aarjaneiro/planetmath huggingface dataset:
Nina Bari

Nina Bari

Nina Karlovna Bari

(1901 - 1961) Soviet mathematician renowned for her work in the

trigonometric series

. In her lifetime, her interest in descriptive mathematics was derided as being “mathematics for ladies.” This didn’t stop her from being appointed professor of mathematics at the university in Moscow. Not directly related to

Ruth Bari

.

References

1

J. Spetich & Douglas E. Cameron “Nina Karlovna Bari” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 6 - 12

Title

Nina Bari

Canonical name

NinaBari

Date of creation

2013-03-22 16:38:41

Last modified on

2013-03-22 16:38:41

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Nina Karlovna Bari

Generated on Thu Feb 8 19:12:23 2018 by

LaTeXML
Olga Oleinik

Olga Oleinik

Olga Arsenievna Oleinik

(1925 - 2001) Soviet mathematician, best known for her work on

partial differential equations

.

She studied with Ivan Petrovsky at a university in Moscow, later she taught there.

A prolific author, Oleinik has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 3: With Vladimir Ilin and others, she co-authored a biographical sketch of Andrey Tikhonov in honor of his 80th birthday, while Ilin co-authored with István Joó a paper giving “A uniform estimate of

eigenfunctions

and an upper estimate of the number of

eigenvalues

of the Sturm-Liouville operator” in a Soviet journal. Joó co-authored with Erdős “Some remarks on infinite series” in a Hungarian journal.

Title

Olga Oleinik

Canonical name

OlgaOleinik

Date of creation

2013-03-22 17:24:08

Last modified on

2013-03-22 17:24:08

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Synonym

Olga Arsenievna Oleinik

Synonym

Ol’ga Arsen’ievna Oleinik

Generated on Thu Feb 8 19:12:24 2018 by

LaTeXML
origins of Wedderburn’s theorem

origins of Wedderburn’s theorem

Wedderburn and Dickson both published independent proofs of the fact in 1905.
Wedderburn’s publication contains three proofs, the first of which was ultimately flawed. The second two proofs improve the essential trick of Dickson by using Zsigmondy’s theorem, a numerical condition on

prime factors

of

p

n

-

1

. Wedderburn and Dickson were colleagues at the University of Chicago at the time.

The first, mistaken proof, of Wedderburn was later corrected and simplified by Artin and is now the standard proof in most texts.

References

1

Parshall, Karen Hunger

In pursuit of the finite

division algebra

theorem and beyond:
Joseph H. M. Wedderburn, Leonard E. Dickson, and
Oswald Veblen

,
Arch. Internat. Hist. Sci., 33, (1984), 111, pp. 274 – 299.

Title

origins of Wedderburn’s theorem

Canonical name

OriginsOfWedderburnsTheorem

Date of creation

2013-03-22 16:08:18

Last modified on

2013-03-22 16:08:18

Owner

Algeboy (12884)

Last modified by

Algeboy (12884)

Numerical id

9

Author

Algeboy (12884)

Entry type

Derivation

Classification

msc 01A60

Classification

msc 12E15

Generated on Thu Feb 8 19:12:26 2018 by

LaTeXML
Otto Hölder

Otto Hölder

Otto Hölder

German mathematician (1859–1937) best known for Hölder’s

inequality

and the Jordan-Hölder

theorem

(

http://planetmath.org/JordanHolderDecompositionTheorem

). Hölder also made many essential first steps in the then emerging study of groups. Some of his results include a

complete

classification

of the groups of order (

http://planetmath.org/OrderGroup

)

p

2

,

p

3

,

p

4

,

p

⁢

q

and

p

2

⁢

q

(

p

and

q

different primes) and are an early example of the power of the

Sylow theorems

for

finite group

theory.

He studied at the University of Berlin, got his doctorate from the University of Tübingen, and taught at the University of Leipzig.

The

generalized mean

is sometimes called the “Hölder mean”.

Title

Otto Hölder

Canonical

name

OttoHolder

Date of creation

2013-03-22 16:14:22

Last modified on

2013-03-22 16:14:22

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

11

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A60

Synonym

Otto Holder

Synonym

Otto Hoelder

Generated on Thu Feb 8 19:12:28 2018 by

LaTeXML
Paul-André Meyer

Paul-André Meyer

Paul-André Meyer

(1934 - 2003) French mathematician best known for the Doob-Meyer decomposition. He mainly researched

stochastic processes

and

Markov processes

.

Title

Paul-André Meyer

Canonical name

PaulAndreMeyer

Date of creation

2013-03-22 16:23:11

Last modified on

2013-03-22 16:23:11

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A60

Classification

msc 01A61

Synonym

Paul-Andre Meyer

Generated on Thu Feb 8 19:12:30 2018 by

LaTeXML
Pelageya Polubarinova-Kochina

Pelageya Polubarinova-Kochina

Pelageya Yakovlevna Polubarinova-Kochina

née

Pelageya Yakovlevna Polubarinova

(1899 - ) Soviet Russian mathematician with a degree in pure mathematics best known for her work on the application of

Fuchsian differential equations

to hydrodynamics.

Born in czarist Russia of an accountant and a housewife, young Pelageya was the second youngest of four children, she studied at a women’s high school in St. Petersburg and went on to Petrograd University (after the Revolution of 1917). Her father died in 1918 so she started to take care of the family by working at the laboratory of geophysics. There she met Nikolai Kochin, and they married in 1925 and she bore him two daughters. The two taught there until World War II, when Polubarinova-Kochina and their daughters were evacuated to Kazan and Kochin stayed in Moscow to work on aiding the military effort. He died before the war was over. After the war, she edited his lectures and continued to teach applied mathematics. She was given the Stalin Prize in 1946.

References

1

G. W. Phillips “Pelageya Yakovlevna Polubarinova-Kochina” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 95 - 102

Title

Pelageya Polubarinova-Kochina

Canonical name

PelageyaPolubarinovaKochina

Date of creation

2013-03-22 17:05:51

Last modified on

2013-03-22 17:05:51

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

Pelageya Yakovlevna Polubarinova-Kochina

Synonym

Pelageya Yakovlevna Polubarinova

Synonym

Pelageya Kochina

Generated on Thu Feb 8 19:12:31 2018 by

LaTeXML
Putnam Competition

Putnam Competition

The

William Lowell Putnam Mathematical Competition

, often called just the

Putnam Competition

, is an annual competition for college math students sponsored by the

Mathematical Association of America

in which the contestants try to solve twelve mathematical problems in less than 8 hours. Each university may send as many contestants as it wants but must designate three of those to be the official team representing the college in the competition, and there are prizes given to the colleges with the best-scoring official teams. The top five individual scorers, regardless of whether or not they are on an official team, are then given the title

Putnam Fellow

and a US$2500 scholarship. The competition was established in 1927 by Elizabeth Putnam to the memory of her late husband William Lowell Putnam, Sr.

Title

Putnam Competition

Canonical

name

PutnamCompetition

Date of creation

2013-03-22 16:44:16

Last modified on

2013-03-22 16:44:16

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

William Lowell Putnam Competition

Synonym

William Lowell Putnam Mathematical Competition

Defines

Putnam Fellow

Generated on Thu Feb 8 19:12:33 2018 by

LaTeXML
Richard Stanley

Richard Stanley

Richard Peter Stanley

(1944 - ) is an American mathematician.
He is a student of Gian-Carlo Rota.

A Harvard graduate, Stanley went on to teach at MIT. His book

Enumerative Combinatorics

is seen as a landmark

introduction

to

combinatorics

. The book is infamous for its exercise which presents
66 objects counted by the

Catalan numbers

, then challenges the reader
to give a bijective proof of that fact. On his website, he maintains
the “Catalan addendum”, which as of 26 February 2007 includes 147
different combinatorial

interpretations

for the Catalan numbers.

Stanley was awarded the

Schock prize

in 2003 for his contributions to
combinatorics, in particular his proof of the

necessity

of McMullen’s
conditions for a tuple

(

f

0

,

…

,

f

d

-

1

)

to be the f-vector of a
simplicial polytope (one half of the g-theorem), and for his advancement
of graduate-level mathematical exposition.

In 1978, Stanley co-authored a paper on the “Enumeration of power
sums modulo a prime” in

J.

Number Theory

10

with

Andrew
Odlyzko

, giving Stanley an Erdős number (

http://

planetmath

.org/ErdHosNumber

)
of 2.

Title

Richard Stanley

Canonical name

RichardStanley

Date of creation

2013-03-22 17:01:02

Last modified on

2013-03-22 17:01:02

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

7

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

Richard Peter Stanley

Generated on Thu Feb 8 19:12:35 2018 by

LaTeXML
Robert Calderbank

Robert Calderbank

Robert Calderbank

(195? - ) British mathematician and electrical engineer, husband of

Ingrid Daubechies

.

Only a year after earning a bachelor’s degree, Calderbank earned a master’s degree from Oxford University in 1976. He began working at the New Jersey AT & T Bell Labs in 1980, and in 1987 met Ingrid Daubechies there, and married her the same year. In 1993, he began teaching at Princeton University as an adjunct professor, that same year he coauthored with

Ronald Graham

a paper on “The Sperner capacity of linear and nonlinear codes for the cyclic triangle” in

J. Algebraic Combin.

2

, giving Calderbank an Erdős number (

http://

planetmath

.org/ErdHosNumber

) of 2. At the turn of the century, Calderbank was appointed an AT & T Fellow in recognition of his achievements in data compression and forward error correction. Upon retiring from AT & T to devote himself to teaching, he was promoted to full professor at Princeton.

0.1

External link

http://www.ee.princeton.edu/people/Calderbank.php

Prof. Calderbank’s page at Princeton University

Title

Robert Calderbank

Canonical name

RobertCalderbank

Date of creation

2013-03-22 16:49:59

Last modified on

2013-03-22 16:49:59

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

Bob Calderbank

Generated on Thu Feb 8 19:12:37 2018 by

LaTeXML
Ronald Graham

Ronald Graham

Ronald Lewis Graham

(1935 - ) American mathematician and juggler, perhaps best known for Graham’s number, husband of

Fan Chung

.

In 1962, Graham earned a Ph.D at the University of California-Berkeley. In 1972, he coauthored with Erdős a paper on the sums of terms of the

Fibonacci sequence

in the

Fibonacci Quarterly

, giving him an Erdős number (

http://

planetmath

.org/ErdHosNumber

) of 1. His most famous paper, however, came in 1977. Concerning itself with

Ramsey theory

, the paper gave a spectacularly large

upper bound

on the solution to one of the problems, which the

Guinness Book of World Records

acknowledged the next year as the largest number ever used in a professional mathematician’s paper, which came to be known as Graham’s number. (According to Wells, the solution could be as small as 6). Graham was president of the International Jugglers Union for a year.

References

1

Wells, D. .

The Penguin Dictionary of Curious and Interesting Numbers

London: Penguin Group. (1987): 255 - 256

Title

Ronald Graham

Canonical name

RonaldGraham

Date of creation

2013-03-22 16:50:02

Last modified on

2013-03-22 16:50:02

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

Ronald Lewis Graham

Synonym

Ron Graham

Generated on Thu Feb 8 19:12:39 2018 by

LaTeXML
Rózsa Péter

Rózsa Péter

Rózsa Péter

née

Rósza Politzer

(1905 - 1977) Hungarian mathematician and textbook author, best known for her work on

recursive functions

.

Born in Budapest of a lawyer and a housewife, young Rósza’s education began at the public schools in her native city. Because of her father’s wishes, she enrolled in the Eötvös Loránd University to major in chemistry. However, she realized that she preferred pure mathematics and changed her major. In 1935 she earned a doctorate and

summa cum laude

honors. After graduation, she had various jobs tutoring in mathematics. It wasn’t until 1955 that she began teaching at her alma mater.

References

1

H. Andréka “Rózsa Péter” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 171 - 174

Title

Rózsa Péter

Canonical name

RozsaPeter

Date of creation

2013-03-22 17:25:01

Last modified on

2013-03-22 17:25:01

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Rozsa Peter

Synonym

Rozsa Politzer

Synonym

Rosza Peter

Generated on Thu Feb 8 19:12:40 2018 by

LaTeXML
Ruth Bari

Ruth Bari

Ruth Aaronson Bari

(1917 - 2005) American mathematician renowned for her work in

graph theory

. Almost 50, she was appointed professor of mathematics at George Washington University. Not directly related to

Nina Bari

.

References

1

F. Fasanelli “Ruth Aaronson Bari” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 13 - 20

Title

Ruth Bari

Canonical name

RuthBari

Date of creation

2013-03-22 16:38:44

Last modified on

2013-03-22 16:38:44

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Synonym

Ruth Aaronson Bari

Generated on Thu Feb 8 19:12:42 2018 by

LaTeXML
Ruth Moufang

Ruth Moufang

Ruth Moufang

(1905 - 1977) German mathematician, best known for her work on

projective geometry

. She was the first woman to teach at the University of Frankfurt, though she didn’t start until 1946, having been able to start earlier had it not been for the Nazis. Moufang loops are named after her.

Title

Ruth Moufang

Canonical name

RuthMoufang

Date of creation

2013-03-22 17:21:03

Last modified on

2013-03-22 17:21:03

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Generated on Thu Feb 8 19:12:44 2018 by

LaTeXML
Sarah Flannery

Sarah Flannery

Sarah Flannery

(1982 - ) Irish mathematician and child prodigy, best known for her work on the

Cayley-Purser algorithm

.

The eldest among five children, Flannery went to high school at Scoil Mhuire Gan Smal in Blarney, where she gave a science fair

presentation

on

cryptography

. In researching

RSA encryption

, she created her own encryption

algorithm

, which earned her an Esat Young Scientist Exhibition and later an Intel Fellows Achievement Award. She went to college at the University of Cambridge, graduating in 2003 with a degree in computer engineering. Now she works for American video game developer Electronic Arts.

Title

Sarah Flannery

Canonical name

SarahFlannery

Date of creation

2013-03-22 16:51:48

Last modified on

2013-03-22 16:51:48

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Generated on Thu Feb 8 19:12:45 2018 by

LaTeXML
Schock Prize

Schock Prize

The

Schock Prize

is a prize awarded by the estate of the philosopher Rolf Schock bi-annually in the categories of philosophy, mathematics, visual arts and music. The prize of 400000 Swedish kronor is decided by one of the Swedish Royal Academies, the Royal Swedish Academy of Sciences in the case of mathematics.

Title

Schock Prize

Canonical

name

SchockPrize

Date of creation

2013-03-22 16:59:58

Last modified on

2013-03-22 16:59:58

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Generated on Thu Feb 8 19:12:47 2018 by

LaTeXML
Sheila Scott Macintyre

Sheila Scott Macintyre

Sheila Scott Macintyre

nèe

Sheila Scott

(1910 - 1960) Scottish mathematician best known for her work on the Whittaker constant.

Born of the rector of Trinity Academy and a housewife, young Sheila studied at the Edinburgh Ladies’ College, where she was acknowledged as the best student in mathematics and in general. She continued at the University of Edinburgh and published her first paper in 1935. Professor Edmund Whittaker introduced Scott to Archibald Macintyre, a professor from Aberdeen who had earned a doctorate at Cambridge. The two married in 1940 and the next year she began teaching at Aberdeen, filling in for faculty serving in the war. While pregnant with her second child, Sheila Macintyre stopped teaching but continued work on a thesis. In 1952, she co-authored with her husband a paper on “Theorems on the convergence and asymptotic validity of Abel’s series” in the

Proceedings of the Royal Society of Edinburgh Section A

; two years later Archibald published with Erdős a paper on integral functions in another Scottish journal, giving her Erdős number (

http://

planetmath

.org/ErdHosNumber

) 2. In 1958, the Macintyres moved with their children to Cleveland, and both taught at the University of Cincinnati.

References

1

F. D. Fasanelli “Sheila Scott Macintyre” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 140 - 143

Title

Sheila Scott Macintyre

Canonical name

SheilaScottMacintyre

Date of creation

2013-03-22 17:17:16

Last modified on

2013-03-22 17:17:16

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Sheila Scott

Synonym

Sheila Macintyre

Generated on Thu Feb 8 19:12:49 2018 by

LaTeXML
Shri Dattathreya Ramachandra Kaprekar

Shri Dattathreya Ramachandra Kaprekar

Shri Dattathreya Ramachandra Kaprekar

(1905 - 1986) Indian mathematician and mathematics educator mostly concerned with radix representation and other digital problems in recreational

number theory

. He is best known for being among the first (if not the first) to study

Harshad numbers

, self numbers,

Kaprekar numbers

and the

Kaprekar constant

. He also studied magic squares.

Kaprekar attended the university of his native Mumbai, receiving his bachelor’s degree in 1929. From 1930 until his retirement in 1962, he worked as a teacher in Devlali.

Title

Shri Dattathreya Ramachandra Kaprekar

Canonical

name

ShriDattathreyaRamachandraKaprekar

Date of creation

2013-03-22 16:16:27

Last modified on

2013-03-22 16:16:27

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

D. R. Kaprekar

Generated on Thu Feb 8 19:12:50 2018 by

LaTeXML
Simon Donaldson

Simon Donaldson

Simon Kirwan Donaldson

(1957 - ) British mathematician, perhaps famous for his work on the topology of smooth four-dimensional manifolds published when he was still a graduate student.

Earning a bachelor’s in mathematics from Pembroke College, Cambridge in 1979, Donaldson began postgraduate work at Worcester College, Oxford, in 1980. In 1983 he published the famous paper ”Self-dual connections and the topology of smooth 4-manifolds” which appeared in 1983 (the same year he got a doctorate degree from Oxford). Michael Atiyah said that that paper ”stunned the mathematical world.” In 1986, Donaldson was awarded the

Fields medal

, and almost a decade later, he was awarded the

Crafoord Prize

in mathematics with Shing-Tung Yau.

Title

Simon Donaldson

Canonical name

SimonDonaldson

Date of creation

2013-03-22 16:21:29

Last modified on

2013-03-22 16:21:29

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

Simon Kirwan Donaldson

Generated on Thu Feb 8 19:12:52 2018 by

LaTeXML
Sofya Yanovskaya

Sofya Yanovskaya

Sofya Aleksandrovna Yanovskaya

(sometimes transliterated

Sof’ja Aleksandrovna Janovskaja

) (1896 – 1966) Soviet Jewish mathematician, educator, perhaps best known for translating Karl Marx’s mathematical works to Russian.

Born in what was at the time Poland, her family moved to Odessa, where she studied mathematics. Yanovskaya’s schooling was interrupted by the uprising of 1917, and she helped as a nurse for political prisoners. By 1924 she was able to resume her studies in Moscow, and in 1931 she began teaching there. During World War II, she was evacuated to the Ural mountains, but afterwards resumed teaching in Moscow. In 1951, she was awarded the of Lenin.

References

1

I. H. Annellis “Sof’ja Aleksandrovna Janovskaja” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 80 - 85

Title

Sofya Yanovskaya

Canonical name

SofyaYanovskaya

Date of creation

2013-03-22 17:05:28

Last modified on

2013-03-22 17:05:28

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A55

Synonym

Sofya Aleksandrovna Yanovskaya

Synonym

Sof’ja Aleksandrovna Janovskaya

Synonym

Sof’ja Janovskaya

Generated on Thu Feb 8 19:12:54 2018 by

LaTeXML
Srinivasa Ramanujan

Srinivasa Ramanujan

Srinivasa Aiyangar Ramanujan

(1887 - 1920) Indian mathematician who made significant contributions to the development of

partition functions

and

summation

formulas involving constants such as

π

. He is best known for an anecdote of a discussion he had with G. H. Hardy on the dullness of 1729.

Some of his discoveries have been found to have applications in physics, particularly crystallography.

Title

Srinivasa Ramanujan

Canonical

name

SrinivasaRamanujan

Date of creation

2013-03-22 16:17:18

Last modified on

2013-03-22 16:17:18

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A55

Synonym

Srinivasa Aiyangar Ramanujan

Synonym

Ramanujan

Related topic

RamanujanTauFunction

Generated on Thu Feb 8 19:12:56 2018 by

LaTeXML