aarjaneiro/planetmath huggingface dataset:
Blaise Pascal

Blaise Pascal

Blaise Pascal

(1623 - 1662) French mathematician, best known for Pascal’s

triangle

and Pascal’s

theorem

.

The son of a judge, young Blaise was at first discouraged from studying mathematics despite showing talent for it. The father finally relented when the son came up with his own proof of the

Pythagorean theorem

. Barely 18-years-old, Blaise invented one of the first mechanical

calculators

, the Pascaline.

As an adult, Pascal became interested in the mathematics of gambling. To study probabilities, he studied a triangular

arrangement

of

binomial coefficients

he called an “arithmetic triangle.” The triangle had been studied long before by the ancient Chinese, but Pascal’s treatise on it was so influential to the modern study of mathematics that his name became attached to the triangle.

In 1658, Pascal caused controversy when he published a

solution

to a prize problem of his (the

quadrature

of a cycloid) under a pseudonym so as to not have to pay out the prize. Pascal made significant contributions to physics, and the metric unit of pressure is now called the pascal.

Towards the end of his life Pascal became increasingly interested in religion, and published a theological treatise.

The PASCAL programming language is named after him.

Title

Blaise Pascal

Canonical

name

BlaisePascal

Date of creation

2013-03-22 16:51:57

Last modified on

2013-03-22 16:51:57

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A45

Generated on Thu Feb 8 19:08:47 2018 by

LaTeXML
Elena Cornaro Piscopia

Elena Cornaro Piscopia

Elena Lucrezia Piscopia Cornaro

(1646 - 1684) Italian theologist and mathematician, the first woman to earn a doctorate at the University of Padua (the second did so in the 20th Century).

Born of a church lawyer and a housewife, young Elena, unlike other girls of her time, was taught Greek and Latin, and other languages. She also studied mathematics and theology.
After becoming a deaconess at a Benedictine convent, she went on to study at the University of Padua where she earned a philosophy doctorate, becoming the first woman to earn such a degree. She began teaching mathematics at the university until her death, however, she is more remembered for her charity work.

References

1

“Elena Lucrezia Piscopia Cornaro” in

Catholic Encyclopedia

New York: Encyclopedia Press (1913)

Title

Elena Cornaro Piscopia

Canonical

name

ElenaCornaroPiscopia

Date of creation

2013-03-22 17:26:04

Last modified on

2013-03-22 17:26:04

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A45

Synonym

Elena Lucrezia Piscopia Cornaro

Synonym

Elena Lucrezia Cornaro Piscopia

Synonym

Elena Cornaro

Generated on Thu Feb 8 19:08:48 2018 by

LaTeXML
Pietro Mengoli

Pietro Mengoli

Pietro Mengoli

(1625 or 1626 - 1686) Italian mathematician, lawyer, priest, author and educator.

Baptized in the Roman Catholic faith, Mengoli was ordained a priest in 1660 and said Mass in Bologna until his death. Taught by Bonaventura Cavalieri, Mengoli succeeded him as chair of the University of Bologna. In 1644 he posed the

Basel problem

, which remained unsolved until Euler tackled it in the next century, unaware when he confirmed the correctness of the

Wallis formulae

that

π

was also involved in it, nor did his successful work on the sums of the

reciprocals

of the

triangular numbers

help him solve the problem.

Unlike

Pietro Cataldi

, Pietro Mengoli preferred to teach and write in Latin rather than in a modern language. Besides mathematical topics, Mengoli also wrote on atmospheric refraction and musical harmony.

Title

Pietro Mengoli

Canonical

name

PietroMengoli

Date of creation

2013-03-22 18:05:11

Last modified on

2013-03-22 18:05:11

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A45

Classification

msc 01A50

Generated on Thu Feb 8 19:08:52 2018 by

LaTeXML
Adrien-Marie Legendre

Adrien-Marie Legendre

Adrien-Marie Legendre

(1752 - 1833) French mathematician, perhaps best known for the

Legendre symbol

. Born into wealth, he studied physics in Paris and later taught at a military academy because he liked to teach and not because he needed the money. His earliest work in physics concerned the trajectories of cannonballs. As he moved more towards mathematics, he made major contributions to the study of

elliptic integrals

.

In the French Revolution, Legendre lost his money. His

Éléments de Géométrie

was a lucrative book and was much reprinted and translated, but it was his various teaching positions and pensions that kept him at an acceptable standard of living. A mistake in office politics in 1824 led to the loss of his pension and he lived the rest of his years in poverty.

Two streets in Paris are named after Legendre as well as a lunar crater.

Title

Adrien-Marie Legendre

Canonical name

AdrienMarieLegendre

Date of creation

2013-03-22 16:39:40

Last modified on

2013-03-22 16:39:40

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A50

Classification

msc 01A45

Generated on Thu Feb 8 19:08:53 2018 by

LaTeXML
Benjamin Franklin

Benjamin Franklin

Benjamin Franklin

(born January 17 (by the Gregorian calendar), 1706 in Boston, died April 17, 1790 in Philadelphia) was one of the Founding Fathers of the

United States of America

. His key role during the War of Independence of the American Colonies from the British Empire, when he was appointed as an Ambassador to France, was crucial in arranging for prompt financial and military

support

from France during the war. Today he is also remembered for his other many achievements, such as being the first to study electricity, coming up with Daylight Savings Time, public libraries, bifocals, odometers, refining the Americal postal service, etc. His likeness appears on the American $100 bill.

Many well-known proverbs and sayings come from his

Poor Richard’s Almanack

, which in

addition

to the usual calculations on sunrises and sunsets, ebbs and tides, also

contained

population statistics.

Franklin has sometimes been described as “a polymath who did everything but mathematics.” However, in a recent book, Paul Pasles argues that Franklin did a lot more in mathematics than has been previously acknowledged. Besides the

Franklin magic square

, Franklin also tackled the problem of circling the square, statistical projections, etc. Somewhat of an anti-war activist and an abolitionist, Franklin argued against war and slavery using

arguments

pertaining to economics rather than morality.

References

1

Paul Pasles,

Benjamin Franklin’s numbers : an unsung mathematical odyssey

. Princeton: Princeton University Press (2008)

Title

Benjamin Franklin

Canonical name

BenjaminFranklin

Date of creation

2013-03-22 17:46:16

Last modified on

2013-03-22 17:46:16

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A50

Classification

msc 01A45

Synonym

Ben Franklin

Generated on Thu Feb 8 19:08:55 2018 by

LaTeXML
Francesco Faà di Bruno

Francesco Faà di Bruno

Francesco Faà di Bruno

(1825 - 1888) Italian mathematician and saint, best known for the Faà di Bruno formula. He was a captain in an Italian militia, but gave up the post to become a Catholic priest. Instead of saying Mass, however, Bruno dedicated himself to teaching and studying mathematics, publishing dozens of articles in important mathematical journals of the day. He began what would have been a multi-volume book about

elliptic functions

but did not

complete

the work.

1

Bibliography

P. H. Linehan, ”

Francesco Faa di Bruno

” in

The Catholic Encyclopedia

1909. New York: Robert Appleton Company

Title

Francesco Faà di Bruno

Canonical name

FrancescoFaaDiBruno

Date of creation

2013-03-22 16:31:51

Last modified on

2013-03-22 16:31:51

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A50

Synonym

Francesco Faa di Bruno

Generated on Thu Feb 8 19:08:59 2018 by

LaTeXML
Gabrielle-Émilie le Tonnelier de Breteuil

Gabrielle-Émilie le Tonnelier de Breteuil

The

Marquise du Châtelet

, née

Gabrielle-Émilie le Tonnelier de Breteuil

(1706 - 1749) French mathematician and physicist. The daughter of an important functionary in King Louis XIV’s court, she was well-educated in languages, sciences, mathematics, arts and sports. Barely 20, she married the Marquis du Châtelet and bore him three children, possibly by other men. To educate her children, she wrote a textbook on physics and made a French

translation

of Isaac Newton’s

Philosophie naturalis principia mathematica

that is still used today. Her approximation

e

∼

m

⁢

v

2

(the energy

e

of a moving object is proportional to its mass

m

times the square of its velocity

v

) presaged Einstein’s equation

e

=

m

⁢

c

2

by a century and a half.

References

1

G. J. Tee “Gabrielle-Émilie le Tonnelier de Breteuil, Marquise du Châtelet” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 21 - 25

Title

Gabrielle-Émilie le Tonnelier de Breteuil

Canonical name

GabrielleEmilieLeTonnelierDeBreteuil

Date of creation

2013-03-22 16:41:52

Last modified on

2013-03-22 16:41:52

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A50

Synonym

Gabrielle-Émilie le Tonnelier de Breteuil

Synonym

Marquise du Chatelet

Synonym

Châtelet

Synonym

Chatelet

Synonym

Émilie Breteuil

Synonym

Emilie Breteuil

Synonym

Émilie du Châtelet

Synonym

Emilie du Chatelet

Generated on Thu Feb 8 19:09:01 2018 by

LaTeXML
Maria Gaetana Agnesi

Maria Gaetana Agnesi

Maria Gaetana Agnesi

(1718 - 1799) Italian linguist, mathematician and women’s rights activist, best known for her study of the versiera curve, nowadays known as the “

witch of Agnesi

” or Agnesi curve. Her

Instituzioni Analitiche

was one of the first mathematics books printed in Italian (although she could have as easily written it in Latin or Greek) and was of great use to many other mathematicians, Joseph-Louis Lagrange (in a French

translation

) among them. After the death of her father, she devoted herself to theology and charitable work.

References

1

H. Kennedy “Maria Gaetana Agnesi” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 1 - 5

Title

Maria Gaetana Agnesi

Canonical name

MariaGaetanaAgnesi

Date of creation

2013-03-22 16:35:50

Last modified on

2013-03-22 16:35:50

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

6

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A50

Generated on Thu Feb 8 19:09:02 2018 by

LaTeXML
Sophie Germain

Sophie Germain

Marie-Sophie Germain

(1776 - 1831) French mathematician. In her lifetime, she published some of her work as

Monsieur Le Blanc

and also carried on a correspondence with Carl Friedrich Gauss under that name. One of her first papers that she wrote using this pseudonym was submitted to Joseph-Louis Lagrange. After meeting Germain in person, he encouraged her and introduced her to various French mathematicians and scientists. Acquiring contacts in this manner was crucial for Germain to be able to progress in mathematics. The only other that Germain had for studying mathematics was by reading. She read mathematical books as well as lecture notes from various courses taught at École Polytechnique.

In 1816, Germain received the French Academy of Science Grand Prize. In 1831, Gauss recommended that Germain receive an honorary doctorate from Göttingen University, but she died before the could be conferred.

Germain made headway towards proving Fermat’s last theorem. Today she is best known for the

Sophie Germain primes

.

References

1

M. W. Gray “Sophie Germain” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 47 - 56

Title

Sophie Germain

Canonical name

SophieGermain

Date of creation

2013-03-22 16:17:43

Last modified on

2013-03-22 16:17:43

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

6

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A50

Classification

msc 01A55

Synonym

Marie-Sophie Germain

Synonym

Monsieur Le Blanc

Synonym

Monsieur LeBlanc

Generated on Thu Feb 8 19:09:04 2018 by

LaTeXML
Ada Lovelace

Ada Lovelace

Countess

Augusta Ada Lovelace

née

Augusta Ada Byron

(1815 - 1852) English mathematician, women’s activist, novelist and playwright.

Born in England of the poet Lord Byron and housewife Anne Isabella Milbanke. Taught by Mary Somerville, Ada later worked with Charles Babbage and married William King, the 1st Earl of Lovelace. More than a

hundred

years after her death, the Ada programming language was named in her honor.

References

1

K. D. Rappaport “Augusta Ada Lovelace” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 135 - 139

Title

Ada Lovelace

Canonical

name

AdaLovelace

Date of creation

2013-03-22 17:15:45

Last modified on

2013-03-22 17:15:45

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 01A55

Synonym

Augusta Ada Lovelace

Synonym

Countess of Lovelace

Generated on Thu Feb 8 19:09:06 2018 by

LaTeXML
Adams Prize

Adams Prize

The

Adams Prize

is a prize awarded by the University of Cambridge to a young mathematician working in the United Kingdom. Like the

Fields Medal

, age 40 is the specific cutoff for this prize.

These prizes were instituted in honor of the British mathematician John Couch Adams in 1850, soon after he discovered Neptune. Each year the prize committee chooses a specific field of mathematics and awards the prize to a mathematician working in that field.

Title

Adams Prize

Canonical

name

AdamsPrize

Date of creation

2013-03-22 16:59:25

Last modified on

2013-03-22 16:59:25

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A55

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Synonym

John Couch Adams Prize

Generated on Thu Feb 8 19:09:07 2018 by

LaTeXML
Allan Joseph Champneys Cunningham

Allan Joseph Champneys Cunningham

Allan Joseph Champneys Cunningham

(1842 - 1928) British mathematician born in India, best known for researching the factorizations of large

Mersenne numbers

and

Fermat numbers

. In

connection

to these he also studied

cuban primes

. The Cunningham project was named in his honor.

Title

Allan Joseph Champneys Cunningham

Canonical name

AllanJosephChampneysCunningham

Date of creation

2013-03-22 16:25:33

Last modified on

2013-03-22 16:25:33

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

A. J. C. Cunningham

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

LaTeXML
American Mathematical Society

American Mathematical Society

The

American Mathematical Society

(AMS) is an association of professional mathematicians in the

United States

. Best known as the inventor of the

Mathematics Subject Classification

codes used by many math journals and

PlanetMath

, the AMS is a staunch advocate of TeX and LaTeX. The AMS publishes

Mathematical Reviews

.

Originally called the New York Mathematical Society, the AMS was founded in 1888 by Thomas Fiske upon returning to the New York after attending a meeting of the

London Mathematical Society

. In 1894 the name was changed to the American Mathematical Society and later on the headquarters were moved to Providence, Rhode Island, and offices were added in Ann Arbor, Michigan, and Washington D.C.

Today, the AMS has more than 550 institutional members and almost thirty

thousand

individual members, and does much to support young people studying mathematics.

One of four partners of the Joint Policy Board for Mathematics, the AMS should not be confused with the

Mathematical Association of America

. The official website of the AMS is

http://www.ams.org/

www.ams.org.

Title

American Mathematical Society

Canonical

name

AmericanMathematicalSociety

Date of creation

2013-03-22 16:42:04

Last modified on

2013-03-22 16:42:04

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Definition

Classification

msc 01A55

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Generated on Thu Feb 8 19:09:14 2018 by

LaTeXML
André Bloch

André Bloch

André Bloch

(1893 - 1948) French mathematician perhaps best known for Bloch’s theorem on holomorphic disks (not to be confused with Felix Bloch’s theorem on eigenfunctions of periodic particle wavefunctions).

In 1914, André Bloch briefly served in the French Army during World War I. Three years later, Bloch killed three relatives and was confined to a mental institution. From there he collaborated by mail with important mathematicians such as

Jacques Hadamard

and George Pólya. In 1948, Bloch was awarded the Becquerel Prize.

Title

André Bloch

Canonical name

AndreBloch

Date of creation

2013-03-22 16:23:58

Last modified on

2013-03-22 16:23:58

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Andre Bloch

Generated on Thu Feb 8 19:09:16 2018 by

LaTeXML
Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi

(1804 - 1851) Jewish-German mathematician best known for the Jacobian matrix and the

Jacobi symbol

.

The second son of a successful banker, young Carl was home-schooled until the age of 12, when he entered the Potsdam high school. Four years after earning a degree from Berlin University in 1825 and converting to Catholicism, Jacobi became a mathematics professor there and taught for a dozen years. He read Greek and Latin fluently, and was quite familiar with the work of Leonhard Euler (

http://

planetmath

.org/EulerLeonhard

). In the late 1820s, Jacobi did significant work on

elliptic functions

in relation to

fractions

, attracting the interest and praise of Carl Friedrich Gauss (

http://planetmath.org/CarlFriedrichGauss

) and

Adrien-Marie Legendre

. In 1843, Jacobi went on a vacation to Italy, beginning his retirement.

A lunar crater is named after Jacobi.

Title

Carl Gustav Jacob Jacobi

Canonical name

CarlGustavJacobJacobi

Date of creation

2013-03-22 16:49:51

Last modified on

2013-03-22 16:49:51

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Synonym

Jacques Simon Jacobi

Generated on Thu Feb 8 19:09:17 2018 by

LaTeXML
Carl Størmer

Carl Størmer

Carl Størmer

(1874 - 1957) Norwegian physicist, mathematician and historian, best known for his atmospherical research, particularly his work on the aurora borealis. He collaborated with Ludvig Sylow and Elling Holst on the published correspondence of

Niels Henrik Abel

.

In mathematics, Størmer is known for Størmer’s theorem and the Størmer numbers (

http://

planetmath

.org/StormerNumber

).

References

1

Joseph Warren Dauben & Christoph J. Scriba,

Writing the History of Mathematics: Its Historical Development

. Basel: Birkhäuser (2002): 153

Title

Carl Størmer

Canonical name

CarlStormer

Date of creation

2013-03-22 17:52:36

Last modified on

2013-03-22 17:52:36

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Carl Stormer

Synonym

Carl Störmer

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

LaTeXML
Christine Ladd-Franklin

Christine Ladd-Franklin

Christine Ladd-Franklin

nèe

Christine Ladd

(1847 - 1930) American mathematician and educator.

Born in Connecticut of a merchant and the daughter of officeholders, young Christine started her studies at Portsmouth and then Wesleyan in Massachusetts, and was among the first students of the newly opened Vassar College. There she focused on linguistics and physics. After graduation she was not surprised to find that women were not granted much access to labs and observatories, so “she took up, as the next best subject, mathematics, which could be carried on without any apparatus.” Ladd taught and published articles on various topics. Thanks to

James Joseph Sylvester

, Ladd was able to study at John Hopkins, where she married a mathematics professor who taught there, Fabian Franklin, and bore him two children. The son did not survive infancy, but the daughter, Margaret Ladd Franklin grew up to be a major scholar in the women’s suffrage movement. At the end of the 19th Century, Ladd-Franklin wrote extensively on the mathematics of optics. In 1926, decades after her doctoral work at John Hopkins, she was finally given the she had earned. In the time prior, she helped many women go on to grad work.

References

1

J. Green “Christine Ladd-Franklin” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 121 - 128

Title

Christine Ladd-Franklin

Canonical name

ChristineLaddFranklin

Date of creation

2013-03-22 17:15:10

Last modified on

2013-03-22 17:15:10

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Christine Ladd

Synonym

Christine Franklin

Synonym

Mrs. Fabian Franklin

Generated on Thu Feb 8 19:09:21 2018 by

LaTeXML
Claribel Kendall

Claribel Kendall

Claribel Kendall

(1889 - 1965) American mathematician and educator.

Born in Colorado to a former lawyer and a housewife, Claribel obtained undergraduate and graduate degrees from the University of Colorado, joining the mathematics faculty in 1913. In 1917 she helped found the Rocky Mountain Section of the

Mathematical Association of America

. In 1944 the University of Colorado gave her the title of full professor, she had been instrumental in boosting the

percentage

of women earning master’s degrees in mathematics. Kendall lived for a few years after retirement. After her death, the Phi Beta Kappa of the school started giving awards named in her honor.

References

1

R. R. Struik “Claribel Kendall” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 92 - 94

Title

Claribel Kendall

Canonical

name

ClaribelKendall

Date of creation

2013-03-22 17:05:33

Last modified on

2013-03-22 17:05:33

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Generated on Thu Feb 8 19:09:23 2018 by

LaTeXML
David Hilbert

David Hilbert

David Hilbert

(1862 - 1943) German mathematician, perhaps best known for

Hilbert space

and Hilbert’s problems. He also did much to axiomatize

geometry

and pondered philosophical questions of infinity with Georg Cantor and Kurt Gödel. Hilbert has Erdős number 4.

Title

David Hilbert

Canonical name

DavidHilbert

Date of creation

2013-03-22 16:34:17

Last modified on

2013-03-22 16:34:17

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Generated on Thu Feb 8 19:09:24 2018 by

LaTeXML