Mathematicians at a glance
1. Name and life period: Niels Henrik Abel (1802 - 1829) Norwegian Mathematician.
Birth place: Nedstrand, Norway.
Research area: Abel was the one who invented the group theory which paved
a way for modern algebra. He happened to invent this while proving that there
is no general algebraic solution for the roots of a polynomial equation of degree
greater than four, in terms of explicit algebraic operations. His another major
work was on elliptic functions.
Any other information:
• The prestigious Abel prize is named after him.
2. Name and life period: Stefan Banach (1892 - 1945) - Polish Mathematician.
Birth place: Kraków, Austria-Hungary (now Poland).
Research: Banach was the one who founded modern functional analysis. Banach proved many fundamental results on normed linear spaces in functional
analysis. To cite a few, Hahn-Banach theorem, uniform boundedness theorem
popularly known as Banach-Steinhaus theorem, Banach-Alaoglu theorem, Banach fixed point theorem.
Any other information:
• Student of Hugo Steinhaus.
• Teacher of well known mathematicians Stanislaw Mazur and Stanislaw Ulam.
• In Mathematics, Banach spaces and Banch algebras are named after Stefan
Banach.
3. Name and life period: Valentine Bargmann (1908 - 1989) - German Born.
Birth place: Berlin, Germany.
Research: One of Bargmann’s major contributions was the study of irreducible
unitary representations of SL(2, R) and the Lorentz group. His other famous
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work which influences the present day mathematicians is the study of characterizing the image of certain function spaces in the real line as a reproducing
kernel Hilbert space of analytic functions under certain transform, nowadays
known as Bargmann transform.
4. Name and life period: Daniel Bernoulli (1700 - 1782) Swiss Mathematician.
Birth Place: Groningen, Netherlands.
Research: Some of his works include the study of vibrating strings, flow of fluids, kinetic theory of gases, thermodynamics and elasticity. Some of his popular
works are Exercitationes (Mathematical Exercises), published in 1724 Hydrodynamique (Hydrodynamica), published in 1738, Specimen theoriae novae de
mensura sortis (Exposition of a New Theory on the Measurement of Risk), published in 1738.
Any other information:
• Son of Johann Bernoulli (Calculus).
• Nephew of Jakob Bernoulli (Theory of probability).
• Contemporary and close friend of Leonhard Euler.
5. Name and birth place: Friedrich Wilhelm Bessel (1784 - 1846) German
Mathematician.
Birth place: Minden, Germany.
Research: He is a mathematician and an astronomer. He worked on the orbital
calculations of Halley’s comet, published tables of atmospheric refraction and
was the first one to use parallax in calculating the distance to a star. It is said
that his work in astronomy was useful at a stage in the discovery of Neptune.
While working with the study of dynamics of certain gravitational systems, he
developed certain special functions, which are now popularly known as Bessel
functions.
Any other information:
• The largest crater in the Moon’s Mare Serenitatis is named Bessel after him.
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• Student of Carl Friedrich Gauss.
6. Name and life period: Augustin-Louis Cauchy (1789 - 1857) - French Mathematician.
Birth place: Paris, France.
Research: Cauchy’s major contributions are in mathematical analysis and
complex analysis. He defined the concept of continuity rigorously using infinitesimals. He developed the fundamental concepts in complex analysis such
as residues, Cauchy’s integral formula, argument principle, rigorous Taylor series expansion for an analytic function and so on. He also made contributions
in wave mechanics, optics, elasticity and so on.
Any other information:
• Some of Cauchy’s students were Francesco Faá di Bruno, Viktor Bunyakovsky.
• There are several basic theorems in sequences and series named after Cauchy.
7. Name and life period: Ernéto Cesáro (1859 - 1906) Italian Mathematician.
Birth place: Naples, Italy.
Research: His work on averaging of the divergent series of numbers is an
important concept in mathematical analysis. His work Lezione di geometria
intrinseca (1890) for the description of curves in differential geometry is also
quite popular. He later used these ideas to study the Koch curves which are
continuous everywhere but nowhere differentiable. He also worked in number
theory and mathematical physics.
8. Name and life period: Jean Le Rond D’Alembert (1717 - 1783) French Mathematician.
Birth place: Paris, France.
Research: His areas of interest included Fluid Mechanics wherein he published
the work Mémoire sur la réfraction des corps solides in 1740. In this, he theoretically explained the phenomenon of refraction. In 1743 his famous work, Traité
de dynamique, was published in which he developed his own laws of motion.
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In 1752, D’Alembert proved that for an incompressible and inviscid potential
flow, the drag force is zero on a body moving with constant velocity relative to
the fluid, which is now popularly known as D’Alembert’s paradox. D’Alembert
also worked on theory of music. In particular, he has discussed various aspects
of the state of music in his celebrated work, Discours préliminaire of Diderot’s
Encyclopédie.
Any other information:
• The D’Alembert ratio test is used as an elementary tool in testing the convergence of a series of numbers.
9. Name and life period: Paul Adrien Maurice Dirac (1902 - 1984) - British
Mathematician.
Birth place: Bristol, England.
Research: Dirac’s initial work was on quantization rules which were obtained
while studying the analogy between the Poisson brackets of classical mechanics
and Heisenberg’s matrix formulation of quantum mechanics. Dirac’s Principles
of quantum mechanics, published in 1930 introduced the famous Dirac-delta
function. Dirac is regarded as one of the founders of quantum mechanics and
quantum electrodynamics. He is widely regarded as one of the world’s greatest
physicists.
Any other information:
• Dirac’s doctoral adviser was Ralph Fowler.
• Some of Dirac’s students were Homi Bhabha, Harish-Chandra, Dennis Sciama,
Fred Hoyle, Behram Kurunolu, John Polkinghorne.
• Dirac shared the Nobel Prize in Physics for 1933 with Erwin Schrödinger.
10. Name and life period: Johann Peter Gustav Lejeune Dirichlet (1805 - 1859)
French Mathematician.
Birth place: Düren, French Empire (now Germany).
Research: Dirichlet solved Fermat’s last theorem for the cases n = 5 and 14.
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Although he started his first mathematical work in analytical number theory,
he worked on algebraic number theory, mechanics, potential theory, hydrodynamics, trigonometric series, harmonic functions and so on. Dirichlet was the
one who first obtained the conditions for the convergence of trigonometric series
and the use of the series to represent arbitrary functions.
Any other information:
• Student of Fourier and Poisson.
• Teacher of well known mathematicians such as Gotthold Einstein, Leopold
Kronecker, Rudolf Lipschitz, Moritz Cantor, Richard Dedekind, Bernhard Riemann and so on.
11. Name and life period: Lipót Fejér (1880 - 1959) Hungarian Mathematician.
Birth place: Pécs, Hungary.
Research: Some of his well known works are on Fourier series, entire functions
and conformal mappings.
Any other information:
• Student of Hermann Schwartz.
• Teacher of well known mathematicians such as Paul Erdös, Pál Turán, Marcel
Riesz, Gábor Szegö and so on.
12. Name and life period: Jean Baptiste Joseph Fourier (1768 - 1830) French
Mathematician.
Birth place: Auxerre, France.
Research: One of the areas of the mathematical research work of Fourier
is the study of heat conduction. He worked on this problem for many years
and published Théorie analytique de la chaleur (Analytical Theory of Heat) in
1822. In this, he stated that certain functions can be expressed as the sum of an
infinite series of sines and cosines, now popularly known as Fourier series. He
also showed that musical sounds which have three components namely pitch,
loudness and quality can be written in terms of a mathematical expression.
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Fourier also left an unfinished work on determinate equations which was edited
by Claude-Louis Navier and published in 1831. The work of Fourier paved
the way for the modern day research work including mathematical physics,
harmonic analysis, partial differential equations, signal and image processing
and so on.
Any other information:
• Taught by Laplace, Lagrange and Monge.
• Lagrange was the doctoral adviser.
• Participated as scientific adviser in Napoleon’s army in its invasion of Egypt.
13. Name and life period: Guido Fubini (1879 - 1943) - Italian Mathematician.
Birth place: Venice, Italy.
Research: Fubini worked on various research areas including differential geometry, complex analysis, several complex variables, differential equations, calculus
of variations, integral equations, linear groups, automorphism groups, projective
geometry.
14. Name and life period: Johann Carl Friedrich Gauss (1777- 1855) - German
Mathematician.
Birth place: Brunswick, Duchy of Brunswick (now Germany).
Research: Gauss has made major contributions to various parts of pure mathematics. He worked on modular arithmetic, especially obtained theorems on
distribution of primes, quadratic reciprocity law, decomposition of a positive
integer. He worked on polynomials with coefficients from finite fields, quadratic
forms, class number problem. He introduced an important concept in differential geometry, namely Gaussian curvature. He also developed fundamental
ideas in real analysis, numerical analysis, vector calculus, special functions and
so on.
Any other information:
• Gauss was a student of Johann Friedrich Pfaff.
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• Some of Gauss’s students were Friedrich Bessel, Christoph Gudermann, Christian Ludwig Gerling, Richard Dedekind, Johann Encke, Johann Listing, Bernhard Riemann, Christian Peters, Moritz Cantor.
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• The function e−x is named Gaussian after him.
15. Name and life period: Hans Hahn (1879 - 1934) - Austrian Mathematician.
Birth place: Vienna, Austria.
Research: Hahn’s research areas include real analysis, set theory, functional
analysis, calculus of variations, theory of curves, quadratic forms, measure theory, Fourier Analysis. He is best known for Hahn decomposition theorem, HahnBanach theorem and so on.
Any other information:
• Hahn’s doctoral adviser was Gustav Ritter von Escherich. Some of Hahn’s
doctoral students were Karl Menger, Witold Hurewicz, Kurt Gödel.
16. Name and life period: Hermann Hankel (1839 - 1873) - German Mathematician.
Birth place: Halle, Germany.
Research: Hankel is well known for certain transform known as Hankel transform. He also contributed to various parts of mathematics such as function
theory, integration theory, linear algebra, complex numbers and quaternions.
Any other information:
• Hankel studied and worked with great mathematicians like Móbius, Riemann,
Weierstrass and Kronecker.
17. Name and life period: Godfrey Harold Hardy (1877 - 1947) - British Mathematician.
Birth place: Cranleigh, Surrey, England.
Research: Hardy worked on various problems including Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function,
the distribution of primes, complex analysis,certain inequalities and popula7
tion genetics. He along with J.E. Littlewood made major contribution in the
fields of analytic number theory and mathematical analysis. A few among
are Hardy-Littlewood circle method, Hardy-Littlewood conjectures. Hardy’s
theorem which describes the qualitative uncertainty principle is very useful in
mathematical physics and harmonic analysis.
Any other information:
• Student of A. E. H. Love, E. T. Whittaker.
• Teacher of well known mathematicians such as Srinivasa Ramanujan, Sydney
Chapman, I. J. Good, Frank Morley, Cyril Offord, Harry Pitt, Richard Rado,
Robert Rankin, Donald Spencer, Edward Titchmarsh, Tirukkannapuram Vijayaraghavan, E. M. Wright.
• He was the one who brought out the mathematical excellence of Srinivasa
Ramanujan to the world.
• Hardy spaces named after Hardy is a hard core in function theory especially
from complex analysis to real variable theory.
18. Name and life period: Felix Hausdorff (1868 - 1942) - German Mathematician.
Birth place: Breslau, Germany (now Wroclaw, Poland).
Research: Hausdorff made major contribution in set theory and topology. He
introduced the concept of a partially ordered set and obtained several results in
it. Hausdorff introduced fundamental concepts such as certain dimensions and
some positive quantities known as Hausdorff dimension and Hausdorff measure.
Any other information:
• Hausdorff’s doctoral advisers were Heinrich Bruns and Adolph Mayer.
• Hausdroff’s students were Karl Bögel, Franz Hallenbach, Gustav Steinbach.
• In mathematics, Hausdorff spaces are named after him.
19. Name and life period: Oliver Heaviside (1850 - 1925) - British Mathematician.
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Birth place: Camden Town, London, England.
Research: Heaviside was an electrical engineer and a physicist. He discovered
the unit step function named after him in order to model the current in an
electric circuit. His work on vector calculus is remarkable. He also invented
the operator method for solving linear differential equations. He contributed to
transmission line theory (also known as the “telegrapher’s equations”).
20. Name and life period: Werner Karl Heisenberg (1901- 1976) - German Mathematician and Theoretical Physicist.
Birth place: Würzburg, Bavaria, Germany.
Research: Heisenberg made major contribution in the fields of quantum mechanics, quantum field theory, scattering theory and so on. He is well known for
his uncertainty principle, which was obtained while he was working on mathematical foundations of quantum mechanics. He formulated neutron-proton
model of the nucleus. He developed the theory of positron. He was awarded
Nobel Prize in Physics in 1932.
Any other information:
• Student of Arnold Sommerfeld.
• Teacher of Felix Bloch, Edward Teller, Rudolph E. Peierls, Reinhard Oehme,
Friedwardt Winterberg, Peter Mittelstaedt, Ivan Supek, Erich Bagge, Hermann
Arthur Jah.
• The group named after Heisenberg is an important Lie group which is very
useful in modern analysis and representation theory.
21. Name and life period: Charles Hermite (1822 - 1901) - French Mathematician.
Birth place: Dieuze, Lorraine, France.
Research: Hermite’s major contributions are in various areas such as orthogonal polynomials, number theory, elliptic functions, quadratic forms, invariant
theory, interpolation and approximation, matrix theory and so on.
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Any other information:
• Hermite was the student of Eugéne-Charles Catalan. Some of Hermite’s students were Léon Charve, Henri Padé, Mihailo Petrović, Henri Poincaré, Thomas
Stieltjes, Jules Tannery.
• In mathematics Hermite polynomials and Hermitian matrices are named after
him.
22. Name and life period: David Hilbert (1862 -1943) - German Mathematician.
Birth place: Königsberg, Prussia (now Kaliningrad, Russia).
Research: Hilbert proved the famous finite basis theorem in 1890. He made
major contributions in functional analysis, Euclidean geometry, integral equations, mathematical physics and algebraic number fields. Hilbert published a
set of twenty three unsolved problems in 1900 and presented ten of them in the
international congress of mathematicians. These were unsolved at that time and
they influenced the twentieth century mathematical research to a great extent.
Any other information:
• Student of Ferdinand von Lindemann.
• Teacher of well known mathematicians such as Wilhelm Ackermann, Richard
Courant, Erich Hecke, Oliver Kellogg, Robert König, Emanuel Lasker, Erhard
Schmidt, Hugo Steinhaus, Hermann Weyl and so on.
• In Mathematics, Hilbert spaces are named after David Hilbert.
23. Name and life period: Otto Ludwig Hölder (1859 - 1937) - German Mathematician.
Birth place: Stuttgart, Germany.
Research: Hölder’s research areas include complex analysis, Fourier series and
group theory. While working on the convergence of Fourier series, he found
the inequality, which is named after him. In group theory he worked on factor
groups where his remarkable contribution is nowadays known as Jordan-Hölder
theorem.
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Any other information:
• Student of Paul du Bois-Reymond.
24. Name and life period: Carl Gustav Jacob Jacobi (1804 - 1851) - German
Mathematician.
Birth place: Potsdam, Kingdom of Prussia.
Research: Jacobi’s major contribution was on the study of elliptic functions
and their relation to the elliptic theta function. He obtained several basic properties of theta functions, the corresponding functional equation and fundamental
results on q-series and hypergeometric series. He is also famous for HamiltonJacobi theory in Mechanics. He also worked on continued fractions, quadratic
reciprocity and other problems in number theory. He was also one of the early
founders of determinants.
Any other information:
• Student of Enno Dirksen.
• Teacher of Paul Gordan, Otto Hesse, Friedrich Julius Richelot.
25. Name and life period: Henri Léon Lebesgue (1875 - 1941) - French Mathematician.
Birth Place: Beauvais, Oise, France.
Research: Lebesgue’s major contribution to mathematics is the theory of integration. Lebesgue formulated the theory of measure and gave the definition of
the Lebesgue integral which generalizes the notion of the Riemann integral by
including integration for discontinuous functions on unbounded domains. His
integration theory is a major breakthrough in the history of modern analysis.
His contributions are also in other areas of mathematics such as topology, potential theory, calculus of variations and dimension theory. In the later period
of his life, he also worked on pedagogical issues, historical work, and elementary
geometry.
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Any other information:
• Student of Émile Borel.
• Served in the defense of France as a soldier during the first world war.
26. Name and life period: Ernst Leonard Lindelöf, (1870 - 1946) Finnish Mathematician.
Birth place: Helsingfors, Russian Empire (now Helsinki, Finland).
Research: Lindelöf’s worked on wide range of areas such as differential equations, conformal mappings, analytic continuation, calculus, function theory,
gamma functions and topology. As mentioned earlier, his work with Phragmen is a major contribution in complex analysis.
Any other information:
• In Mathematics, Lindelöf spaces are named after Ernst Leonard Lindelöf.
27. Name and life period: Joseph Liouville (1809 - 1882) - French Mathematician.
Birth place: Saint-Omer, France.
Research: Liouville not only worked on pure mathematics but also in mathematical physics and astronomy. In mathematics his major contributions are in
fractional calculus, integration of algebraic functions, transcendental numbers,
boundary value problems, known nowadays as Sturm-Liouville eigen value problems, differential geometry and complex analysis.
Any other information:
Liouville’s doctoral advisers were Siméon Poisson and Louis Jacques Thénard.
• Liouville’s doctoral student was Eugéne Charles Catalan.
• The crater Liouville on the Moon is named after him.
• Liouville’s theorem named after him in complex analysis is fundamental and
extremely useful.
28. Name and life period: Rudolf Otto Sigismund Lipschitz (1832 - 1903) German Mathematician.
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Birth Place: Königsberg, Germany.
Research: Lipschitz was the one who invented spin groups while looking at
Clifford algebras from a new perspective. The continuity condition named after
him has various applications including the study of existence of solution of a
differential equation and so on. He also worked on various fields such as number
theory, potential theory, special functions and mechanics.
Any other information:
• Student of Peter Gustav Dirichlet and Martin Ohm.
• Teacher of Felix Klein.
29. Name and life period: John Edensor Littlewood (1885 - 1977) - British
Mathematician.
Birth place: Rochester, Kent, England.
Research: Littlewood’s major area of research was mathematical analysis. But
in collaboration with G.H.Hardy, he worked in analytic number theory, Riemann
zeta function, function theory and inequalities. He also made contributions
to Diophantine approximation, Waring’s problem, dynamical systems and so
on. He is also best known for his collaborative work with Paley, known as
Littlewood-Paley theory in Euclidean Fourier analysis. The conjectures made
by him along with Hardy are named after them in number theory.
Any other information:
• Littlewood’s doctoral adviser was Ernest William Barnes.
• Some of Littlewood’s doctoral students were A. O. L. Atkin, Sarvadaman
Chowla, Harold Davenport, Stanley Skewes, Donald C. Spencer, Albert Ingham.
• Littlewood served in the British Army during the first world war in the Royal
Garrison Artillery.
30. Name and life period: Hermann Minkowski (1864 - 1909) - German Mathematician.
Birth place: Alexotas, Russian Empire (now Kaunas, Lithuania).
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Research: Minkowski at the age of eighteen, reconstructed Eisenstein’s theory
of quadratic forms and produced a nice solution to the Grand Prix problem. He
laid the mathematical foundation of relativity. He worked on the geometry of
numbers and its applications to the theories of Diophantine approximation of
algebraic numbers. His other works include non euclidean geometry, inequalities and continued fractions.
Any other information:
• Minkowski’s doctoral adviser was Ferdinand von Lindemann.
• Some of Minkowski’s students were Constantin Carathéodory, Louis Kollros,
Dénes König.
31. Name and life period: Giacinto Morera (1856 - 1909) - Italian Mathematician.
Birth place: Novara, Italy.
Research: Morera’s major contribution is in the field of Complex analysis,
especially his famous theorem named after him is even useful in proving holomorphicity of functions in higher dimensions of complex plane. He also made
fundamental contributions to mechanics.
32. Name and life period: Otto Marcin Nikodým (1887 - 1974) - Polish Mathematician.
Birth place: Zablotow, Galicia, Austria-Hungary (now Ukraine).
Research: Nikodym’s research areas include measure theory, functional analysis, set theory, differential equations and quantum mechanics. He extended the
work of Radon to a general setting (Radon-Nikodym theorem) which is a major
contribution in the topic of measure and integration. It is not only applied in
mathematical analysis but also in probability theory, statistics and so on.
Any other information:
• Nikodym was able to give lectures in various languages including English,
French, German and Italian.
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33. Name and life period: Raymond Edward Alan Christopher Paley (1907 1933) British Mathematician.
Birth place: Bournemouth, England.
Research: His contributions include Paley-Wiener theorem, a very important
contribution in complex analysis and current work in harmonic analysis for
various group settings, the Paley construction for Hadamard matrices. He also
worked on Fourier series. His collaboration with Littlewood namely Littlewood
- Paley theory, is an excellent application of real-variable techniques in Fourier
analysis.
Any other information:
• Paley won the Smith’s prize in 1930.
34. Name and life period: Marc-Antoine Parseval des Chenes (1755 - 1836) French Mathematician.
Birth place: Rosiéres-aux-Salines, France.
Research: Parseval’s theorem on trigonometric series is very fundamental and
important which has been generalized to various abstract settings in Harmonic
analysis.
Any other information:
• Parseval was a monarchist and opposed the French revolution. He was brave
enough to write and publish a poetry against the government of Napoleon.
35. Name and life period: Lars Edvard Phragmén (1863 - 1937) - Swedish Mathematician.
Birth place: Örebro, Sweden.
Research: Phragmen’s major contribution is in complex analysis and elliptic
functions. His joint work with Lindelof, known as Phragmen-Lindelof theorem
is a very important work in complex analysis. In topology, his joint work with
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Brouwer known as Phragmen-Brouwer theorem is another major contribution.
He is also popular for his new proof of the Cantor-Bendixson theorem.
36. Name and life period: Michel Plancherel (1885 - 1967) - Swiss Mathematician.
Birth place: Bussy, Fribourg, Switzerland.
Research: Plancherel’s primary research areas include analysis, mathematical
physics and algebra. His theorem known as Plancheral formula has been generalized to study integrated representations on various locally compact groups.
He made contributions to study the solutions to variational problems. He also
worked on statistical mechanics, in particular ergodic theory. He is also famous
for the Plancherel-Godement theorem in algebra on solvability of systems of
equations.
Any other information:
• Student of Mathias Lerch.
• Placherel served as officer responsible for press and radio division in the Swiss
army during the second world war.
37. Name and life period: Siméon Denis Poisson (1781 - 1840) French mathematician.
Birth place: Pithiviers, Loiret, France.
Research: Poisson was not only a mathematician but also carried out his mathematical ideas to physics, mechanics and statistics. He wrote his research work
in more than 300 memoires. The most popular ones were Traité de mécanique
(volume 1-1811 and volume 2-1833), Théorie mathématique de la chaleur (1835)
and Recherches sur la probabilité des jugements (1837). He worked on definite
integrals, Fourier series, calculus of variations, differential equations, electrostatics and magnetism, probability, celestial mechanics and so on.
Any other information:
• Student of Lagrange and Laplace.
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• Teacher of well known mathematicians such as Michel Chasles, Dirichlet,
Joseph Lioville and so on.
38. Name and life period: Johann Karl August Radon (1887 - 1956) - Austrian
Mathematician.
Birth place: Děčı́n, Bohemia, Austria-Hungary.
Research: Radon’s research areas include differential geometry and integration
theory. He worked on calculus of variations and studied their applicability in
differential geometry. He also studied certain geometrical problems related to
the theory of relativity. His work in measure theory known nowadays as RadonNikodym theorem was first proved by Radon for the real Euclidean space.
Any other information:
• Student of Gustav Ritter von Escherich.
39. Name and life period: Georg Friedrich Bernhard Riemann (1826 - 1866) German Mathematician.
Birth Place: Breselenz, Kingdom of Hanover (Germany).
Research: Riemann made major contributions to the foundation of real analysis and differential geometry. In real analysis, the theory of integration of
bounded functions namely Riemann integration, named after him is due to him.
He introduced topological methods to study complex function theory. His basic
questions about geometry in real world and his deep insights to such questions
resulted in Riemannian geometry later. In analytical number theory, Riemann
studied the convergence of the series representation of the zeta function and
found a functional equation for it. He conjectured that the zeta function had
infinitely many nontrivial roots and all have real part 12 , which is the famous
Riemann hypothesis , a longstanding challenge for several eminent mathematicians.
Any other information:
• Student of Carl Friedrich Gauss.
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40. Name and life period: Marcel Riesz (1886 - 1969) - Hungarian Mathematician.
Birth place: Györ, Hungary.
Research: Riesz is well known for his work on interpolation theory and potential theory. He formulated the interpolation theorem for trigonometric polynomials and gave simple proof of Bernstein’s inequality and Markov’s inequality.
He also showed that certain bound of a function, nowadays known as Riesz
function is equivalent to Riemann hypothesis. He also contributed to functional
analysis, partial differential equations, mathematical physics, Clifford algebra
and spinors.
Any other information:
• Riesz’s doctoral advisor was Lipót Fejér.
• Some of Riesz’s students were Harald Cramér, Otto Frostman, Lars Garding,
Einar Carl Hille, Lars Hörmander, Olaf Thorin.
41. Name and life period: Laurent-Moı̈se Schwartz (1915 - 2002) - French Mathematician.
Birth place: Paris, France.
Research: Schwartz made an outstanding contribution to mathematics by introducing and developing the theory of distributions. Initially Heaviside and
Dirac generalized the ideas of calculus with specific applications. But Schwartz
was the one who completely developed rich theory of distributions, which are
not only interesting and useful from mathematics point of view but are also
applied to various engineering problems.
Any other information:
• Student of Georges Valiron.
• Teacher of students Maurice Audin, Bernard Beauzamy, Alexander Grothendieck,
Jacques - Louis Lions, Bernard Malgrange, Henri Hogbe Nlend, Gilles Pisier,
Francois Treves.
• In 1950, Schwartz was awarded the Fields medal for his work on distributions.
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42. Name and life period: Irving Ezra Segal (1918 - 1998) - American Mathematician.
Birth Place: The Bronx, New York, United States of America.
Research: He worked on several mathematical problems including representation theory of locally compact groups, abstract integration theory in order to
answer certain questions from quantum mechanics. His work on automorphisms
of the symmetric group is quite popular. In his later part of life, he worked on
Cosmology.
Any other information:
• Student of Einar Hille.
• Teacher of known mathematicians such as Jacob Feldman, Roe Goodman,
Leonard Gross, Bertram Kostant, Ray Kunze, Edward Nelson, Niels Poulsen
and so on.
• Served in the U.S. Army conducting research in ballistics during the second
world war.
43. Name and life period: Alfred Tauber (1866 - 1942) - Austrian Mathematician.
Birth place: Pressburg (now Bratislava), Slovakia.
Research: Tauber’s main areas of research include function theory, potential
theory, differential equations and gamma functions. His work on summability
theory is popularly known as Tauber theorem. His work on studying the asymptotic behavior of certain sequences or functions are called Tauberian conditions,
which was further developed by Wiener, nowadays known as Wiener-Tauberian
theorems. It is interesting to note that the phrase “Tauberian conditions” were
suggested by Hardy and Littlewood.
Any other information:
• Student of Gustav Ritter von Escherich and Emil Weyr.
• Tauber died in the Theresienstadt concentration camp which was created by
the Nazi’s to kill jews.
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44. Name and life period: G. Olof Thorin (1912 - 2004) - Swedish Mathematician.
Birth place: Halmstad, Sweden.
Research: Oolf Thorin’s major contribution is in the fields of functional analysis and probability theory. He is famous for his interpolation theorem known
as Riesz-Thorin convexity theorem.
45. Name and life period: John Wallis (1616 - 1703) - British Mathematician.
Birth place: Ashford, Kent, England.
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Research: In attempting to compute the integral of (1 − x2 ) 2 from 0 to 1 and
finding the area of a circle of unit radius, Wallis found a nice approximation to
π. It was published in his famous work Arithmetica infinitorum in 1656. His
another remarkable work is treatise on Algebra which provided a good history
of mathematics wherein he also discussed roots of a cubic polynomial including
complex roots. He is also famous for doing very big mental calculations and
one among them is the square root of a 53 digit number.
Any other information:
• Student of William Oughtred.
• Teacher of William Brouncker. Served as the chief cryptographer of the British
Parliament between 1643 and 1689.
46. Name and life period: Karl Theodor Wilhelm Weierstrass (1815 - 1897) German Mathematician.
Birth place: Ostenfelde, Province of Westphalia, Kingdom of Prussia.
Research: Weierstrass’s remarkable work is on real analysis starting with his
precise definition of continuity to various fundamental aspects of the theory of
uniform convergence including his famous theorem of approximation of continuous functions by polynomials. His major contribution is also in calculus of
variations including the study of the existence of extrema of variational problems.
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Any other information:
• Student of Christoph Gudermann.
• Teacher of well known mathematicians such as Georg Cantor, Georg Frobenius, Carl Runge, Hermann Schwartz and so on.
• A test named after Weierstrass is used as an elementary tool in investigating
the uniform convergence of series of functions.
47. Name and life period: Hermann Klaus Hugo Weyl (1885 - 1955) - German
Mathematician.
Birth place: Elmshorn, Germany.
Research: Weyl’s major contribution was setting the group theoretical ideas
on which quantum mechanics was based. This later led to the study of Lie
groups and Lie algebras which is the current fantasy of analysts, algebraists
and physicists. Weyl also made major contributions to the study of relativity,
Riemannian geometry and number theory. Weyl developed the representation
theory of compact groups and obtained the fundamental character formula.
Weyl also developed the logic of predicative analysis.
Any other information:
• Student of David Hilbert.
• Teacher of Saunders Mac Lane.
48. Name and life period: Norbert Wiener (1894 -1964) - American Mathematician.
Birth place: Columbia, Missouri, USA.
Research: Wiener had wide range of research interests starting with Brownian
motion, stochastic processes to harmonic analysis, communication theory, cybernetics, quantum theory, control theory and so on. Many of his fundamental
concepts and results are named after him. To cite a few, Wiener processes,
Wiener equation, Wiener filter, Wiener Tauberian theorem, Paley-Wiener theorem, Wiener-Khinchin theorem and so on.
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Any other information:
• Wiener’s doctoral advisers were Karl Schmidt and Josiah Royce.
• Some of Wiener’s students were Amar Bose, Colin Cherry, Shikao Ikehara,
Norman Levinson.
49. Name and life period: Wilhelm Wirtinger (1865 - 1945) - Austrian Mathematician.
Birth place: Ybbs, Austria.
Research: Wirtinger made contributions to various branches of mathematics
such as function theory, geometry, algebra, number theory including the study
of the fundamental group of a knot in knot theory.
Any other information:
• Student of Emil Weyr and Gustav Ritter von Escherich.
• Teacher of Wilhelm Blaschke, Hans Hornich, Karl Strubecker, Leopold Vietoris.
50. Name and life period: Alfred Young (1873 - 1940) - British Mathematician.
Birth place: Widnes, Lancashire, England.
Research: Young introduced Young tableau, in 1900, which is a very famous
method and is highly useful in studying the representations of the symmetric
and general linear groups and their properties. The inequality named after him
is a fundamental work in harmonic analysis.
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