aarjaneiro/planetmath huggingface dataset:
Prime Pages

Prime Pages

The Prime Pages

are described by their maintainer, Chris Caldwell, as “The ‘Guinness book’ of

prime number

records.” They contain information on the largest known primes with subclassifications by kinds of primes (e.g.,

Sophie Germain primes

,

multifactorial

primes, etc.)

The primes that the Prime Pages concern themselves are too large to write out in base 10. Even as a binary

integer

, the largest known

Mersenne prime

would require a 32 megabyte file to contain it. Thus the primes are written “indirectly” (e.g.,

2

32582657

-

1

for the largest known Mersenne prime).

The Prime Pages also serve as a clearinghouse of information on the latest

primality testing

algorithms and programs.

Chris Caldwell teaches mathematics at the University of Tennessee at Martin. The prime pages are at

http://primes.utm.edu

primes.utm.edu.

Title

Prime Pages

Canonical name

PrimePages

Date of creation

2013-03-22 16:29:27

Last modified on

2013-03-22 16:29:27

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A65

Classification

msc 01A61

Classification

msc 01A60

Generated on Thu Feb 8 19:15:11 2018 by

LaTeXML
Rolf Nevanlinna

Rolf Nevanlinna

Rolf Herman Nevanlinna

(1895-10-22 à 1980-5-28), a Finnish matematician, was born in Joensuu, Finland. He has acted as high school teacher 1918–1926, docent of mathematics 1922–1926, professor of mathematics in University of Helsinki 1926–1946. He has teached also in the Technical university of Zürich and the University of Göttingen. Later, Nevanlinna has worked as rector of the University of Helsinki and as chairman of

http://www.mathunion.org/

International Mathematical Union (IMU). In 1948, Nevanlinna was appointed to the Academy of Finland.

Nevanlinna has acted on several of mathematics, but especially won international fame in the

complex analysis

, where his most known work is his value-distribution theory of

holomorphic functions

. This wide, profound and in formal respects polished

Nevanlinna theory

was published in 1925.

Lars Ahlfors

has said that after it, the function theory was not any more the same as before. Hermann Weyl wrote in 1940s that Nevanlinna theory belongs to the great mathematical achievements of the twentieth century. The point of departure of the theory is Picard’s theorem (

http://

planetmath

.org/PicardsTheorem

) (1879), which had been already improved, among others, by Borel, but the work of Nevanlinna was entirely on a new . The essential contents of the theory may be described so that a

meromorphic function

attains all

complex

values “approximately equally often”. If some value appears less frequently than others among the values of

function

, then to counterbalance, the function comes nearer to that value “more often” than to the others.

Title

Rolf Nevanlinna

Canonical name

RolfNevanlinna

Date of creation

2013-03-22 17:43:22

Last modified on

2013-03-22 17:43:22

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

9

Author

pahio (2872)

Entry type

Biography

Classification

msc 01A65

Classification

msc 01A60

Synonym

Rolf Herman Nevanlinna

Related topic

ErnstLindelof

Related topic

PeriodicFunctions

Related topic

ZerosAndPolesOfRationalFunction

Related topic

AnalyticContinuationOfGammaFunction

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

LaTeXML
scientific calculator

scientific calculator

A

scientific calculator

is a

calculator

with all the

arithmetic

capabilities of a basic calculator plus trigonometric, statistical, logarithmic, binary logic, etc. which are useful in various scientific applications. A typical scientific calculator has some forty to fifty keys and is capable of performing about twice as many

operations

than that (necessitating a “Shift” or “2nd” key). They are often capable of displaying results in binary, octal and hexadecimal, but are usually limited to integers in those bases.

The

calculator trigonometric functions

are

sin

,

cos

, and

tan

, which have their own keys. The arc versions of these are usually obtainable by using the “Shift” or “2nd” key.

A scientific calculator may have a single memory register with the associated keys M+, MR and MC, but they often have several more registers to hold various values for use in statistical computations.

For values greater than about

10

12

or smaller than

10

-

12

(slightly more or less depending on the model) hardware scientific calculators must switch to scientific notation.

Title

scientific calculator

Canonical

name

ScientificCalculator

Date of creation

2013-03-22 16:39:19

Last modified on

2013-03-22 16:39:19

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A65

Classification

msc 00A05

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

LaTeXML
Sun Zhiwei

Sun Zhiwei

Sun Zhiwei

(or

Chihwei Sun

, depending on romanization, generally given as

Zhi-Wei Sun

in journals in English) (born 1965) Chinese mathematician and educator, Editor-in-Chief of the

International Journal of Modern Mathematics

.

Born in Lianshui, China, Sun earned degrees in mathematics at Nanjing University and started teaching

number theory

,

combinatorics

, logic and set theory soon after earning his Ph.D. in 1992. The next year he joined the

American Mathematical Society

. Since 1999, he supervises Ph.D. students at Nanjing.

Zhi-Wei’s twin brother Zhihong is also interested in mathematics; the two of them with Donald Dines Wall searched for

counterexamples

to Fermat’s last

theorem

prior to

Andrew Wiles

proving it in 1994. More recently, Zhi-Wei Sun has been researching sums of a

prime number

to

figurate numbers

.

In 1996, Sun co-authored with Andrew Granville a paper on “Values of

Bernoulli polynomials

” for the

Pacific Journal of Mathematics

. Years before, Granville had co-authored with Erdős a paper “On the normal behavior of the

iterates

of some

arithmetic functions

” in

Progress in Mathematics

, giving Sun Erdős number (

http://

planetmath

.org/ErdHosNumber

) 2.

Title

Sun Zhiwei

Canonical

name

SunZhiwei

Date of creation

2013-03-22 18:04:12

Last modified on

2013-03-22 18:04:12

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A65

Classification

msc 01A61

Classification

msc 01A60

Synonym

Chihwei Sun

Synonym

Sun Chihwei

Synonym

Sun Zhi-Wei

Synonym

Zhi-Wei Sun

Generated on Thu Feb 8 19:15:17 2018 by

LaTeXML
suppression of science

suppression of science

In the Archive Freedom site many scientists complain about the freedom of scientific speech.

”Genius is condemned by a malicious social organization
to an eternal denial of justice in favor of fawning mediocrity”
said

Evariste Galois

, author of

Galois Theory

.

Most of them complain against arXiv.org blacklisting, but also about the mainstream science people who slander them, systematically reject their papers from mainstream journals, refuse to sponsor their research, deny their work or promotion or research positions.

They are slandered in many sites, such as

wikipedia

, even

PlanetMath

, diverse forums, etc.

Some of them filled lawsuits, but of course dismissed by contemporary controllers of scientific research.

See their list in the order presented by archivefreedom.org, among them there is a 1973 Nobel laureate, Brian Josephson (see Josephson junction):
G. Alvarado (U.S.), T. Butler (U.S.), Carlos Castro Perelman (U.S.), Dimiter Chakalov (Bulgaria), Saurav Dwiivedi (India), Roger Ellman (U.S.), Robert Gentry (U.S.), Michael Ibison (U.S.), Radi Khrapko (Russia), Paul LaViolette (U.S.), Danny Lunsford (U.S.), Jacques Moret-Bailly (France), Matti Pitkanen (Finland), F. Julio Palacios (U.S.), Peter Rowlands (UK), Gao Shan (China), Frank (Tony) Smith (U.S.), Edmund Storms (U.S.); Brian Josephson (U.K.), Gustavo Gonazlez-Martin (Venezuela), MarK Hadley (UK ), Andrei Kirilyuk (Ukraine), Angelo Loinger, Eric Lerner (U.S.), Martin Lopez Corredoira (Switzerland/Canary Islands), Alex Rivero (Spain). Shervgi Shahverdiyev (U.S.), Jack Sarfatti (U.S.), B. G. Sidharth (India).

References

1

Archive Freedom,

http://archivefreedom.org

Addressing the Need for freedom in Scientific Research.

Title

suppression of science

Canonical name

SuppressionOfScience

Date of creation

2013-03-22 17:16:43

Last modified on

2013-03-22 17:16:43

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A65

Generated on Thu Feb 8 19:15:18 2018 by

LaTeXML
Texas Instruments

Texas Instruments

Texas Instruments

(stock symbol TXN in the New York Stock Exchange) is the best known manufacturer of

scientific calculators

and programmable

calculators

. The company also produces semiconductors and microchips for cellular telephones.

Calculator models

TI-10

A basic calculator that can also handle

fractions

and test less than and

greater

than

inequalities

. Intended for use in kindergarten classrooms.

TI-15

Not quite a scientific calculator, but definitely more advanced.

Intended for elementary school classrooms.

TI-30

The company’s oldest model of scientific calculator, variants are still produced today,

like the TI-30Xa and the TI-30X IIS. All variants are capable of handling fractions,

with the exception of a version designed specifically for certain standardized tests.

None of them binary, octal or

hexadecimal

display.

TI-81

The company’s oldest model of graphing calculator. It uses TI-BASIC, which is a variant

of BASIC (

http://

planetmath

.org/BASICProgrammingLanguage

).

TI-89

A graphing calculator permitted for use in some standardized tests.

TI-92

A programmable graphing calculator, not allowed for use in standardized tests.

Title

Texas Instruments

Canonical

name

TexasInstruments

Date of creation

2013-03-22 16:47:10

Last modified on

2013-03-22 16:47:10

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

10

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A65

Classification

msc 01A61

Classification

msc 01A60

Generated on Thu Feb 8 19:15:20 2018 by

LaTeXML
The Fibonacci Quarterly

The Fibonacci Quarterly

The

Fibonacci Quarterly

(sometimes

Fib. Quart.

in bibliographies) is the official publication of the

Fibonacci Association

, intended “to serve as a focal point for interest in

Fibonacci numbers

and related questions, especially with respect to new results, research proposals, challenging problems, and innovative proofs of old ideas.” Published since 1962, it is available in hard copy from most libraries as well as online.

The journal has its own editorial board, but the board of directors of the Fibonacci Association also helps. Additionally, there is a rotating group of additional referees consisting of “mathematicians, engineers and physicists”; for example, the referees for

42

included

Ron Graham

, Jud McCranie,

Carl Pomerance

, and Samuel Wagstaff Jr, among a couple dozen others.

Starting with the February 2004 issue, the journal invites “well known mathematicians and scientists” to write articles on how they “use Fibonacci numbers, or similar recurrence sequences, in their research and writing.” The first such article was by George Andrews on the Fibonacci numbers and the Rogers-Ramanujan identities. Articles in the journal touch on various topics of different obviousness of relation to the Fibonacci numbers, such as the

Fibonacci fractions

, the

Collatz sequence

, cryptography, etc.

http://www.engineering.sdstate.edu/ fib/

Fibonacci Quarterly Homepage

Title

The Fibonacci Quarterly

Canonical name

TheFibonacciQuarterly

Date of creation

2013-03-22 17:21:32

Last modified on

2013-03-22 17:21:32

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A65

Classification

msc 01A61

Classification

msc 01A60

Synonym

Fibonacci Quarterly

Generated on Thu Feb 8 19:15:22 2018 by

LaTeXML
United States of America Mathematical Olympiad

United States of America Mathematical Olympiad

The

United States of America Mathematical Olympiad

(USAMO) is an invitation-only mathematical competition sponsored by the

Mathematical Association of America

and hosted by the University of Nebraska-Lincoln. It is a 2-day event in which the contestants try to give proofs to six mathematical problems. The judges award 0 to 7 points to each solution, thus a perfect score is 42 (

http://

planetmath

.org/FortyTwo

) points. The winners go on to represent the

United States

in the International Mathematical Olympiad. Currently, the

Internet

is used to present the problems the first day of the competition; on the second day the contestants fax back their answers. The official website of the competition is

http://www.unl.edu/amc/e-exams/e8-usamo/usamo.shtml

http://www.unl.edu/amc/e-exams/e8-usamo/usamo.shtml.

Title

United States of America Mathematical Olympiad

Canonical

name

UnitedStatesOfAmericaMathematicalOlympiad

Date of creation

2013-03-22 16:52:51

Last modified on

2013-03-22 16:52:51

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A65

Classification

msc 01A61

Classification

msc 01A60

Generated on Thu Feb 8 19:15:24 2018 by

LaTeXML
Wikipedia

Wikipedia

Wikipedia

is a free online encyclopedia that anyone may edit. Its coverage of

elementary

mathematical topics is almost , and its coverage of intermediate and advanced topics is adequate. Wikipedia has articles on the integers in the

-

2

<

n

<

201

as well as 220, 284, 496, 666, 720, 1138, 1729, 69105 and certain powers of ten. Its biographical coverage of the most famous mathematicians and physicists (

Albert Einstein

, Gauss,

Ramanujan

, Wiles, etc.) is on par with that of the best paper encyclopedias, and there is often at least a couple of on the more obscure mathematicians.

The Wikipedia articles on mathematical (and other) themes are not only in English, but also in many other

languages

; the available language alternatives of a given article are found in a box in the left margin.  The contents of distinct language versions are not identical, and the English version is not always the most comprehensive. Although Wikipedia can usually be relied on for definitions of mathematical terms, it is by design not meant for mathematical proofs; Wikipedia has only the most famous and

elementary proofs

(such as Euclid’s proof that there are infinitely many primes).

Because anyone may edit Wikipedia and introduce intentional or unintentional computational errors, it is advisable to double-check or recalculate any number from Wikipedia before using it in any intensive calculations. Unlike

PlanetMath

, Wikipedia does not use the

Mathematics Subject Classification

codes to organize its entries on mathematical topics; however, the PlanetMath Exchange does use the MSC codes to coordinate exchange between PlanetMath and Wikipedia. This would seem to reveal the same as PlanetMath, but Wikipedia has articles on those topics from a more physics-oriented standpoint.

Title

Wikipedia

Canonical name

Wikipedia

Date of creation

2013-03-22 16:45:13

Last modified on

2013-03-22 16:45:13

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

12

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A65

Classification

msc 01A61

Generated on Thu Feb 8 19:15:25 2018 by

LaTeXML
William Thurston

William Thurston

William Paul Thurston

(born 1946) American mathematician, recipient of the

Fields medal

in 1982, perhaps best known for Thurston’s

geometrization conjecture

.

After earning a doctorate at the University of California, Berkeley, Thurston taught at MIT, Princeton (where he worked on foliation and lectured on the

orbifold

theorem), UC Davis. Since 2003 he has been a professor of mathematics and computer science at Cornell University.

Title

William Thurston

Canonical name

WilliamThurston

Date of creation

2013-03-22 16:15:30

Last modified on

2013-03-22 16:15:30

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A65

Classification

msc 01A61

Classification

msc 01A60

Synonym

William Paul Thurston

Synonym

Bill Thurston

Generated on Thu Feb 8 19:15:27 2018 by

LaTeXML
Bernhard Riemann

Bernhard Riemann

The German mathematician Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was born in Breselenz, Hanover, and died in Selasca, Italy.  In spite of his short life, he made important pioneering works in

mathematical analysis

,

differential geometry

,

analytic number theory

and mathematical physics.  He is one of the most notable mathematicians.

In his PhD thesis in 1851, supervised by Gauss,

Riemann

developed the theory of

functions

of one complex variable, the function theory, introducing among other things the surfaces which carry his name, the

Riemann surfaces

, and the Riemann sphere.  In his habilitation work

Über die Hypothesen welche der Geometrie zu Grunde liegen

he created the of the differential geometry, which has profoundly changed the notion of

geometry

, especially opening the for the

non-Euclidean geometries

and the

http://en.

wikipedia

.org/wiki/Theory_of_relativity

theory of relativity.

The only work of Riemann on

number theory

,

Über die Anzahl der Primzahlen unter einer gegebenen Größe

, forms together with some works of

Chebyshev

and Dirichlet the of analytic number theory.  It was a question of proving and sharpening the

prime number theorem

, assumed by Gauss.  Riemann applies function theory making far-reaching consequences on the

distribution

of primes.  In this context is born the

Riemann hypothesis

on the zeroes (

http://

planetmath

.org/ZeroOfAFunction

) of

Riemann zeta function

.

Title

Bernhard Riemann

Canonical name

BernhardRiemann

Date of creation

2013-03-22 18:34:21

Last modified on

2013-03-22 18:34:21

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

5

Author

pahio (2872)

Entry type

Biography

Classification

msc 01A70

Classification

msc 01A55

Synonym

Riemann

Generated on Thu Feb 8 19:15:34 2018 by

LaTeXML
Charles Sanders Peirce

Charles Sanders Peirce

Forthcoming …

In the mean time —

1

Resources

•

“

http://www.mywikibiz.com/Charles_Sanders_Peirce

Charles Sanders Peirce

”,

http://www.mywikibiz.com/

MyWikiBiz Directory.

•

Burch, Robert (2006), “

http://plato.stanford.edu/entries/peirce/

Charles Sanders Peirce”,

http://plato.stanford.edu/

Stanford Encyclopedia of Philosophy.

•

Hammer, Eric (2007), “

http://plato.stanford.edu/entries/peirce-logic/

Peirce’s Logic”,

http://plato.stanford.edu/

Stanford Encyclopedia of Philosophy.

•

O’Connor, J.J., and Robertson, E.F. (2005), “

http://www-history.mcs.st-andrews.ac.uk/Biographies/Peirce_Charles.html

Charles Sanders Peirce”,

http://www-history.mcs.st-andrews.ac.uk/

MacTutor History of Mathematics Archive.

Title

Charles Sanders Peirce

Canonical name

CharlesSandersPeirce

Date of creation

2013-03-22 18:02:21

Last modified on

2013-03-22 18:02:21

Owner

Jon Awbrey (15246)

Last modified by

Jon Awbrey (15246)

Numerical id

6

Author

Jon Awbrey (15246)

Entry type

Biography

Classification

msc 01A70

Generated on Thu Feb 8 19:15:38 2018 by

LaTeXML
Øystein Ore

Øystein Ore

Norwegian mathematician (7 October 1899 - 13 August 1968).

A graduate of Oslo University, he later taught at Yale. He mostly worked on

combinatorics

and ring theory.

Among the concepts named after him are

Ore numbers

and Ore’s theorem. Dover continues to republish his most famous book,

Number Theory

and its History

, McGraw-Hill, 1948. Ore’s writing style energetically discusses the

central

problems and solutions in the history of number theory, with

Gaussian

congruences

playing a central role in the 1800’s. Earlier, Ore details astronomical problems and solutions from India (Brahmagupta) and China related to the

Chinese Remainder Theorem

, and the indeterminate equations used by Diophantus and

Fibonacci

.

Title

Øystein Ore

Canonical name

OysteinOre

Date of creation

2013-03-22 15:59:43

Last modified on

2013-03-22 15:59:43

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

9

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A70

Classification

msc 01A60

Synonym

Oystein Ore

Generated on Thu Feb 8 19:15:42 2018 by

LaTeXML
Thabit ibn Qurra

Thabit ibn Qurra

Thabit ibn Qurra

(836 - 901), an astronomer and mathematician born in present day Turkey, best known for translating classic Greek works on astronomy, and for coming up with a

formula for amicable pairs

.

Muhammad bin Musa bin Shakir invited Thabit to work in Baghdad’s House of Wisdom translating Greek and Syrian works (such as Apollonius’s

Conics

or works of Euclid and Archimedes). As he translated the texts, Thabit produced a mathematical body of his own.

Thabit was one of the Sabians. Their worship of planets and stars was tolerated by the Muslim caliphs, who were interested in their work on astronomy. It is believed that Thabit came up with early theories about the equinoxes, and made a pretty good estimate of the length of the sidereal year that was off by just a couple of seconds.

Thabit’s son was a doctor, and his grandson studied curves in order to make better sundials.

Title

Thabit ibn Qurra

Canonical name

ThabitIbnQurra

Date of creation

2013-03-22 15:53:01

Last modified on

2013-03-22 15:53:01

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A70

Classification

msc 01A30

Synonym

Thabit ibn Kurra

Synonym

Thabit ibn Kurrah

Synonym

Thabit ibn Qurrah

Synonym

Thabit bin Kurra

Synonym

Thabit bin Kurrah

Synonym

Thabit bin Qurra

Synonym

Thabit bin Qurrah

Synonym

Thebit

Synonym

Thâbit ibn Kurrah

Generated on Thu Feb 8 19:15:43 2018 by

LaTeXML
Štefan Znám

Štefan Znám

Slovak mathematician and mathematics professor, (February 9, 1936 - July 17, 1993), posed Znám’s problem.

His ErdÃâs number is 2 by at least six different paths. For example, in 1968, ZnÃÂ¡m wrote a paper on ”Strongly geodetic graphs” with Juraj BosÃÂ¡k in the

Journal of Combinatorial Theory

. Three years later, BosÃÂ¡k co-authored ”Decompositions of

complete graphs

into factors with

diameter

two” with ErdÃâs and Alexander Rosa in

Mathematics Casopis Slovene Akademie Vied

.

Title

Štefan Znám

Canonical

name

vStefanZnam

Date of creation

2013-03-22 15:59:41

Last modified on

2013-03-22 15:59:41

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

6

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A70

Classification

msc 01A60

Synonym

Stefan Znám

Synonym

Stefan Znam

Generated on Thu Feb 8 19:15:45 2018 by

LaTeXML