aarjaneiro/planetmath huggingface dataset:
Ellen Hayes

Ellen Hayes

Ellen Amanda Hayes

(1851 - 1930) American mathematician, astronomer, labor rights activist and suffragist.

Born of a Union Army officer and a teacher, Ellen was as a child as interested in literature, sports and politics as she was in gardening. Admitted to Oberlin College in 1872, Hayes focused her studies on science and mathematics, but did not neglect to study history and literature. After graduating, Hayes briefly taught at Adrian College but soon moved to Wellesley College. In 1888, Hayes worked at the University of Virginia’s McCormick Observatory, calculating the orbit of the newly discovered asteroid 267 Tirza, and developed equations to calculate shadows of asteroids and other heavenly bodies. At Wellesley in 1897 appointed head of the applied mathematics department. Her colleagues questioned her admissions policies and complained her

trigonometry

textbook caused many students to get low grades. She was demoted, and after retiring in 1916, was denied the title professor emeritus. She intensified her activist activities.

References

1

A. Moskol “Ellen Amanda Hayes” in

Women of Mathematics: A Bibliographic Sourcebook

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

Title

Ellen Hayes

Canonical name

EllenHayes

Date of creation

2013-03-22 17:00:44

Last modified on

2013-03-22 17:00:44

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Amanda Hayes

Synonym

Ellen Amanda Hayes

Generated on Thu Feb 8 19:09:26 2018 by

LaTeXML
Farkas Bolyai

Farkas Bolyai

Farkas Bolyai

(1775 - 1856) Hungarian mathematician, father of János Bolyai. Educated by Calvinists, young Farkas’s talent for

arithmetic

was recognized early on, and soon he was tutoring the children of nobility in mathematics. This opened up and opportunity for him to study mathematics more rigorously in Jena and Göttingen. Upon returning to Hungary, Bolyai married Zsuzsanna Benkö, who bore him János. Bolyai spent the rest of his life teaching mathematics to Calvinists in Hungary.

Title

Farkas Bolyai

Canonical

name

FarkasBolyai

Date of creation

2013-03-22 16:32:21

Last modified on

2013-03-22 16:32:21

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

5

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A50

Synonym

Wolfgang Bolyai

Synonym

Bolyai Farkas

Generated on Thu Feb 8 19:09:31 2018 by

LaTeXML
Friedrich Bessel

Friedrich Bessel

Friedrich Wilhelm Bessel

(1784 - 1846) German astronomer and mathematician, perhaps best known for the

Bessel function

.

As a teenager, he was apprenticed to a merchant and soon became his accountant. As the merchant did a lot of business with ships, Bessel developed an interest in astronomy. After publishing tables of atmospheric refraction, Bessel came up with the idea of using the parallax effect to measure the

distance

from the Earth to a star on the sky. In recognition of his achievements in astronomy, an asteroid was named after him.

Title

Friedrich Bessel

Canonical name

FriedrichBessel

Date of creation

2013-03-22 16:33:12

Last modified on

2013-03-22 16:33:12

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Synonym

Friedrich Wilhelm Bessel

Generated on Thu Feb 8 19:09:33 2018 by

LaTeXML
Georg Frobenius

Georg Frobenius

Ferdinand Georg Frobenius

(1849 - 1917) German mathematician, best known for being the first to prove the

Cayley-Hamilton theorem

. Several different mathematical concepts now bear his name, including the Frobenius algebra, various Frobenius morphisms, the

Frobenius map

, the Frobenius group, the

Frobenius inequality

, etc.

Born in Charlottenburg, Frobenius earned a doctorate at the University of Berlin for his thesis on

differential equations

with Karl Weierstraß (

http://

planetmath

.org/KarlWeierstrass

) as his advisor. After that he taught mathematics in Berlin and Zürich, and researched group theory (proving the existence of Sylow groups) and

number theory

. In the lead-up to World War I, Frobenius began investigating matrices. He died in Berlin in 1917 and was buried there.

Title

Georg Frobenius

Canonical

name

GeorgFrobenius

Date of creation

2013-03-22 17:24:45

Last modified on

2013-03-22 17:24:45

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

7

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Ferdinand Georg Frobenius

Generated on Thu Feb 8 19:09:35 2018 by

LaTeXML
Giuseppe Peano

Giuseppe Peano

Giuseppe Peano

(1858 - 1932) Italian mathematician, linguist and author, perhaps best known for the

Peano curve

.

Born in Piedmont, Peano studied at the university in Turin. After graduating, Peano ghostwrote a calculus textbook for Angelo Genocchi. In his first book published under his own name, Peano introduced our modern symbols for set union and set

intersection

. Work on a

Formulario

, a comprehensive encyclopedia of mathematical

formulas

, led him to invent a new

language

in which he sought to do for Latin what Ludwig Zamenhof was trying to do with Esperanto. The final edition of

Formulario

was written in the language he invented.

Title

Giuseppe Peano

Canonical name

GiuseppePeano

Date of creation

2013-03-22 16:32:35

Last modified on

2013-03-22 16:32:35

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 19:09:37 2018 by

LaTeXML
Helen Merrill

Helen Merrill

Helen Abbot Merrill

(1864 - 1949) American mathematician, educator and textbook author. Not related to the jazz singer Helen Merrill.

Born in New Jersey of an insurance claims adjuster and a housewife, and raised in Massachusetts, her family tree included colonial settlers. Young Helen’s formal education started at a high school in Massachusetts, and after graduating went to Wellesley College, where she intended to major in Greek and Latin. Unusually, the mathematics faculty at the college consisted mostly of women, including

Ellen Hayes

, and before completing her first years, Helen Merrill had decided to major in mathematics instead of languages. In 1893 she began teaching at Wellesley while also studying and guest lecturing abroad. In 1920 she was appointed vice-president of the

Mathematical Association of America

. Upon her retirement from Wellesley, she was given the title Professor Emerita. In addition to textbooks for use at Wellesley, Merrill also wrote as a popularizer a book titled

Mathematical Excursions

in 1933.

References

1

C. Henrion “Helen Abbot Merrill” in

Women of Mathematics: A Bibliographic Sourcebook

L. Grinstein, P. Cambpell, ed.s New York: Greenwood Press (1987): 147 - 151

Title

Helen Merrill

Canonical name

HelenMerrill

Date of creation

2013-03-22 17:20:15

Last modified on

2013-03-22 17:20:15

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Helen Abbot Merrill

Generated on Thu Feb 8 19:09:38 2018 by

LaTeXML
history of mathematics in the United States of America

history of mathematics in the United States of America

The

United States of America

By necessity, the leading intellectuals of the insurgency era were Renaissance men who dabbled in various arts and sciences, a far cry from today’s mathematician who specializes in one . So, for example,

Benjamin Franklin

was well-versed in various astronomical computations, but he also studied

magic squares

, such as the

Franklin magic square

, and he conducted some of the earliest experiments in electrodynamics and had a hand in the founding of many important American government agencies.

geometry

of circles and spheres.

In 1888, Thomas Fiske founded the New York Mathematical Society, later renamed the

American Mathematical Society

.

Albert Einstein

,

John von Neumann

, Enrico Fermi, Hans Albrecht Bethe and Edward Teller (Ede Teller). Many of them helped in the war effort, with cryptographers forming a signficant portion of the American mathematicians working during the war.

In 1950, by of Congress, the

National Science Foundation

was founded.

For the second half of the 20th Century, the United States had significantly more native-born prominent specializing mathematicians than in the past:

Carl Pomerance

, William Fulton and John Cocke to name just a few.

Title

history of mathematics in the United States of America

Canonical name

HistoryOfMathematicsInTheUnitedStatesOfAmerica

Date of creation

2013-03-22 16:53:11

Last modified on

2013-03-22 16:53:11

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

11

Author

PrimeFan (13766)

Entry type

Topic

Classification

msc 01A55

Classification

msc 01A60

Classification

msc 01A61

Classification

msc 01A65

Classification

msc 01A50

Classification

msc 01A45

Synonym

United States

Synonym

United States of America

Generated on Thu Feb 8 19:09:43 2018 by

LaTeXML
Hjalmar Mellin

Hjalmar Mellin

Robert Hjalmar Mellin (1854–1933), a Finnish function-theorist. He studied in Helsinki University under Gösta Mittag-Leffler, in Berlin under

Karl Weierstrass

and

Leopold Kronecker

. He worked as professor of mathematics in the Helsinki Polytechnic Institute (later the Technical University of Finland).

Mellin is best known for his

integral transform

, the

Mellin transform

(

http://

planetmath

.org/MellinTransform

)

F

⁢

(

s

)

:=

∫

0

∞

t

s

-

1

⁢

f

⁢

(

t

)

⁢

𝑑

t

,

which he utilised in study of

gamma function

,

hypergeometric functions

,

Dirichlet series

,

Riemann zeta function

and related number-theoretic functions. Mellin’s transform and its

inverse

transform

f

⁢

(

t

)

=

1

2

⁢

π

⁢

i

⁢

∫

a

-

i

⁢

∞

a

+

i

⁢

∞

t

-

z

⁢

F

⁢

(

z

)

⁢

𝑑

z

are much used also in physics. Mellin himself applied his

transformations

for solving

partial differential equations

and the inverse transformations for forming

asymptotic series

expansions

.

Mellin has addressed of relativity.

Title

Hjalmar Mellin

Canonical name

HjalmarMellin

Date of creation

2015-02-17 14:49:42

Last modified on

2015-02-17 14:49:42

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

8

Author

pahio (2872)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Mellin

Related topic

MellinsInverseFormula

Generated on Thu Feb 8 19:09:45 2018 by

LaTeXML
Ivan Pervushin

Ivan Pervushin

Ivan Mikheevich Pervushin

(1827 - 1900) Russian priest and mathematician, best known for finding factors of the

Fermat numbers

2

2

12

+

1

and

2

2

23

+

1

and finding the ninth

Mersenne prime

,

2

61

-

1

.

Born in Perm, he studied to be a priest in Kazan and later moved to practice in Zamaraevo. When Pervushin was not saying Mass, he devoted himself to studying

number theory

. It was in Zamaraevo that Pervushin pondered Marin Mersenne’s list of prime numbers of the form

2

p

-

1

and discovered that Mersenne was mistaken to exclude 61, for 2305843009213693951 is in fact prime. Today

computers

can verify this practically instantaneously, but in Pervushin’s day, it took Hudelot 54 hours in 1887 to confirm Pervushin’s result, performing the

Lucas-Lehmer primality test

by hand.

The same year that Pervushin discovered the ninth Mersenne prime, he visited Shadrinsk and wrote an article critical of the government there. The government exiled him to Mehonskoe, where he spent the rest of his life. Still, the ninth Mersenne prime, the largest

prime number

known at the time, was for a while known as “Pervushin’s number.”

References

1

Eric Bach & Jeffrey Shallit,

Algorithmic Number Theory: Volume 1: Efficient Algorithms

. Cambridge: MIT Press (1996): 7

Title

Ivan Pervushin

Canonical

name

IvanPervushin

Date of creation

2013-03-22 18:04:53

Last modified on

2013-03-22 18:04:53

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

5

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Synonym

Ivan Mikheevich Pervushin

Generated on Thu Feb 8 19:09:47 2018 by

LaTeXML
James Joseph Sylvester

James Joseph Sylvester

James Joseph Sylvester

(1814 - 1897) British mathematician, poet and author, best known for Sylvester’s

sequence

and for coining mathematical terms, some of which are still in use today (such as “

totient

” and “

totative

”).
Together with Arthur Cayley, he invented the theory of subject of invariant theory, which became one of the
most actively studied branches of algebra during the nineteenth century.

Born in England of a Jewish family, Sylvester studied in England and Scotland, and taught in the

United States

. He also studied law.

References

1

R. C. Archibald, “James Joseph Sylvester”,

Studies and Essays in the History of Science and Learning Offered in Homage to George Sarton on the Occasion of his Sixtieth Birthday

. New York: H. Schuman (1947): 209 - 217

2

L. S. Feuer, “Sylvester in Virginia”

The Mathematical Intelligencer

9

(1987): 13 - 20

3

K. H. Parshall,

James Joseph Sylvester: Jewish Mathematician in a Victorian World

. Baltimore: The Johns Hopkins University Press (2006)

Title

James Joseph Sylvester

Canonical name

JamesJosephSylvester

Date of creation

2013-03-22 18:20:12

Last modified on

2013-03-22 18:20:12

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

6

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Generated on Thu Feb 8 19:09:49 2018 by

LaTeXML
János Bolyai

János Bolyai

János Bolyai

(1802 - 1860) Hungarian mathematician, son of

Farkas Bolyai

. In the 1820s, János studied in Vienna, where he developed a keen interest in Euclid’s

parallel postulate

, to the dismay of his father. By 1832, however, Farkas acknowledged his son’s innovations in the field and published them as an appendix to his textbook. He accomplished a lot in the advancement of the study of

non-Euclidean geometry

. A 135 km crater on the moon is named after János Bolyai.

Title

János Bolyai

Canonical name

JanosBolyai

Date of creation

2013-03-22 16:32:45

Last modified on

2013-03-22 16:32:45

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

6

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Synonym

Janos Bolyai

Synonym

Bolyai János

Synonym

Bolyai Janos

Generated on Thu Feb 8 19:09:50 2018 by

LaTeXML
Joseph Bertrand

Joseph Bertrand

Joseph Louis-François Bertrand

(1822 - 1900) French mathematician, economist and translator who translated Carl Friedrich Gauss’s books to French. Bertrand is perhaps best known for Bertrand’s

conjecture

regarding the distribution of prime numbers between a given integer and its double.

In 1884 he took over seat 40 of the Academie Française for Jean-Baptiste Dumas. Upon his death, Bertrand’s seat was given to Marcellin Berthelot.

Title

Joseph Bertrand

Canonical

name

JosephBertrand

Date of creation

2013-03-22 16:24:21

Last modified on

2013-03-22 16:24:21

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Synonym

Joseph Louis-François Bertrand

Synonym

Joseph Louis-Francois Bertrand

Generated on Thu Feb 8 19:09:52 2018 by

LaTeXML
Joseph Liouville

Joseph Liouville

Joseph Liouville

(1809 – 1882) was a French mathematician, editor and author who proved that

∑

i

=

1

∞

1

10

i

!

is a

transcendental number

(that is 0.11000100000000000000…  and sometimes called the “basic

Liouville number

”).

After graduating from the École Polytechnique, Liouville taught at several places before getting a job teaching at his old

alma mater

. He was pen pals with Christian Goldbach and Daniel Bernoulli. Liouville tried to prove that the

natural log base

e

is transcendental. Though he did not succeed in this, he did prove in 1844 that transcendental numbers exist, and gave the aforementioned Liouville number as an example. This paved the way for other mathematicians to prove the transcendality of

e

and other important

irrational

constants. Liouville also introduced the

Liouville function

λ

⁢

(

n

)

=

(

-

1

)

Ω

⁢

(

n

)

(equal in value to the Möbius

function

μ

⁢

(

n

)

when

n

is

squarefree

).

Liouville wrote many papers as well as edited the writings of Évariste Galois and started the

Journal de Mathématiques Pures et Appliquées

that is still published today. A lunar crater near Dubyago is named after him.

Title

Joseph Liouville

Canonical name

JosephLiouville

Date of creation

2013-03-22 17:16:52

Last modified on

2013-03-22 17:16:52

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

6

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Related topic

DecimalExpansion

Generated on Thu Feb 8 19:09:54 2018 by

LaTeXML
Joseph Wedderburn

Joseph Wedderburn

Joseph Henry Maclagen Wedderburn

(1882 - 1948) Scottish mathematician, perhaps best known for the

Wedderburn-Artin theorem

and his paper on

hypercomplex numbers

. He also worked on

graph theory

and the

Wedderburn-Etherington numbers

are named after him.

Trained mainly in Scotland, Wedderburn also studied briefly in Germany and America, where he worked with Leonard Dickson. Wedderburn began teaching at Princeton University before World War I, during which time he served in the British Army. After the war, he resumed teaching at Princeton and began editing

Annals of Mathematics

.

Title

Joseph Wedderburn

Canonical name

JosephWedderburn

Date of creation

2013-03-22 16:17:05

Last modified on

2013-03-22 16:17:05

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Classification

msc 01A60

Synonym

Joseph Henry Maclagen Wedderburn

Synonym

Joe Wedderburn

Related topic

WedderburnsTheorem

Generated on Thu Feb 8 19:09:56 2018 by

LaTeXML
Karl Weierstraß

Karl Weierstraß

Karl Theodor Wilhelm Weierstraß

(often

Karl Theodor Wilhelm Weierstrass

in English texts) (1815 - 1897) German mathematician, the father of modern analysis.

Born in Ostenfelde, of a government official from Paderborn, young Karl showed an aptitude for mathematics but his father intended for him to follow in his footsteps to a career in public office. The son went to the University of Bonn to study law and economics but focused his attention on mathematics to the of ignoring the requirements of the his father intended him to obtain. Karl left Bonn for Münster and studied

elliptic functions

extensively. After being appointed chairman at an university in Berlin, Karl Weierstraß proved the fundamental calculus notion of the limit, regaining Bernard Bolzano’s forgotten results in the famous Bolzano-Weierstraß theorem (

http://

planetmath

.org/BolzanoWeierstrassTheorem

). Several other important calculus notions bear Weierstraß’s name.

Title

Karl Weierstraß

Canonical name

KarlWeierstrass

Date of creation

2013-03-22 17:06:40

Last modified on

2013-03-22 17:06:40

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

7

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Synonym

Karl Theodor Wilhelm Weierstraß

Synonym

Karl Theodor Wilhelm Weierstrass

Synonym

Karl Weierstrass

Generated on Thu Feb 8 19:09:57 2018 by

LaTeXML
Leopold Kronecker

Leopold Kronecker

Leopold Kronecker

(1823 - 1891) German mathematician, famous for saying “God created the

integers

, all else is the work of man.” Concepts named after him include the

Kronecker symbol

and the

Kronecker product

.

Born to Jewish parents in what is now Legnica, Poland, Kronecker studied with Ernst Eduard Kummer there, and later at the university in Berlin with Peter Gustav Dirichlet. After earning a doctorate, rather than teach at the university, Kronecker returned to his birthplace and put his mathematical knowledge to practical use in the family business, becoming quite wealthy in

addition

to his family inheritance. In the 1850s he published a lot of papers which were quite influential and gained him acceptance to various societies, starting with the Berlin Academy.

Being a member of the Berlin Academy, Kummer persuaded Kronecker to take advantage of his privilege of being able to lecture at the university. Not many students showed up to his lectures, so when he was offered a position at Göttingen, he declined. It wasn’t until 1883 that Kronecker began teaching as a professor, at his old alma mater. There he taught Franz Mertens and Kurt Hensel, to name just a few. In 1880, Kronecker became editor of

Crelle’s Journal

. A year before his death, Kronecker converted to Lutheranism.

References

1

James Tanton,

Encyclopedia of Mathematics

. New York: Facts on File Library (2005):296 - 297

Title

Leopold Kronecker

Canonical name

LeopoldKronecker

Date of creation

2013-03-22 18:15:23

Last modified on

2013-03-22 18:15:23

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Biography

Classification

msc 01A55

Generated on Thu Feb 8 19:09:59 2018 by

LaTeXML
Lewis Carroll

Lewis Carroll

Charles Lutwidge Dodgson

(January 27, 1832 - January 14, 1898), better known by the pen name

Lewis Carroll

, was an English author, mathematician, logician, Anglican clergyman, and photographer.

His most famous writings are

Alice’s Adventures in Wonderland

and its sequel

Through the Looking-Glass

as well as the poems “The Hunting of the Snark” and “Jabberwocky”, all usually assessed to be within the genre of literary nonsense. However, amid the nonsense there are hints of an interest in mathematics, which prompted mathematician Martin Gardner to publish

The Annotated Alice

.

There is an urban legend that Queen Victoria, having enjoyed one of Carroll’s children’s books, wrote to him graciously suggesting that he dedicate his next book to her. Carroll, according to the story, obligingly did so dedicate it, but the work happened to be a mathematical opus (which did not amuse her) entitled

An Elementary Treatise on

Determinants

. Although he did write a work with that title, he did not dedicate it to anyone in particular.

His early academic career veered between high-octane promise and irresistible distraction. He may not always have worked hard, but he was exceptionally gifted and achievement came easily to him. In 1852 he received a first in Honour Moderations, and shortly after he was nominated to a Studentship, by his father’s old friend Canon Edward Pusey. However, a little later he failed an important scholarship through his self-confessed inability to apply himself to study. Even so, his talent as a mathematician won him the Christ Church Mathematical Lectureship, which he continued to hold for the next twenty-six years. The income was good, but the work bored him. Many of his pupils were older and richer than he was, and almost all of them were uninterested. However, despite early unhappiness, Dodgson was to remain at Christ Church, in various capacities, until his death.

There are societies dedicated to the enjoyment and promotion of his works and the investigation of his life in many parts of the world including North America, Japan, the United Kingdom, and New Zealand.

This entry was adapted from the

Wikipedia

article

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

Lewis Carroll as of May 16, 2007.

Title

Lewis Carroll

Canonical name

LewisCarroll

Date of creation

2013-03-22 17:05:42

Last modified on

2013-03-22 17:05:42

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Biography

Classification

msc 01A55

Synonym

Charles Lutwidge Dodgson

Generated on Thu Feb 8 19:10:01 2018 by

LaTeXML