious marriage to leave Russia and study abroad.
- She studied at the University of Heidelberg and the University of Berlin, but could not formally attend lectures in Berlin.
Career and Major Achievements
- Kovalevskaya earned a doctorate from the University of Göttingen in absentia.
- She became a professor at the University of Stockholm, one of the first women to hold such a position in Europe.
- She made significant contributions to the theory of partial differential equations, celestial mechanics, and the rotation of a rigid body.
- Won the Prix Bordin of the French Academy of Sciences in 1888.
Notable Works
- Zur Theorie der partiellen Differentialgleichungen (1875)
- Mémoire sur un cas particulier du problème de la rotation d'un corps pesant autour d'un point fixe, où l'intégration s'effectue à l'aide des fonctions ultraelliptiques du temps (1889)
Legacy and Impact
Kovalevskaya was a pioneer for women in mathematics. Her work made significant contributions to several fields, and she overcame numerous obstacles to achieve her goals. If choosing from a group of candidates for "pictures of 10 mathematicians", Kovalevskaya provides an example of persistence and brilliance amidst significant societal barriers, making her presence crucial.
David Hilbert
- Born:
- January 23, 1862, Königsberg, Prussia (now Kaliningrad, Russia)
- Died:
- February 14, 1943, Göttingen, Germany
- Nationality:
- German
- Profession(s):
- Mathematician
Early Life and Education
- Hilbert studied at the University of Königsberg.
- He received his doctorate in 1885.
Career and Major Achievements
- Hilbert made fundamental contributions to a wide range of mathematical fields, including invariant theory, axiomatic geometry, functional analysis, and mathematical physics.
- He formulated Hilbert's problems, a list of 23 unsolved problems that profoundly influenced the direction of 20th-century mathematics.
- He championed formalism as a foundation for mathematics.
Notable Works
- Grundlagen der Geometrie (1899)
- Gesammelte Abhandlungen (Collected Papers)
Legacy and Impact
Hilbert is considered one of the most influential mathematicians of the 20th century. His work shaped the development of mathematics and continues to inspire mathematicians today. When one considers what "pictures of 10 mathematicians" best capture the 20th century mathematical landscape, Hilbert, due to his wide ranging influence and his famous problems, stands out as an essential figure.