aarjaneiro/planetmath huggingface dataset:
Efim Zelmanov

Efim Zelmanov

Efim Isaakovich Zelmanov

(born 1955) Russian (formerly Soviet) mathematician, perhaps best known for his

solution

of the restricted

Burnside problem

. Almost half a decade before the collapse of the Soviet Union, Zelmanov left for America and taught at Yale University and most recently at UCSD. In 1994 he was awarded the

Fields medal

.

Title

Efim Zelmanov

Canonical name

EfimZelmanov

Date of creation

2013-03-22 16:19:50

Last modified on

2013-03-22 16:19:50

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

Efim Isakovich Zelmanov

Synonym

Efim Isaakovich Zelmanov

Synonym

Efraim Zelmanov

Generated on Thu Feb 8 19:10:41 2018 by

LaTeXML
Elizaveta Litvinova

Elizaveta Litvinova

Elizaveta Fedorovna Litvinova

née

Elizaveta Fedorovna Ivanshkina

(1845 - 1919?) Russian mathematician, biographer and women’s activist.

Born in czarist Russia, young Elizaveta’s early education was at a women’s high school in St. Petersburg. In 1866 Elizaveta married Viktor Litvinov and took his last name. Unlike Vladimir Kovalevskii (

Sofia Kovalevskaya

’s husband), Litvinov would not allow his wife to travel to Europe to study at the universities there. Litvinova studied with Strannoliubskii (who had also privately tutored Kovalevskaya). As soon as her husband died, Litvinova went to Zürich and enrolled at a polytechnic institute. In 1873 the Russian czar decreed all Russian women studying in Zürich had to return to Russia or the consequences. Litvinova was one of the few to ignore the decree and continue her studies in Zürich. When Litvinova returned to Russia, she was denied university appointments because she had defied the 1873 recall. She taught at a women’s high school and supplemented her income by writing biographies of more famous mathematicians such as Kovalevskaya and

Aristotle

. After retiring, it is believed that Litvinova died during the Russian Revolution in 1919.

References

1

A. H. Koblitz “Sofia Vasilevna Kovalevskaia” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 129 - 134

Title

Elizaveta Litvinova

Canonical

name

ElizavetaLitvinova

Date of creation

2013-03-22 17:15:41

Last modified on

2013-03-22 17:15:41

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A60

Classification

msc 01A55

Synonym

Elizaveta Fedorovna Litvinova

Synonym

Elizaveta Fedorovna Ivanshkina

Synonym

Elizaveta Ivanshkina

Generated on Thu Feb 8 19:10:43 2018 by

LaTeXML
Erdős number

Erdős number

The shortest number of collaborations with other mathematicians through which a particular mathematician can be

connected

to Paul Erdős is the

Erdős number

of that mathematician. For example, N. J. A. Sloane coauthored

Sphere Packings

, Lattices and Groups

with

John Horton Conway

. In turn, Conway coauthored a paper with Erdős in 1979, thus Sloane’s Erdős number is 2. Since Erdős died in 1996, 2 is the lowest Erdős number a mathematician working today can achieve.

One way to visualize the Erdős number is by drawing up a collaboration graph

G

whose

vertex set

consists of all persons, where two vertices

x

and

y

are connected by an edge if and only if

x

and

y

have a joint publication. Then the Erdős number of a person

x

is the

distance

in

G

(possibly infinity) of

x

from Erdős.

Title

Erdős number

Canonical name

ErdHosNumber

Date of creation

2013-03-22 16:15:59

Last modified on

2013-03-22 16:15:59

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A60

Classification

msc 01A61

Synonym

Erdos number

Synonym

Erdös number

Related topic

ErdoesNumber

Related topic

RosettaGroupoids

Generated on Thu Feb 8 19:10:47 2018 by

LaTeXML
Erdős number

Erdős number

A low Erdős number is a status symbol among 20th century mathematicians and is similar to the 6-degrees-of-separation concept.

Let

e

⁢

(

p

)

be the Erdős number of person

p

. Your Erdős number is

•

0 if you are Paul Erdős

•

min

⁡

{

e

⁢

(

x

)

|

x

∈

X

}

+

1

, where

X

is the set of all persons you have authored a paper with.

Title

Erdős number

Canonical

name

ErdHosNumber

Date of creation

2013-03-22 13:10:55

Last modified on

2013-03-22 13:10:55

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

12

Author

mathcam (2727)

Entry type

Definition

Classification

msc 01A60

Related topic

ErdHosNumber

Generated on Thu Feb 8 19:10:48 2018 by

LaTeXML
Erich Kähler

Erich Kähler

Erich Kähler

(1906 - 2000) German geometer and philosopher, after whom the Kähler

manifold

is named.

Kähler studied at the University of Leipzig, where he worked on celestial mechanics and what would later become scheme theory. After earning his Ph.D., he taught in his hometown and in Berlin and Hamburg. Building on Élie Cartan’s work on

differential geometry

, Kähler made advances in

algebraic geometry

.

Title

Erich Kähler

Canonical

name

ErichKahler

Date of creation

2013-03-22 16:33:53

Last modified on

2013-03-22 16:33:53

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A60

Synonym

Erich Kahler

Generated on Thu Feb 8 19:10:50 2018 by

LaTeXML
Ernst Straus

Ernst Straus

Ernst Gabor Straus

(1922 - 1983) German-American Jewish mathematician and physicist, best known in mathematics for his work on

Ramsey theory

.

Born in Munich of a lawyer and a doctor, young Ernst showed an ability for mathematics from early on. But with Hitler’s rise to power in Germany in the 1930s and the death of the Straus paterfamilias, the surviving Strauses fled to Israel and later the

United States

, where he co-authored papers with

Albert Einstein

and Paul Erdős. Straus stayed in America for the rest of his life.

Title

Ernst Straus

Canonical name

ErnstStraus

Date of creation

2013-03-22 17:24:49

Last modified on

2013-03-22 17:24:49

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Synonym

Ernst Gabor Straus

Generated on Thu Feb 8 19:10:52 2018 by

LaTeXML
Evelyn Boyd Granville

Evelyn Boyd Granville

Evelyn Boyd Granville

née

Evelyn Boyd

(1924 - ) American mathematician and educator, the first African American woman to earn a doctorate degree in mathematics in the

United States

, co-author with Jason Frand of

Theory and Application of Mathematics for Teachers

.

As a teenager, Granville attended the blacks-only Paul Dunbar High School in Washington, D. C. She obtained a scholarship to Smith College but it was only with her family’s financial help that she was able to graduate. At first Granville considered majoring in astronomy, but opted for mathematics instead with Neal McCoy and Susan Rambo as her primary instructors Graduating summa cum laude, Granville received more substantial scholarships to continue graduate studies at Yale, where she earned master’s degrees in physics and mathematics.

Despite all the awards and fellowships she accumulated, at the time she couldn’t get work teaching in the best-known universities because of her race. The then blacks-only Fisk University gave her a position, though. The military and the computer industry had no problem with her race, and she worked for the U. S. Army and IBM.

After a failed marriage to a preacher in the 1960s, Evelyn married the real estate broker Edward Granville and began teaching at the California State University. When the couple moved to Texas, she taught at Texas College and even tried her hand at teaching elementary school.

References

1

P. C. Kenschaft “Evelyn Boyd Granville” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 57 - 61

Title

Evelyn Boyd Granville

Canonical name

EvelynBoydGranville

Date of creation

2013-03-22 16:57:31

Last modified on

2013-03-22 16:57:31

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

Evelyn Boyd

Synonym

Evelyn Granville

Generated on Thu Feb 8 19:10:53 2018 by

LaTeXML
Evelyn Nelson

Evelyn Nelson

Evelyn Merle Nelson

née

Evelyn Merle Roden

(1943 - 1987) Canadian mathematician, best known for her work in theoretical computer science.

Born in Ontario of Russian immigrants, young Evelyn’s education began at a high school in her native town and continued at the University of Toronto, then returned to her home town to study at McMaster University, where she began researching after earning her .D. and later taught in the computer science department.

Nelson has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 2. With Saharon Shelah and Alan Mekler she published an article on “A variety with solvable, but not uniformly solvable, word problem” in the

Proceedings of the

London Mathematical Society

of 1993, while Shelah co-authored with Erdős a paper on the “Separability properties of almost-disjoint families of sets” in the

Israel Journal of Mathematics

12

.

Title

Evelyn Nelson

Canonical name

EvelynNelson

Date of creation

2013-03-22 17:22:34

Last modified on

2013-03-22 17:22:34

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Evelyn Merle Nelson

Synonym

Evelyn Merle Roden

Generated on Thu Feb 8 19:10:55 2018 by

LaTeXML
Fan Chung Graham

Fan Chung Graham

Fan Chung Graham

(1949 - ) Chinese American mathematician, author and educator specializing in

graph theory

, the third wife of

computer

theorist

Ronald Graham

, and one of the most prolific Erdős collaborators, co-author with him of 14 papers, primarily dealing with graphs. After earning a doctorate from the University of Pennsylvania in 1974 with Herbert Wilf as her advisor, Chung went on to teach at the University of California-San Diego, where she is now Akamai Professor in

Internet

Mathematics.

0.1

External link

http://www.math.ucsd.edu/ fan/

Fan Chung Graham’s home page One of the busiest (i.e., less professional-looking) websites by a mathematician, making heavy use of frames, animated GIFs, Javascript and Dynamic HTML.

Title

Fan Chung Graham

Canonical

name

FanChungGraham

Date of creation

2013-03-22 16:43:03

Last modified on

2013-03-22 16:43:03

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

Fan Chung

Synonym

Fan Rong K Chung Graham

Synonym

Fan Chung-Graham

Synonym

Jin Fangróng

Synonym

Jin Fangrong

Generated on Thu Feb 8 19:10:57 2018 by

LaTeXML
Fibonacci Association

Fibonacci Association

The

Fibonacci Association

is an association of professional mathematicians dedicated to furthering research on the

Fibonacci numbers

. Their official publication is the

Fibonacci Quarterly

.

http://www.mscs.dal.ca/

Fibonacci

/index.html

Official Website of the Fibonacci Association

Title

Fibonacci Association

Canonical name

FibonacciAssociation

Date of creation

2013-03-22 17:21:28

Last modified on

2013-03-22 17:21:28

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 19:10:59 2018 by

LaTeXML
Frances Kirwan

Frances Kirwan

Frances Clare Kirwan

(? - ) British mathematician, president of the

London Mathematical Society

from 2004 to 2006.

Kirwan studied at Cambridge, and went on to graduate work at Oxford, where she now teaches mathematics. In 2005, the Engineering and Physical Sciences Research Council awarded her a Senior Research Fellowship for her work in

algebraic geometry

. As of 2007, Kirwan has Oxford University Press preprints on Morse stratification, Riemann surfaces and modular cohomology, as well as collaborations on related topics.

Kirwan has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 3. With David Mumford she published an article on geometric invariant theory in

Ergebnisse der Mathematik und ihrer Grenzgebiete

, while Mumford co-authored a paper on

planar graphs

with

Fan Chung Graham

.

Title

Frances Kirwan

Canonical

name

FrancesKirwan

Date of creation

2013-03-22 16:57:46

Last modified on

2013-03-22 16:57:46

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

Frances Clare Kirwan

Generated on Thu Feb 8 19:11:00 2018 by

LaTeXML
Frank Ramsey

Frank Ramsey

Frank Plumpton Ramsey

(1903 - 1930) English mathematician and economist. In mathematics he’s best known for

Ramsey numbers

and his theorem on

complete graphs

, but he also studied

combinatorics

and logic. In economics he’s best known for formulating a pricing model for monopolies that would theoretically maximize social welfare.

As Ramsey did important work on decision analysis, the Decision Analysis Society named its annual medal after him.

Title

Frank Ramsey

Canonical name

FrankRamsey

Date of creation

2013-03-22 16:16:35

Last modified on

2013-03-22 16:16:35

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Synonym

Frank Plumpton Ramsey

Synonym

Frank P. Ramsey

Synonym

F. P. Ramsey

Generated on Thu Feb 8 19:11:02 2018 by

LaTeXML
Gaston Julia

Gaston Julia

Gaston Maurice Julia

(1893 - 1978) French mathematician best known for Julia sets.

In his 20s, Julia served in the French Army in World War I, losing his nose in the conflict. Coming home from the war, Julia attracted the attention of mathematicians for his paper on iterated

rational functions

. Even in those days before computer graphics, he was able to visualize which are

connected

and which are not. During World War II, he taught at the École Polytechnique. One of his students there, Benoît Mandelbrot, would grow up to popularize his work on fractals.

Title

Gaston Julia

Canonical name

GastonJulia

Date of creation

2013-03-22 16:58:08

Last modified on

2013-03-22 16:58:08

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Gaston Maurice Julia

Generated on Thu Feb 8 19:11:04 2018 by

LaTeXML
George Dantzig

George Dantzig

George Bernard Dantzig

(1914 - 2005) American mathematician and programmer, the “father of

linear programming

.”

The son of

Tobias Dantzig

, George began his formal studies at the University of Maryland. As the

United States

became involved in World War II, Dantzig was drafted by the U. S. Air Force to help with supply logistics. After the war, he obtained master’s degrees from the University of Michigan and the University of California at Berkeley, where he famously solved two specially difficult problems believing them to be run-of-the-mill homework assignments.

Title

George Dantzig

Canonical name

GeorgeDantzig

Date of creation

2013-03-22 16:41:29

Last modified on

2013-03-22 16:41:29

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A61

Synonym

George Bernard Dantzig

Generated on Thu Feb 8 19:11:06 2018 by

LaTeXML
Gertrude Blanch

Gertrude Blanch

Gertrude Blanch

née

Gittel Kaimowitz

(1897? - 1996) Polish-born American mathematician and educator, considered one of the pioneers of numerical analysis and computation.

When she was barely 10-years-old, her family moved to the

United States

. She attended a high school in New York and worked full-time in order to afford to go to college. In the 1930s she earned degrees from New York University and Cornell University in mathematics and phsyics. In 1938 she was director of the Mathematical Tables Project which computed ballistics for the Army and the Navy. The FBI, however, questioned her patriotism and fingered her as a communist. A hearing cleared her name.

After retirement in 1967, Blanch devoted the rest of her life to studying the Matthieu

functions

by means of

continued fractions

.

Title

Gertrude Blanch

Canonical name

GertrudeBlanch

Date of creation

2013-03-22 16:41:50

Last modified on

2013-03-22 16:41:50

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Gittel Kaimowitz

Generated on Thu Feb 8 19:11:07 2018 by

LaTeXML
Gertrude Cox

Gertrude Cox

Gertrude Mary Cox

(1900 - 1978) American statistician, first woman elected to the International Statistical Institute and president of the American Statistical Association from 1956 to 1959.

Born in Dayton, Iowa, Cox at first intended to become a Methodist Episcopal minister and director of an orphanage, but in college she heeded a new calling of statistics to help Iowan farmers make better agricultural research, and she earned degrees from Iowa State College and later the Univesity of California-Berkeley. In 1940, Cox became the first director of experimental statistics at North Carolina State University, where she trained the staff of the Crop Reporting Service of the USDA. She spent the last decades of her life lobbying to improve the teaching of statistics in the South.

References

1

M. Nichols “Gertrude Mary Cox” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 26 - 29

Title

Gertrude Cox

Canonical name

GertrudeCox

Date of creation

2013-03-22 16:43:31

Last modified on

2013-03-22 16:43:31

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Gertrude Mary Cox

Generated on Thu Feb 8 19:11:09 2018 by

LaTeXML
Grace Hopper

Grace Hopper

Grace Hopper

, née

Grace Brewster Murray

(1906 - 1992) American mathematician, computer engineer and U. S. Navy Admiral.

After earning master’s degrees in mathematics and physics from Yale, Hopper taught at Vassar for a few years before joining the Navy, which assigned her to work on the Mark I computer. One day she extracted an insect from the machinery and helped popularize the preexisting term ”bug” for computer malfunctions. Later on she worked on a compiler for COBOL.

References

1

A. C. King & Tina Schalch “Grace Brewster Murray Hopper” in

Women of Mathematics: A Bibliographic Sourcebook

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

Title

Grace Hopper

Canonical name

GraceHopper

Date of creation

2013-03-22 16:25:27

Last modified on

2013-03-22 16:25:27

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Grace Brewster Murray

Synonym

Grace Brewster Murray Hopper

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

LaTeXML
Great Internet Mersenne Prime Search

Great Internet Mersenne Prime Search

The

Great Internet Mersenne Prime Search

(or

GIMPS

for short) is a

distributed computing

effort to find

Mersenne primes

. The project was started by computer programmer George Woltman. Volunteers to allow GIMPS to use their own personal computers to test Mersenne primes and send the results back to a

central

database.

As of 2006, the ten largest known Mersenne primes have been found by GIMPS. The project has also motivated Woltman to write some of the fastest

integer

multiplication

subroutines available today.

http://www.mersenne.org/

Official website

The latest (June 15, 2009) results confirm that the 47th Mersenne prime has been found. Mersenne primes are factors of even perfect numbers. This means we have a new

perfect number

.

As the newest, it is not the largest. A larger one was found in August 2008. However, the latest is a very big number. The Mersenne prime: 242,643,801-1 is a 12,837,064 digit number. The perfect number has twice as many digits.

It was actually found in April. It took two months to confirm.

Title

Great Internet Mersenne Prime Search

Canonical name

GreatInternetMersennePrimeSearch

Date of creation

2013-03-22 16:22:06

Last modified on

2013-03-22 16:22:06

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

10

Author

PrimeFan (13766)

Entry type

Topic

Classification

msc 01A60

Classification

msc 01A65

Classification

msc 01A61

Synonym

GIMPS

Generated on Thu Feb 8 19:11:13 2018 by

LaTeXML
Grete Hermann

Grete Hermann

Grete Hermann

(1901 - 1984) German mathematician perhaps most famous for discovering a flaw in

John von Neumann

’s proof of the impossibility of hidden variable theory in quantum mechanics. As a student of

Emmy Noether

at Göttingen University, Hermann showed in her thesis that her teacher’s proof of the

Lasker-Noether theorem

could be turned into an efficient algorithm for computing

primary decompositions

of

polynomial

ideals in

Noetherian rings

.

As Adolf Hitler came to in Germany, Hermann participated in the underground movement against the Nazis, but by 1936 she left Germany for Denmark and later England. She returned when World War II was over. In her later years she was more interested in politics and philosophy than in physics and mathematics.

Title

Grete Hermann

Canonical name

GreteHermann

Date of creation

2013-03-22 16:57:11

Last modified on

2013-03-22 16:57:11

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Generated on Thu Feb 8 19:11:14 2018 by

LaTeXML
Hanna Neumann

Hanna Neumann

Hanna Neumann

nèe

Hanna von Caemmerer

(1914 - 1971) German mathematician, best known for her work on varieties in group theory.

Her father died soon after her birth, and as a teen young Hanna supplemented the family’s pension by tutoring at school. As a child she showed a strong interest in botany, but from her adolescence onwards, mathematics became her main focus. In 1932, she started studying at the University of Berlin where she met Käte Fenchel and Bernhard Neumann, a British Jewish mathematician born in Germany. Bernhard Neumann and Hanna vacationed in England in 1934 and engaged to be married, but as Adolf Hitler rose to power in Germany, it became obvious that the Aryan Hanna’s marriage to the British Jew would have to wait, or even seeing each other. Hanna was openly critical of the Nazis, and this would be an obstacle to her obtaining a doctorate degree from a German university. It wasn’t until 1938 that Bernhard and Hanna married in England; she took his name and bore him five children. Bernhard was drafted into the Royal Army and Hanna completed her doctorate at Oxford. After the war, Hanna Neumann taught in the

United States

, in Australia and in Canada.

References

1

M. F. Newman “Hanna Neumann” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Campbell, eds. New York: Greenwood Press (1987): 156 - 160

Title

Hanna Neumann

Canonical name

HannaNeumann

Date of creation

2013-03-22 17:21:22

Last modified on

2013-03-22 17:21:22

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Hanna von Caemmerer

Generated on Thu Feb 8 19:11:16 2018 by

LaTeXML