aarjaneiro/planetmath huggingface dataset:
Stanisław Ulam

Stanisław Ulam

Stanisław Marcin Ulam

(1909 - 1984) Polish mathematician, participant in the Manhattan Project at Los Alamos, perhaps best-known for Ulam’s spiral, the

Ulam numbers

and the

Borsuk-Ulam theorem

. The

Collatz problem

is occasionally referred to as Ulam’s problem.

Born in Lwów to Jewish parents and educated in mathematics by Stefan Banach, Ulam went to the

United States

more than a year prior to the Nazi invasion of Poland. Although Ulam restated many ideas about the mathematics of the hydrogen bomb that had already been given by other Manhattan Project participants and much of the credit went to Edward Teller, the physicist Hans Bethe considered Ulam to be the true father of the H-bomb. After World War II, Ulam began teaching at the University of Colorado and shifted his focus to pure mathematics, but continued research at the Los Alamos National Laboratory.

Title

Stanisław Ulam

Canonical name

StanislawUlam

Date of creation

2013-03-22 16:46:07

Last modified on

2013-03-22 16:46:07

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Synonym

Stanislaw Ulam

Synonym

Stanisław Marcin Ulam

Synonym

Stanislaw Marcin Ulam

Generated on Thu Feb 8 19:12:57 2018 by

LaTeXML
Susan Howson

Susan Howson

Susan Howson

(? - ) British mathematician, the first woman to win the Adams Prize. Her research focuses primarily on

elliptic curves

and extending the theories of Kenkichi Iwasawa.

Howson has taught at MIT, Cambridge, Oxford and Nottingham.

Howson has Erdős number (

http://planetmath.org/ErdHosNumber

) 3. With Paul Balister she published an article on Nakayama’s lemma for

compact

Λ

-modules in

Asian J. Math

, while Balister co-authored a paper on amsey size-linear graphs with Miklós Simonovits, who co-authored with Erdős a paper regarding a

graph theory

limit theorem in

Studia Sci. Math. Hungar

.

Title

Susan Howson

Canonical name

SusanHowson

Date of creation

2013-03-22 16:59:13

Last modified on

2013-03-22 16:59:13

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 19:12:59 2018 by

LaTeXML
Tatyana Pavlovna van Aardenne-Ehrenfest

Tatyana Pavlovna van Aardenne-Ehrenfest

Tatyana Pavlovna van Aardenne-Ehrenfest

, nèe Tatyana Pavlovna Ehrenfest (1905 - 1984) Dutch mathematician, best known for her collaboration on the BEST theorem (together with Nicolaas Govert de Bruijn, Cedric Smith and Bill Tutte).

The eldest daughter of

Paul Ehrenfest

and

Tatyana Afanasyeva

, young Tatyana Pavlovna was home-schooled at first with a solid background in physics and mathematics. She continued studying these subjects at the University of Leiden, where she later taught and where her father had taught in the past. Unlike her mother, Tatyana Pavlovna added her husband’s last name to her own when she married the surgeon Dr. van Aardenne and bore him Gijs van Aardenne, who would later become a prominent politician in the Dutch parliament.

Title

Tatyana Pavlovna van Aardenne-Ehrenfest

Canonical name

TatyanaPavlovnaVanAardenneEhrenfest

Date of creation

2013-03-22 16:50:18

Last modified on

2013-03-22 16:50:18

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A60

Synonym

Tatyana Pavlovna Ehrenfest

Synonym

Tatyana Ehrenfest

Synonym

Tatyana van Aardenne-Ehrenfest

Synonym

Tatyana van Aardenne

Generated on Thu Feb 8 19:13:01 2018 by

LaTeXML
the top 10 most beautiful theorems

the top 10 most beautiful theorems

A 1988 poll of readers of the

Mathematical Intelligencer

ranked some of the most well-known

theorems

in mathematics thus:

1.

Euler’s identity,

e

i

⁢

π

=

-

1

2.

Euler’s formula for a

polyhedron

,

V

+

F

=

E

+

2

3.

There are infinitely many

prime numbers

. See Euclid’s proof that there are infinitely many primes.

4.

There are only 5

regular polyhedra

5.

The sum of the

reciprocals

of the squares of the

positive integers

is

π

2

6

. See the

Basel problem

.

6.

A

continuous mapping

of a

closed unit disk

into itself has a

fixed point

7.

The

square root of 2

is

irrational

8.

π

is a

transcendental number

9.

Every plane map can be colored with just 4 colors

10.

Every prime number of the form

4

⁢

n

+

1

is the

sum of two square

integers

in only one way

References

1

David Wells,

The Penguin Book of Curious and Interesting Mathematics

. London: Penguin Books (1997): 126 - 127

Title

the

top 10 most beautiful theorems

Canonical

name

TheTop10MostBeautifulTheorems

Date of creation

2013-03-22 18:53:52

Last modified on

2013-03-22 18:53:52

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Feature

Classification

msc 01A60

Classification

msc 00A99

Generated on Thu Feb 8 19:13:03 2018 by

LaTeXML
Tobias Dantzig

Tobias Dantzig

Tobias Dantzig

(1884 - 1956) Latvian mathematician, the father of

George Dantzig

, author of

Number: The Language of Science

.

Dantzig began his formal studies in Paris with Henri Poincaré. With his wife he moved the

United States

where she bore him George. After earning a Ph.D. in mathematics from Indiana University, he taught at the University of Maryland.

Title

Tobias Dantzig

Canonical name

TobiasDantzig

Date of creation

2013-03-22 16:41:31

Last modified on

2013-03-22 16:41:31

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A55

Generated on Thu Feb 8 19:13:04 2018 by

LaTeXML
Vladimir Fock

Vladimir Fock

Vladimir Aleksandrovich Fock

(or

Vladimir Alexandrovich Fok

depending on the transliteration from Cyrillic) (1898 - 1974) Soviet physicist, one of the pioneers of quantum mechanics.

Just a few years after graduating from the university in Petrograd, he studied the

Klein-Gordon equation

and provided a

generalization

of it. For more than a dozen years he concentrated his work on optics, but around World War II his interest shifted to quantum mechanics. Today he is perhaps best known for the Bargmann-Fock space. Among theoretical physicists he’s also well-known for the Hartree-Fock method still used today by chemists and molecular physicists.

References

1

Charlotte Froese Fischer,

The Hartree-Fock Method for Atoms: A Numerical Approach

. New York: Wiley (1977)

2

Peter Ring, Peter Schuck & W. Beiglböck,

The Nuclear Many-body Problem

. New York: Springer Verlag (1980): v

Title

Vladimir Fock

Canonical name

VladimirFock

Date of creation

2013-03-22 16:42:47

Last modified on

2013-03-22 16:42:47

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Synonym

Vladimir Fok

Synonym

Vladimir Aleksandrovich Fok

Synonym

Vladimir Alexandrovich Fok

Synonym

Vladimir Aleksandrovich Fock

Synonym

Vladimir Alexandrovich Fock

Generated on Thu Feb 8 19:13:06 2018 by

LaTeXML
Wacław Sierpiński

Wacław Sierpiński

Wacław Franciszek Sierpiński

(1882 - 1969) Polish mathematician, best known for the Sierpiński

triangle

(

http://

planetmath

.org/SierpinskiGasket

) and the Sierpiński numbers.

Sierpiński studied physics and mathematics at the University of Warsaw, graduating in 1903, then went for a doctorate at university in Kraków. In 1908 he started teaching at the University of Lwów. A prolific author of books and papers, Sierpiński wrote on many subjects but focused on

irrational numbers

and

set theory

. During World War I, Sierpiński was stuck in Russia, but the experience proved useful when he returned to Poland and helped his comrades break Russian cryptography. During this time he also founded and edited the journal

Fundamenta Mathematicae

. From 1929 to the end of his life, he received various honors at home and abroad. In 1964, he was elected to the

London Mathematical Society

.

In 1954, Sierpiński published a French paper on some properties of Euler’s

totient function

and the

sum of divisors function

in

Bull. Acad. Polon. Sci. Cl. III

2

with Andrzej Schinzel, who a few years later co-authored with Erdős a paper on the “

Distributions

of the values of some

arithmetical functions

” in

Acta Arithmetica

6

, giving Sierpiński an Erdős number (

http://planetmath.org/ErdHosNumber

) of 2.

Title

Wacław Sierpiński

Canonical name

WaclawSierpinski

Date of creation

2013-03-22 17:03:45

Last modified on

2013-03-22 17:03:45

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

8

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Classification

msc 01A55

Synonym

Wacław Franciszek Sierpiński

Synonym

Waclaw Sierpinski

Synonym

Vaclav Sierpinski

Synonym

Wacław František Sierpiński

Generated on Thu Feb 8 19:13:08 2018 by

LaTeXML
Whitehead Prize

Whitehead Prize

The

Whitehead Prize

is a prize awarded by the

London Mathematical Society

to a mathematician working in the United Kingdom who is at an early stage of their career and has not received any other prizes from the Society. More specifically, the person being considered for the award must be resident in the United Kingdom (England, Scotland, Canada, Australia, etc.) on January 1 of the award year and have less than 15 years of work at the postdoctorate level. Since the inception of the prize, no more than two could be awarded per year, but in 1999 this was increased to 4 “to allow for the award of prizes across the whole of mathematics, including applied mathematics,

mathematical physics

, and mathematical aspects of computer science.” The

Senior Whitehead Prize

has similar residence requirements and rules concerning prior prizes, but is intended to recognize more experienced mathematicians. These prizes were instituted in memory of homotopy theory pioneer John Henry Constantine Whitehead.

0.1

External links

http://www.lms.ac.uk/activities/prizes_com/prizes.html

Official Whitehead Prize rules

Title

Whitehead Prize

Canonical

name

WhiteheadPrize

Date of creation

2013-03-22 16:48:54

Last modified on

2013-03-22 16:48:54

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

Defines

Senior Whitehead Prize

Generated on Thu Feb 8 19:13:10 2018 by

LaTeXML
William Feller

William Feller

William Feller

(1906 - 1970) American mathematician who specialized in

probability

, best known for the

Feller process

, and his classic textbook “An Introduction to Probability Theory and Its Applications”, 1.

Feller was born in Zagreb (now the capital of Croatia) and christened after Saint Willibrord. He moved to Germany to study at Göttingen University, where he received his doctoral . Because of Nazism, he fled to Denmark, later Sweden and finally America, becoming a citizen just prior to World War II. As a member of the

American Mathematical Society

, Feller began the publication of the journal

Mathematical Reviews

.

Title

William Feller

Canonical name

WilliamFeller

Date of creation

2013-03-22 16:24:10

Last modified on

2013-03-22 16:24:10

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A60

Synonym

Willibrord Feller

Synonym

Vilim Feller

Generated on Thu Feb 8 19:13:12 2018 by

LaTeXML
Wolf Prize

Wolf Prize

The

Wolf Prize

is a prize awarded by the Wolf to “outstanding scientists and artists - irrespective of nationality, race, color, religion, sex or political views - for achievements in the

interest

of mankind and friendly relations among peoples.” The six categories of the Wolf Prizes are: agriculture, chemistry, mathematics, medicine, physics and the arts. Nominations for a Wolf Prize in Mathematics are only accepted from presidents of mathematical societies, directors of universities or research institutions, dean of math faculty at an university, or from past Wolf Prize in Mathematics recipients.

0.1

External links

http://www.wolffund.org.il/main.asp

Official Wolf Foundation website

Title

Wolf Prize

Canonical

name

WolfPrize

Date of creation

2013-03-22 16:59:52

Last modified on

2013-03-22 16:59:52

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 19:13:13 2018 by

LaTeXML
Adrien Douady

Adrien Douady

Adrien Douady

(1935 - 2006) French mathematician, best known for his work on

dynamical systems

.

From the outset, Douady intended to teach mathematics at the university level and trained specifically for that occupation, then taught at a university in Paris. His research focused on homological algebra at first, but gradually he became more interested in the work of Pierre Fatou and

Gaston Julia

on dynamical systems. In 1997, Douady was appointed to the Académie des Sciences. A

quadratic Julia set

is named after him, the

Douady rabbit

.

Douady has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 2. He wrote a paper with Jacques Dixmier on fiber spaces in a French journal, and Dixmier wrote a paper with Erdős on the number of fundamental invariants of binary forms in another French journal.

Title

Adrien Douady

Canonical name

AdrienDouady

Date of creation

2013-03-22 17:16:08

Last modified on

2013-03-22 17:16:08

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Generated on Thu Feb 8 19:13:15 2018 by

LaTeXML
Andrew Odlyzko

Andrew Odlyzko

Andrew Odlyzko

is a mathematician best known for disproving the

Mertens conjecture

with Herman J. J. te Riele. Odlyzko co-authored “On the Density of

Odd Integers

of the Form

(

p

-

1

)

2

⁢

k

and Related Questions” in

J. of

Number Theory

11 (1979) with Paul Erdős, and thus has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 1. Odlyzko studied at the Massachusetts Institute of Technology.

Title

Andrew Odlyzko

Canonical

name

AndrewOdlyzko

Date of creation

2013-03-22 16:16:59

Last modified on

2013-03-22 16:16:59

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

7

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Classification

msc 01A65

Generated on Thu Feb 8 19:13:17 2018 by

LaTeXML
Andrew Wiles

Andrew Wiles

Sir Andrew John Wiles

(born 1953) is a British mathematician who proved Fermat’s last theorem. It was Fermat’s last theorem that inspired Wiles to go into mathematics at an early age. He studied at Oxford University, later Cambridge, and now teaches at Princeton.

After Kenneth Ribet suggested there might be a connection between the famous Fermat problem and the

Taniyama-Shimura-Weil conjecture

, Wiles decided to focus entirely on that connection. A proof he presented in 1993 was incomplete, but Wiles and his former student Richard Taylor were able to fill in the gaps of the proof. This was after Wiles turned 41, so he was ineligible for the

Fields medal

, but received plenty of other prizes in recognition, such as the Royal Medal and the Clay Research Award. He was knighted in 2000, and the Clay Mathematics Institute asked him to write the official problem description of the

Birch and Swinnerton-Dyer conjecture

for the

Millennium Problems

.

Wiles was mentioned in an episode of

Star Trek: Deep Space Nine

, retconning Picard’s statement in

The Next Generation

that Fermat’s last theorem was still unsolved as of the 24th century.

References

1

P. Farrand

The Nitpicker’s Guide for Next Generation Trekkers

2. New York: Dell (1995): 178

Title

Andrew Wiles

Canonical name

AndrewWiles

Date of creation

2013-03-22 16:32:12

Last modified on

2013-03-22 16:32:12

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

9

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A65

Classification

msc 01A60

Synonym

Sir Andrew John Wiles

Synonym

Andrew John Wiles

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

LaTeXML
Anja Meyer

Anja Meyer

Anja Gabrielle Meyer

is a mathematician. She co-authored “

Intersection

statements for systems of sets” in

J. Combin. Theory Ser.

A

79

(1997) no. 1, 118 with Paul Erdős, W. A. Deuber, D. S. Gunderson and A. V. Kostochka and thus has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 1.

Title

Anja Meyer

Canonical name

AnjaMeyer

Date of creation

2013-03-22 16:16:57

Last modified on

2013-03-22 16:16:57

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Classification

msc 01A65

Synonym

Anja Gabrielle Meyer

Synonym

A. G. Meyer

Generated on Thu Feb 8 19:13:20 2018 by

LaTeXML
Anna Nagurney

Anna Nagurney

Anna Nagurney

(? - ) American applied mathematician, economist and author, best known for her work on Braess’ paradox.

Born of Ukrainian immigrants in Canada, Nagurney graduated from Brown with a undergraduate degrees in Applied Mathematics and Russian Language and Literature and then earned her Sc.M. and Ph.D. in Applied Mathematics at Brown. After her .D., she joined the faculty of the University of Massachusetts at Amherst. She was the first woman to be appointed to a

named professorship

at the University of Massachusetts, where she is the John F. Smith Memorial Professor in the Isenberg School of Management. She teaches Management Science/

Operations Research

.

Nagurney has Erdős number (

http://

planetmath

.org/ErdHosNumber

) 4 by way of Paul Dupuis, Ofer Zeitouni and Persi Diaconis.

Title

Anna Nagurney

Canonical name

AnnaNagurney

Date of creation

2013-03-22 17:23:17

Last modified on

2013-03-22 17:23:17

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Classification

msc 01A65

Generated on Thu Feb 8 19:13:22 2018 by

LaTeXML
David Eppstein

David Eppstein

David Eppstein

(1963 - ) American computer programmer of English birth.

After earning a bachelor’s degree in mathematics from Stanford in 1984 and a Ph.D. in computer science from Columbia university in 1989, Eppstein went on to work at the Palo Alto Research Center and teach computing at the University of California-Irvine. In 1991, he coauthored with Frances Yao and others a paper on horizon theorems for lines and polygons in “Discrete and Computational Geometry: Papers from the DIMACS Special Year”,

DIMACS Ser.

Discrete Math

. and Theoretical Computer Science

6

; since Yao coauthored with

Fan Chung Graham

,

Ronald Graham

, Stanisław Ulam (

http://

planetmath

.org/StanislawUlam

) and Erdős “Minimal decompositions of two graphs into pairwise

isomorphic

subgraphs

” in

Proceedings of the Tenth Southeastern Conference on

Combinatorics

,

Graph Theory

and Computing

in 1979, Eppstein has Erdős number (

http://planetmath.org/ErdHosNumber

) 2.

These days he edits

Wikipedia

articles on mathematical topics.

Title

David Eppstein

Canonical name

DavidEppstein

Date of creation

2013-03-22 16:47:28

Last modified on

2013-03-22 16:47:28

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Classification

msc 01A65

Generated on Thu Feb 8 19:13:24 2018 by

LaTeXML
distributed computing project

distributed computing project

A

distributed computing project

is an application of computer networking in which the computing power of several different computers across a

network

(usually the

Internet

) is harnessed to tackle one monumental problem. Perhaps the most famous distributed computing project is SETI@home, which lets the Search for Extraterrestrial Intelligence use individual computers to analyze radio telescope data. The popularity of this SETI@home has inspired the use of distributed computing in mathematics, with the most famous of these being the

Great Internet Mersenne Prime Search

.

Seventeen or Bust

is another famous mathematical distributed computing project.

Most distributed computing projects involve one server supercomputer to coördinate the rest. The main server parcels out tasks to the other computers and receives results from them. For mathematical distributed computing projects, the verification of results is typically done by a computer at the project headquarters.

Title

distributed computing project

Canonical name

DistributedComputingProject

Date of creation

2013-03-22 17:20:29

Last modified on

2013-03-22 17:20:29

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Topic

Classification

msc 01A61

Classification

msc 01A65

Synonym

distributed computing

Generated on Thu Feb 8 19:13:25 2018 by

LaTeXML
Elias Stein

Elias Stein

Elias Menachem Stein

(1931 - ) Jewish Belgian-born American mathematician and author, best known for his work on

harmonic analysis

. Many of his textbooks on analytical topics are becoming standard for university courses in the

United States

.

Escaping Nazism, the Stein family first arrived in New York. In 1955, he earned a from the University of Chicago and began teaching at Princeton the next decade, receiving the Princeton President’s Award for Distinguished Teaching. Other honors Stein has received include the

Wolf Prize

, the

Schock Prize

and the National Medal of Science (awarded by the

National Science Foundation

). Stein’s Princeton students include

Charles Fefferman

and

Terence Tao

.

Title

Elias Stein

Canonical

name

EliasStein

Date of creation

2013-03-22 17:00:59

Last modified on

2013-03-22 17:00:59

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Classification

msc 01A65

Synonym

Eli Stein

Synonym

Elias Menachem Stein

Generated on Thu Feb 8 19:13:27 2018 by

LaTeXML
Enrico Bombieri

Enrico Bombieri

Enrico Bombieri

(1940 - ) Italian mathematician, best known for the

Bombieri-Vinogradov theorem

regarding the measure of error in Dirichlet’s

theorem

on

arithmetic progressions

, thought to be one possible direction towards proving the

Riemann hypothesis

(so much so that the Clay Mathematics Institute asked Bombieri to write the official description for the

Millennium Problems

). Bombieri was awarded the

Fields medal

in 1974.

Title

Enrico Bombieri

Canonical

name

EnricoBombieri

Date of creation

2013-03-22 16:25:30

Last modified on

2013-03-22 16:25:30

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A61

Classification

msc 01A60

Classification

msc 01A65

Generated on Thu Feb 8 19:13:29 2018 by

LaTeXML