Mathematicians at a glance.pdf

7/25/2019 Mathematicians at a glance.pdf

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Mathematicians at a glance

1. Name and life period: Niels Henrik Abel (1802 - 1829) Norwegian Mathe-matician.

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: Krakow, Austria-Hungary (now Poland).

Research: Banach was the one who founded modern functional analysis. Ba-

nach 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, Ba-

nach 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 Bargmanns major contributions was the study of irreducible

unitary representations ofSL(2,R) and the Lorentz group. His other famous

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work which influences the present day mathematicians is the study of charac-

terizing the image of certain function spaces in the real line as a reproducing

kernel Hilbert space of analytic functions under certain transform, nowadaysknown 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 flu-

ids, kinetic theory of gases, thermodynamics and elasticity. Some of his popular

works are Exercitationes (Mathematical Exercises), published in 1724 Hydro-

dynamique (Hydrodynamica), published in 1738, Specimen theoriae novae de

mensura sortis (Exposition of a New Theory on the Measurement of Risk), pub-

lished in 1738.


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 Halleys 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 Moons 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 Math-

ematician.

Birth place: Paris, France.

Research: Cauchys major contributions are in mathematical analysis and

complex analysis. He defined the concept of continuity rigorously using in-

finitesimals. He developed the fundamental concepts in complex analysis such

as residues, Cauchys integral formula, argument principle, rigorous Taylor se-

ries expansion for an analytic function and so on. He also made contributions

in wave mechanics, optics, elasticity and so on.


Some of Cauchys students were Francesco Faa di Bruno, Viktor Bunyakovsky.

There are several basic theorems in sequences and series named after Cauchy.

7. Name and life period: Erneto Cesaro (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 alsoquite 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 DAlembert (1717 - 1783) French Math-

ematician.


Research: His areas of interest included Fluid Mechanics wherein he published

the work Memoire sur la refraction des corps solides in 1740. In this, he theoret-ically explained the phenomenon of refraction. In 1743 his famous work, Traite

de dynamique, was published in which he developed his own laws of motion.

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In 1752, DAlembert 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 DAlemberts paradox. DAlembertalso worked on theory of music. In particular, he has discussed various aspects

of the state of music in his celebrated work, Discours preliminaire of Diderots

Encyclopedie.


The DAlembert ratio test is used as an elementary tool in testing the con-

vergence of a series of numbers.

9. Name and life period: Paul Adrien Maurice Dirac (1902 - 1984) - British

Mathematician.

Birth place: Bristol, England.

Research: Diracs initial work was on quantization rules which were obtained

while studying the analogy between the Poisson brackets of classical mechanics

and Heisenbergs matrix formulation of quantum mechanics. Diracs 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 worlds greatest

physicists.


Diracs doctoral adviser was Ralph Fowler.

Some of Diracs 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 Schrodinger.

10. Name and life period: Johann Peter Gustav Lejeune Dirichlet (1805 - 1859)

French Mathematician.Birth place: Duren, French Empire (now Germany).

Research: Dirichlet solved Fermats 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, hydrody-

namics, trigonometric series, harmonic functions and so on. Dirichlet was theone who first obtained the conditions for the convergence of trigonometric series

and the use of the series to represent arbitrary functions.


Student of Fourier and Poisson.

Teacher of well known mathematicians such as Gotthold Einstein, Leopold

Kronecker, Rudolf Lipschitz, Moritz Cantor, Richard Dedekind, Bernhard Rie-

mann and so on.

11. Name and life period: Lipot Fejer (1880 - 1959) Hungarian Mathematician.

Birth place: Pecs, Hungary.

Research: Some of his well known works are on Fourier series, entire functions

and conformal mappings.


Student of Hermann Schwartz.

Teacher of well known mathematicians such as Paul Erdos, Pal Turan, Marcel

Riesz, Gabor Szego 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 Theorie 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. Healso 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.


Taught by Laplace, Lagrange and Monge.

Lagrange was the doctoral adviser.

Participated as scientific adviser in Napoleons 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 geom-

etry, 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 math-

ematics. 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 differ-

ential 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 Gausss students were Friedrich Bessel, Christoph Gudermann, Chris-

tian Ludwig Gerling, Richard Dedekind, Johann Encke, Johann Listing, Bern-

hard Riemann, Christian Peters, Moritz Cantor.The function ex

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is named Gaussian after him.

15. Name and life period: Hans Hahn (1879 - 1934) - Austrian Mathematician.

Birth place: Vienna, Austria.

Research: Hahns research areas include real analysis, set theory, functional

analysis, calculus of variations, theory of curves, quadratic forms, measure the-

ory, Fourier Analysis. He is best known for Hahn decomposition theorem, Hahn-

Banach theorem and so on.


Hahns doctoral adviser was Gustav Ritter von Escherich. Some of Hahns

doctoral students were Karl Menger, Witold Hurewicz, Kurt Godel.

16. Name and life period: Hermann Hankel (1839 - 1873) - German Mathemati-

cian.

Birth place: Halle, Germany.

Research: Hankel is well known for certain transform known as Hankel trans-

form. He also contributed to various parts of mathematics such as functiontheory, integration theory, linear algebra, complex numbers and quaternions.


Hankel studied and worked with great mathematicians like Mobius, Riemann,

Weierstrass and Kronecker.

17. Name and life period: Godfrey Harold Hardy (1877 - 1947) - British Math-

ematician.

Birth place: Cranleigh, Surrey, England.

Research: Hardy worked on various problems including Diophantine analy-sis, summation of divergent series, Fourier series, the Riemann zeta function,

the distribution of primes, complex analysis,certain inequalities and popula-

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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. Hardystheorem which describes the qualitative uncertainty principle is very useful in

mathematical physics and harmonic analysis.


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 Vija-

yaraghavan, 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 Mathemati-

cian.

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.


Hausdorffs doctoral advisers were Heinrich Bruns and Adolph Mayer.

Hausdroffs students were Karl Bogel, Franz Hallenbach, Gustav Steinbach.

In mathematics, Hausdorff spaces are named after him.

19. Name and life period: Oliver Heaviside (1850 - 1925) - British Mathemati-

cian.

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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 anelectric 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 telegraphers equations).

20. Name and life period: Werner Karl Heisenberg (1901- 1976) - German Math-

ematician and Theoretical Physicist.

Birth place: Wurzburg, Bavaria, Germany.

Research: Heisenberg made major contribution in the fields of quantum me-

chanics, quantum field theory, scattering theory and so on. He is well known for

his uncertainty principle, which was obtained while he was working on math-

ematical 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.


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 Mathemati-

cian.

Birth place: Dieuze, Lorraine, France.

Research: Hermites major contributions are in various areas such as orthog-onal polynomials, number theory, elliptic functions, quadratic forms, invariant

theory, interpolation and approximation, matrix theory and so on.

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Hermite was the student of Eugene-Charles Catalan. Some of Hermites stu-

dents were Leon Charve, Henri Pade, Mihailo Petrovic, Henri Poincare, ThomasStieltjes, 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: Konigsberg, Prussia (now Kaliningrad, Russia).

Research: Hilbert proved the famous finite basis theorem in 1890. He made

major contributions in functional analysis, Euclidean geometry, integral equa-

tions, 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.


Student of Ferdinand von Lindemann.

Teacher of well known mathematicians such as Wilhelm Ackermann, Richard

Courant, Erich Hecke, Oliver Kellogg, Robert Konig, 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 Holder (1859 - 1937) - German Mathe-

matician.

Birth place: Stuttgart, Germany.

Research: Holders 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 factorgroups where his remarkable contribution is nowadays known as Jordan-Holder

theorem.

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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: Jacobis major contribution was on the study of elliptic functions

and their relation to the elliptic theta function. He obtained several basic prop-

erties of theta functions, the corresponding functional equation and fundamental

results on q-series and hypergeometric series. He is also famous for Hamilton-

Jacobi 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.


Student of Enno Dirksen.

Teacher of Paul Gordan, Otto Hesse, Friedrich Julius Richelot.

25. Name and life period: Henri Leon Lebesgue (1875 - 1941) - French Mathe-

matician.

Birth Place: Beauvais, Oise, France.

Research: Lebesgues major contribution to mathematics is the theory of inte-

gration. 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, po-

tential theory, calculus of variations and dimension theory. In the later period

of his life, he also worked on pedagogical issues, historical work, and elementarygeometry.

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Student ofEmile Borel.

Served in the defense of France as a soldier during the first world war.

26. Name and life period: Ernst Leonard Lindelof, (1870 - 1946) Finnish Math-

ematician.

Birth place: Helsingfors, Russian Empire (now Helsinki, Finland).

Research: Lindelofs worked on wide range of areas such as differential equa-

tions, conformal mappings, analytic continuation, calculus, function theory,

gamma functions and topology. As mentioned earlier, his work with Phrag-

men is a major contribution in complex analysis.


In Mathematics, Lindelof spaces are named after Ernst Leonard Lindelof.

27. Name and life period: Joseph Liouville (1809 - 1882) - French Mathemati-

cian.

Birth place: Saint-Omer, France.

Research: Liouville not only worked on pure mathematics but also in mathe-

matical 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 prob-

lems, differential geometry and complex analysis.


Liouvilles doctoral advisers were Simeon Poisson and Louis Jacques Thenard.

Liouvilles doctoral student was Eugene Charles Catalan.

The crater Liouville on the Moon is named after him.

Liouvilles 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: Konigsberg, Germany.

Research: Lipschitz was the one who invented spin groups while looking at

Clifford algebras from a new perspective. The continuity condition named afterhim 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.


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: Littlewoods 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, Warings 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.


Littlewoods doctoral adviser was Ernest William Barnes.

Some of Littlewoods 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 Mathe-matician.

Birth place: Alexotas, Russian Empire (now Kaunas, Lithuania).

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Research: Minkowski at the age of eighteen, reconstructed Eisensteins 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 ofnumbers and its applications to the theories of Diophantine approximation of

algebraic numbers. His other works include non euclidean geometry, inequali-

ties and continued fractions.


Minkowskis doctoral adviser was Ferdinand von Lindemann.

Some of Minkowskis students were Constantin Caratheodory, Louis Kollros,

Denes Konig.

31. Name and life period: Giacinto Morera (1856 - 1909) - Italian Mathemati-

cian.

Birth place: Novara, Italy.

Research: Moreras major contribution is in the field of Complex analysis,

especially his famous theorem named after him is even useful in proving holo-

morphicity of functions in higher dimensions of complex plane. He also made

fundamental contributions to mechanics.

32. Name and life period: Otto Marcin Nikodym (1887 - 1974) - Polish Mathe-

matician.

Birth place: Zablotow, Galicia, Austria-Hungary (now Ukraine).

Research: Nikodyms research areas include measure theory, functional analy-

sis, 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.


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 Smiths prize in 1930.

34. Name and life period: Marc-Antoine Parseval des Chenes (1755 - 1836) -

French Mathematician.

Birth place: Rosieres-aux-Salines, France.

Research: Parsevals theorem on trigonometric series is very fundamental and

important which has been generalized to various abstract settings in Harmonic

analysis.


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 Phragmen (1863 - 1937) - Swedish Math-

ematician.

Birth place: Orebro, Sweden.

Research: Phragmens major contribution is in complex analysis and ellipticfunctions. 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 Mathemati-

cian.

Birth place: Bussy, Fribourg, Switzerland.

Research: Plancherels primary research areas include analysis, mathematical

physics and algebra. His theorem known as Plancheral formula has been gen-

eralized 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.


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: Simeon Denis Poisson (1781 - 1840) French mathe-

matician.

Birth place: Pithiviers, Loiret, France.

Research: Poisson was not only a mathematician but also carried out his math-

ematical ideas to physics, mechanics and statistics. He wrote his research work

in more than 300 memoires. The most popular ones were Traite de mecanique

(volume 1-1811 and volume 2-1833), Theorie mathematique de la chaleur (1835)

and Recherches sur la probabilite des jugements (1837). He worked on definite

integrals, Fourier series, calculus of variations, differential equations, electro-

statics 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: Decn, Bohemia, Austria-Hungary.

Research: Radons 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 Radon-

Nikodym theorem was first proved by Radon for the real Euclidean space.


Student of Gustav Ritter von Escherich.

39. Name and life period: Georg Friedrich Bernhard Riemann (1826 - 1866) -


Birth Place: Breselenz, Kingdom of Hanover (Germany).

Research: Riemann made major contributions to the foundation of real anal-

ysis 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 mathemati-

cians.Any other information:

Student of Carl Friedrich Gauss.

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40. Name and life period: Marcel Riesz (1886 - 1969) - Hungarian Mathemati-

cian.

Birth place: Gyor, Hungary.Research: Riesz is well known for his work on interpolation theory and poten-

tial theory. He formulated the interpolation theorem for trigonometric polyno-

mials and gave simple proof of Bernsteins inequality and Markovs 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:Rieszs doctoral advisor was Lipot Fejer.

Some of Rieszs students were Harald Cramer, Otto Frostman, Lars Garding,

Einar Carl Hille, Lars Hormander, Olaf Thorin.

41. Name and life period: Laurent-Mose Schwartz (1915 - 2002) - French Math-

ematician.


Research: Schwartz made an outstanding contribution to mathematics by in-

troducing 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.


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 Mathe-

matician.

Birth Place: The Bronx, New York, United States of America.Research: He worked on several mathematical problems including representa-

tion 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.


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 Mathemati-

cian.

Birth place: Pressburg (now Bratislava), Slovakia.

Research: Taubers 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 asymp-

totic 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.


Student of Gustav Ritter von Escherich and Emil Weyr.Tauber died in the Theresienstadt concentration camp which was created by

the Nazis to kill jews.

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44. Name and life period: G. Olof Thorin (1912 - 2004) - Swedish Mathemati-

cian.

Birth place: Halmstad, Sweden.Research: Oolf Thorins major contribution is in the fields of functional anal-

ysis 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.

Research: In attempting to compute the integral of (1x2)1

2 from 0 to 1 and

finding the area of a circle of unit radius, Wallis found a nice approximation to

. 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.


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) -


Birth place: Ostenfelde, Province of Westphalia, Kingdom of Prussia.

Research: Weierstrasss 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 contin-

uous functions by polynomials. His major contribution is also in calculus ofvariations including the study of the existence of extrema of variational prob-

lems.

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Student of Christoph Gudermann.

Teacher of well known mathematicians such as Georg Cantor, Georg Frobe-nius, 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: Weyls 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.


Student of David Hilbert.

Teacher of Saunders Mac Lane.

48. Name and life period: Norbert Wiener (1894 -1964) - American Mathemati-

cian.

Birth place: Columbia, Missouri, USA.

Research: Wiener had wide range of research interests starting with Brownian

motion, stochastic processes to harmonic analysis, communication theory, cy-

bernetics, 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 the-

orem, Wiener-Khinchin theorem and so on.

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Wieners doctoral advisers were Karl Schmidt and Josiah Royce.

Some of Wieners students were Amar Bose, Colin Cherry, Shikao Ikehara,Norman Levinson.

49. Name and life period: Wilhelm Wirtinger (1865 - 1945) - Austrian Mathe-

matician.

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.


Student of Emil Weyr and Gustav Ritter von Escherich.

Teacher of Wilhelm Blaschke, Hans Hornich, Karl Strubecker, Leopold Vi-

etoris.

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 symmetricand general linear groups and their properties. The inequality named after him

is a fundamental work in harmonic analysis.

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