aarjaneiro/planetmath huggingface dataset:
Käte Fenchel

Käte Fenchel

Käte Fenchel

née Kate Sperling (1905 - 1983) Jewish German mathematician, best known for her work on

non-abelian groups

.

Born in Berlin of a newspaper reporter and a bookkeeper, young Käte learned to read and write sooner than most

children

, and after skipping a few grades, was given scholarships to attend private school. She faced some gender discrimination in attempting to

complete

her studies in pure mathematics at the University of Berlin, and went into mathematics education as a fallback at first. As Adolf Hitler came to power, she lost her job and married Werner Fenchel, also a Jew. The newlyweds escaped to Denmark, where she helped other German Jews escape Nazi persecution. But when Denmark was occupied by the Nazis, they had to flee to Sweden. After the war, the Fenchels returned to Denmark, but Käte did not publish any papers until two in 1962, and another in 1978.

References

1

E. Høyrup “Käte Fenchel” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 30 - 32

Title

Käte Fenchel

Canonical name

KateFenchel

Date of creation

2013-03-22 16:50:21

Last modified on

2013-03-22 16:50:21

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Kate Fenchel

Synonym

Kate Sperling

Synonym

Käte Sperling

Generated on Thu Feb 8 19:11:50 2018 by

LaTeXML
Kathleen Ollerenshaw

Kathleen Ollerenshaw

Kathleen Ollerenshaw

née

Kathleen Timpson

(1912 - ) British mathematician and politician, best known in mathematics for her work on

magic squares

.

Born in Manchester with limited hearing, Timpson was completely deaf by the time she applied to Oxford University. After earning a doctorate in mathematics, she married the military doctor Robert Ollerenshaw and took his name. Her political career began in Rusholme, and by the 1980s, she was a trusted advisor to British Prime Minister Margaret Thatcher.

Ollerenshaw has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 5 by way of Hermann Bondi, Ivor Robinson, Peter Gabriel Bergmann and

Ernst Straus

.

Title

Kathleen Ollerenshaw

Canonical name

KathleenOllerenshaw

Date of creation

2013-03-22 17:24:05

Last modified on

2013-03-22 17:24:05

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

Kathleen Timpson

Generated on Thu Feb 8 19:11:51 2018 by

LaTeXML
Kazimierz Zarankiewicz

Kazimierz Zarankiewicz

Kazimierz Zarankiewicz

(1902-1959) Polish topologist. He taught at the Society for Scientific Courses in Warsaw its first year in 1906. His work confirmed a result by Urysohn regarding hereditarily

locally connected

continua. The Zarankiewicz problem concerns the edges of

bipartite graphs

.

L’Europe mathÃÆÃÂ©matique: histoires, mythes, identitÃÆÃÂ©s
By CathÃÆÃÂ©rine Goldstein, Jeremy Gray, Jim Ritter
p. 294

Handbook of the history of general topology, Volume 2
By Charles E. Aull, Robert Lowen
p. 719

Title

Kazimierz Zarankiewicz

Canonical name

KazimierzZarankiewicz

Date of creation

2013-03-22 19:05:30

Last modified on

2013-03-22 19:05:30

Owner

ZZZTopologist (24722)

Last modified by

ZZZTopologist (24722)

Numerical id

4

Author

ZZZTopologist (24722)

Entry type

Biography

Classification

msc 01A60

Generated on Thu Feb 8 19:11:53 2018 by

LaTeXML
Kunihiko Kodaira

Kunihiko Kodaira

Kunihiko Kodaira

, the first Japanese mathematician to receive the

Fields medal

, was best known for his work on the theory of

complex manifolds

and

algebraic geometry

.

Born in Nagano on March 16, 1915, Kodaira taught in Tokyo during World War II and was pressed into cryptographic service for the Axis powers. After the war, he came to the

United States

, where he learned of the latest advances on

Hodge theory

. He collaborated with D. C. Spencer on building up the

deformation theory

of

complex structures

on

manifolds

.

Kodaira died in Kofu on July 26, 1997. The

Kodaira dimension

is named in his honor.

Title

Kunihiko Kodaira

Canonical name

KunihikoKodaira

Date of creation

2013-03-22 16:12:46

Last modified on

2013-03-22 16:12:46

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

7

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Synonym

Kodaira Kunihiko

Generated on Thu Feb 8 19:11:55 2018 by

LaTeXML
Kurt Heegner

Kurt Heegner

Kurt Heegner

(1893 - 1965) was a German high school teacher and radio engineer from Berlin now famous for his mathematical discoveries.

In 1952 Heegner published what he claimed was the solution of a classic problem proposed by the great mathematician Gauss, the

class number

1 problem, a significant and longstanding problem in

number theory

. Heegner’s work was not accepted for years, due mainly to mistakes in the paper, though Harold Stark later showed these could be fixed. Heegner’s proof was finally accepted as essentially correct in 1967 when Stark independently arrived at a

similar

proof, which he then showed was more or less

equivalent

to Heegner’s.

This entry was adapted from the

Wikipedia

article

http://en.wikipedia.org/wiki/Kurt_Heegner

Kurt Heegner as of July 19, 2008.

Title

Kurt Heegner

Canonical

name

KurtHeegner

Date of creation

2013-03-22 18:14:28

Last modified on

2013-03-22 18:14:28

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 19:11:56 2018 by

LaTeXML
Kurt Mahler

Kurt Mahler

Kurt Mahler

(26 July 1903 - 25 February 1988) was a British mathematician who proved that

∑

i

=

1

∞

i

10

∑

j

=

1

i

k

(where

k

is the number of digits of

j

in base 10) is a

transcendental number

(that is, approximately 0.123456789101112131415161718192021…) He also helped prove that certain cases of Waring’s problem do not occur

infinitely often

.

Born in Germany, Mahler left for Manchester to escape Hitler’s genocide. After World War II, Mahler taught in America and Australia.

Title

Kurt Mahler

Canonical name

KurtMahler

Date of creation

2013-03-22 16:22:48

Last modified on

2013-03-22 16:22:48

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Generated on Thu Feb 8 19:11:58 2018 by

LaTeXML
Kustaa Inkeri

Kustaa Inkeri

Kustaa Adolf Inkeri

(1908-11-12 à 1997-3-16), a Finnish number-theorist, was born in Laitila, Finland.  He has acted in astronomical observatorium of university and as high school teacher.  In the Finnish-Russian wars (

http://en.

wikipedia

.org/wiki/Winter_War

1939–1940,

http://en.wikipedia.org/wiki/Continuation_War

1941–1944) he was a company commander and later a staff officer; during a comparatively peaceful studies. After the war, he was first docent and then professor of mathematics in the University of Turku.

Inkeri was the founder of the Finnish school of

algebraic number
theory

. He has published studies concerning Fermat’s last theorem,
Catalan’s conjecture (

http://

planetmath

.org/catalansconjecture

), the

class number

of

cyclotomic number fields

,

primality testing

, Diophantine approximation.  In 1951, Inkeri was
appointed to the Academy of Finland.

Title

Kustaa Inkeri

Canonical name

KustaaInkeri

Date of creation

2014-12-16 15:56:49

Last modified on

2014-12-16 15:56:49

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

9

Author

pahio (2872)

Entry type

Biography

Classification

msc 01A60

Synonym

K. Inkeri

Synonym

Kustaa Adolf Inkeri

Generated on Thu Feb 8 19:12:00 2018 by

LaTeXML
Landau’s problems

Landau’s problems

Landau’s problems

are four

conjectures

about

prime numbers

which were unsolved at the time Edmund Landau presented on them at

International Congress of Mathematicians

of 1912.

1.

Goldbach’s conjecture

2.

The

twin prime conjecture

3.

Legendre’s conjecture

4.

The conjecture that there are infinitely many primes of the form

p

=

n

2

+

1

.

Unlike similar collections of unsolved problems, this collection does not include the

Riemann hypothesis

.

Almost a

hundred

years later, all four of Landau’s problems are still unsolved.

Title

Landau’s problems

Canonical

name

LandausProblems

Date of creation

2013-03-22 16:38:25

Last modified on

2013-03-22 16:38:25

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A60

Generated on Thu Feb 8 19:12:02 2018 by

LaTeXML
Laurent Lafforgue

Laurent Lafforgue

Laurent Lafforgue

(born 1966) French mathematician, educator and research director of National de la Recherche Scientifique (CNRS). After earning in

arithmetic

and

algebraic geometry

, Lafforgue proved Langland’s

conjectures

on

G

⁢

L

n

of a

function field

. In 2002 he was awarded the

Fields medal

.

Title

Laurent Lafforgue

Canonical

name

LaurentLafforgue

Date of creation

2013-03-22 16:19:08

Last modified on

2013-03-22 16:19:08

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

Generated on Thu Feb 8 19:12:03 2018 by

LaTeXML
list of mathematicians awarded the Crafoord Prize

list of mathematicians awarded the Crafoord Prize

This is a list of mathematicians who’ve been awarded the

Crafoord Prize

, sorted by year. In the 25-year history of the award, it has been for mathematics in only four years.

1982: Vladimir Arnold and Louis Nirenberg

1988: Pierre Deligne (and

Alexander Grothendieck

, who turned it down)

1994:

Simon Donaldson

and Shing-Tung Yau

2001: Alain Connes

Title

list of mathematicians awarded the Crafoord Prize

Canonical name

ListOfMathematiciansAwardedTheCrafoordPrize

Date of creation

2013-03-22 16:37:42

Last modified on

2013-03-22 16:37:42

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Example

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Generated on Thu Feb 8 19:12:05 2018 by

LaTeXML
list of mathematicians awarded the Schock Prize

list of mathematicians awarded the Schock Prize

This list of mathematicians awarded the

Schock Prize

in Mathematics is in chronological order.

1993:

Elias Stein

1995:

Andrew Wiles

1997: Mikio Sato

1999: Yuriy Manin

2001: Elliott Lieb

2003:

Richard Stanley

2005: Luis Caffarelli

2007: To be announced

Title

list of mathematicians awarded the Schock Prize

Canonical name

ListOfMathematiciansAwardedTheSchockPrize

Date of creation

2013-03-22 17:00:01

Last modified on

2013-03-22 17:00:01

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Example

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Generated on Thu Feb 8 19:12:07 2018 by

LaTeXML
Mary Ellen Rudin

Mary Ellen Rudin

Mary Ellen Rudin

(née

Mary Ellen Estill

) (1924 - ) American mathematician and author.

The daughter of a civil engineer and a high school teacher, Mary was born in Texas and went to college at the University of Texas. She credits Robert Lee Moore, a professor there, with cultivating her interest in mathematics. Since 1950 she has been active in the

American Mathematical Society

. After earning her Ph.D., she went on to teach at Duke University, where she met Walter Rudin, an Austrian Jew who had served in the British Navy during World War II and earned his Ph.D. at Duke at the same time Mary got hers at Texas. The two married and had four children. They moved to Madison, Wisconsin and both began teaching at the University of Wisconsin, where Mary Rudin has supervised more than a dozen Ph.D. students. They live in a home built by famous architect Frank Lloyd Wright.

Mary Rudin’s interest is primarily in

topological spaces

. She co-authored with Paul Erdős a paper on “A non-normal

box product

” which has been published in two different colloquia, earning her Erdős number (

http://

planetmath

.org/ErdHosNumber

) 1.

References

1

R. McCroskey Karr, J. Rezaie & J. E. Wilson, “Mary Ellen Rudin” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 190 - 192

Title

Mary Ellen Rudin

Canonical name

MaryEllenRudin

Date of creation

2013-03-22 18:17:39

Last modified on

2013-03-22 18:17:39

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

Mary Rudin

Synonym

Mary Ellen Estill

Generated on Thu Feb 8 19:12:09 2018 by

LaTeXML
Mary Frances Winston Newson

Mary Frances Winston Newson

Mary Frances Winston Newson

née

Mary Frances Winston

(1869 - 1935) American mathematician, best known for her work on

differential equations

. She also translated one of

David Hilbert

’s lectures.

Born in Illinois, Newson studied at the University of Wisconsin and later at Bryn Mawr College and the University of Chicago. With help from

Christine Ladd-Franklin

, Newson went to study at Göttingen. After that she was the entire mathematics faculty of the Kansas State Agricultural College and joined the

American Mathematical Society

. She married Henry Byron Newson and they had three children. When her husband died in 1910, she found herself in the difficult position of having to apply for work as a single woman with children.

References

1

B. S. Whitman “Mary Frances Winston Newson” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 161 - 164

Title

Mary Frances Winston Newson

Canonical name

MaryFrancesWinstonNewson

Date of creation

2013-03-22 17:21:19

Last modified on

2013-03-22 17:21:19

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A55

Synonym

Mary Frances Winston

Synonym

Mary Winston

Synonym

Mary Newson

Generated on Thu Feb 8 19:12:10 2018 by

LaTeXML
Maryam Mirzakhani

Maryam Mirzakhani

Maryam Mirzakhani

(1977 - ) Iranian mathematician, two-time gold medalist at the International Mathematical Olympiad.

After graduating from Sharif University in Tehran, Mirzakhani went on to graduate work at Harvard, and now she’s an assistant professor at Princeton. Currently she’s best known for her advances in

hyperbolic geometry

. She’s working on a paper on the growth of the number of simple closed geodesics on hyperbolic surfaces for

Annals of Mathematics

.

Mirzakhani has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 3: With Mahmoodian she co-authored a paper on the “

Decomposition

of

complete tripartite graphs

into

5

-cycles” in Farsi for a Iranian journal, while Mahmoodian co-authored with Charles Colbourn a paper on “The

spectrum

of support sizes for threefold triple systems” in

Discrete Mathematics

. Colbourn co-authored with Erdős a paper concerning “A conjecture on dominating cycles” at a

combinatorics

conference.

References

1

M. Newhall, “’Brilliant’ minds honored”

USA Today

13 September 2005

Title

Maryam Mirzakhani

Canonical name

MaryamMirzakhani

Date of creation

2013-03-22 17:20:59

Last modified on

2013-03-22 17:20:59

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 19:12:12 2018 by

LaTeXML
Mathematics Subject Classification

Mathematics Subject Classification

The

Mathematics Subject Classification

is a system of classifying mathematical papers published in peer-reviewed journals. The system was devised by the

American Mathematical Society

and is also used by

PlanetMath

to classify its content, and to a lesser extent, the mathematical content of

Wikipedia

.

The codes consist of a 2-digit base 10 number (zero-padded when less than 10), followed by a letter of the Roman

alphabet

or a dash, followed by another 2-digit base 10 number. The first two

characters

refer to the most general level (e.g., history, combinatorics,

number theory

, general topology, etc.), with the following character narrowing it down and the last two numbers being the most specific level. The letter X is used as a kind of wildcard to denote a general level that has not been narrowed down. For example, 81-XX refers to quantum theory, 81PXX refers to the foundational axioms, 81P68 refers to quantum computation and quantum cryptography.

The MSC system has been around almost as long as the AMS. The most important changes to the top-level categories began in 1962, when 09-XX was discontinued. Various other reorganizations have occurred since then, such as 04-XX,

set theory

, being merged into 03-XX, logic. The most recent version dates from 2000, and has room in its 01-XX, history, category for four more centuries.

Title

Mathematics Subject Classification

Canonical

name

MathematicsSubjectClassification

Date of creation

2013-03-22 16:45:16

Last modified on

2013-03-22 16:45:16

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

Generated on Thu Feb 8 19:12:14 2018 by

LaTeXML
Michael Golomb

Michael Golomb

Michael Golomb

(1909 - ) Jewish German-born American mathematician, one of the pioneers in the study of

normed vector spaces

using numerical analysis.

With Erhard Schmidt as his teacher, Golomb earned a doctorate from the University of Berlin in 1933. The next year he fleed to Yugoslavia to escape Nazism, four years later he came to the

United States

. In 1942 he started teaching at Purdue, decades later earning the title of Professor Emeritus. In 1955, he co-authored with Erdős a paper on functions which are symmetric about several points in a Dutch journal, giving him an Erdős number (

http://

planetmath

.org/ErdHosNumber

) of 1. When the

International Congress of Mathematicians

chose Berlin for its annual meeting in 1998, the city honored the achievements of Golomb and other Jewish mathematicians who left before World War II.

Title

Michael Golomb

Canonical name

MichaelGolomb

Date of creation

2013-03-22 16:59:43

Last modified on

2013-03-22 16:59:43

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

Generated on Thu Feb 8 19:12:16 2018 by

LaTeXML
Mike Byster

Mike Byster

Michael Byster

, often referred to as

Mike Byster

, (? - ) American stockbroker, arithmetician and math educator.

Byster used to work at the mercantile exchange, but after his cousin, a math teacher in a Chicago

elementary

school, invited him to show the class his shortcuts for doing base 10

arithmetic

, Byster quit his job and income to devote himself to teaching

children

his methods. Byster married Robin and they have a son, Joshua, to whom he has taught his methods.

On the

20/20

newsmagazine show on ABC, Byster demonstrated some of his shortcuts for doing arithmetic without the aid of a

calculator

or even pencil and paper.

0.1

External links

http://mikesmath.com/aboutmike.htm

About Mike from mikesmath.com

http://abcnews.go.com/2020/story?id=2690724

20/20

story on Mike Byster from abcnews.com

Title

Mike Byster

Canonical

name

MikeByster

Date of creation

2013-03-22 17:31:45

Last modified on

2013-03-22 17:31:45

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

Michael Byster

Generated on Thu Feb 8 19:12:17 2018 by

LaTeXML
Mina Rees

Mina Rees

Mina Rees

(1905 - 1977) American mathematician, the first woman to be president of the American Association for the Advancement of Science.

Born in Cleveland of an insurance salesman and a housewife, young Mina began her education in the public schools of New York, earning

straight

A’s on all her report cards. Later on, when barely a freshman at Hunter College, she was offered a teaching position there. She was a member of Phi Beta Kappa. After earning a degree from Columbia, Rees resumed teaching at Hunter College. In 1932 she earned a doctorate from the University of Chicago. After the

United States

entered World War II, Rees heeded the call of duty and began working for the Applied Mathematics Panel of the Office of Scientific Research &

Development

. After the war, Rees worked for the Office of Naval Research and by 1952 she was appointed deputy science

director

. In 1953 she returned to Hunter College as a dean, and later was a dean at the City University of New York. In 1985, the CUNY honored Rees by naming one of its libraries after her.

Rees has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 4 by way of Richard Courant, Kurt Otto Friedrich and Harold Shapiro.

References

1

P. Fox “Mina Rees” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 175 - 181

Title

Mina Rees

Canonical name

MinaRees

Date of creation

2013-03-22 17:25:09

Last modified on

2013-03-22 17:25:09

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 19:12:19 2018 by

LaTeXML
Multiply Perfect Numbers Page

Multiply Perfect Numbers Page

The

Multiply Perfect Numbers Page

, hosted by Bielefeld University, is currently the most up-to-date Webpage for information on

multiply perfect numbers

. Maintained by Achim Flammenkamp, this archive of more than five thousand multiply perfect numbers “grew out” of a similar database of a little more than two thousand which Richard Schroeppel compiled in 1995 but did not update any further.

Because multiply perfect numbers get very large very fast, it is actually not at all practical to archive a text

representation

of the numbers written in a particular base. Instead, the archive gives the logarithm of the logarithm, the number of

distinct prime factors

, the number of consecutive small factors, the

exponents

of the primes, etc. (in short, enough information to construct the base representation of a desired multiply perfect number) plus historical information such as the name of the discoverer and the date of discovery.

The Multiply Perfect Numbers Page is at

http://wwwhomes.uni-bielefeld.de/achim/mpn.html

http://wwwhomes.uni-bielefeld.de/achim/mpn.html.

Title

Multiply Perfect Numbers Page

Canonical name

MultiplyPerfectNumbersPage

Date of creation

2013-03-22 17:50:49

Last modified on

2013-03-22 17:50:49

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 19:12:21 2018 by

LaTeXML