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<title>Beginnings of Modern Algebra</title>
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<H1>Cubic Equations</H1>

<H2>Ferro </H2>

Biography in Dictionary of Scientific Biography


<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Ferro.html">
MACTUTOR<a/>. 
Scipione del Ferro
<br/>
Born: 6 Feb 1465 in Bologna, Italy
<br/>
Died: 5 Nov 1526 in Bologna, Italy
<br>
Summary: 
Scipione del Ferro was an Italian mathematician who is famous for being the first to find a formula to solve a cubic equation.


<p/>
<a href="http://en.wikipedia.org/wiki/Scipione_del_Ferro">
WIKI<a/>.
Scipione del Ferro (February 6, 1465 – November 5, 1526)
<br/>
Summary: 
Italian mathemtatician who first discovered a means to solve cubic equations.


<H2>Tartaglia</H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9071334">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9071334">Academic Edition<a/>,
requires campus password)

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Tartaglia.html">
MACTUTOR<a/>. 
Nicolo Fontana Tartaglia
<br/>
Born: 1500 in Brescia, Republic of Venice (now Italy)
<br/>
Died: 13 Dec 1557 in Venice, Republic of Venice (now Italy)
<br>
Summary: 
Italian mathematician.
Famed for his algebraic solution of cubic equations which was eventually published in 
Cardan's <i>Ars Magna</i>.

<p/>
<a href="http://www.britannica.com/eb/article-9071334">
BRITANNICA<a/>. 
Niccolò Fontana Tartagli
<br/>
Born: 1499, Brescia, republic of Venice [Italy]
<br/>
Died: Dec. 13, 1557, Venice
<br/>
also spelled  Tartalea
<br/>
Summary:
 Italian mathematician who originated the science of ballistics.

<p/>
<a href="http://en.wikipedia.org/wiki/Tartaglia">
WIKI<a/>.
Niccolò Fontana Tartaglia (1499, Brescia, Italy–December 13, 1557, Venice, Italy)
<br/>
Summary: 
Mathematician, an engineer (designing fortifications), 
surveyor (of topography, seeking the best means of defense or offense) 
and bookkeeper from the then-Republic of Venice (now part of Italy). 
Published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. 
The first to apply mathematics to the investigation of the paths of cannonballs; his work was later validated by Galileo's studies on falling bodies.

<p/>
<img src="http://upload.wikimedia.org/wikipedia/en/0/0b/Niccol%C3%B2_Tartaglia.jpg" height="400" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Tartaglia.jpeg"
height="300"/>


<H2>Cardano </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9020283">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9020283">Academic Edition<a/>,
requires campus password)
<br>Crater Cardanus and Rima Cardanus</br>

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Cardan.html">
MACTUTOR<a/>. 
Girolamo Cardano
<br/>
Born: 24 Sept 1501 in Pavia, Duchy of Milan (now Italy)
<br/>
Died: 21 Sept 1576 in Rome (now Italy)
<br>
Summary: 
Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learnt from Tartaglia.

<p/>
<a href="http://www.britannica.com/eb/article-9020283">
BRITANNICA<a/>. 
Girolamo Cardano
<br/>
Born: September 24, 1501, Pavia, duchy of Milan [Italy]
<br/>
Died: September 21, 1576, Rome
<br/>
also Girolamo also spelled  Gerolamo , English  Jerome Cardan
<br/>
Summary:
Italian physician, mathematician, and astrologer.
Gave the first clinical description of typhus fever.
His book <i>Ars magna</i> (The Great Art; or, The Rules of Algebra) 
is one of the cornerstones in the history of algebra.

<p/>
<a href="http://en.wikipedia.org/wiki/Cardano">
WIKI<a/>.
Gerolamo Cardano or Girolamo Cardano, in English Jerome Cardan, or in Latin Hieronymus Cardanus (September 24, 1501 - September 21, 1576) 
<br/>
Summary: 
Celebrated Italian Renaissance mathematician, physician, astrologer, and gambler.

<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Cardan_5.jpeg"
height="400"/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Cardan.jpeg"
height="400"/>
<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Cardan_6.jpeg"
height="300"/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Cardan_4.jpeg"
height="300"/>


<H2>Lodovico Ferrari </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9034087">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9034087">Academic Edition<a/>,
requires campus password)

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Ferrari.html">
MACTUTOR<a/>. 
Lodovico Ferrari
<br/>
Born: 2 Feb 1522 in Bologna, Papal States (now Italy)
<br/>
Died: 5 Oct 1565 in Bologna, Papal States (now Italy)
<br>
Summary: 
Ferrari was an Italian scholar who started as Cardan's secretary and went on to devise the solution of the quartic equation.

<p/>
<a href="http://www.britannica.com/eb/article-9034087">
BRITANNICA<a/>. 
Lodovico Ferrari
<br/>
Born: Feb. 2, 1522, Bologna, Papal States [Italy]
<br/>
Died: Oct. 5, 1565, Bologna
<br/>
also spelled  Ludovico Ferraro
<br/>
Summary:
Italian mathematician.
The first to find an algebraic solution to the or quartic equation.

<p/>
<a href="http://en.wikipedia.org/wiki/Lodovico_Ferrari">
WIKI<a/>.
Lodovico Ferrari (February 2, 1522 – October 5, 1565)
<br/>
Summary: 
Italian mathematician.
Began his career as the servant of Gerolamo Cardano. 
Extremely bright, so Cardano started teaching him mathematics. 
Aided Cardano on his solutions for quadratic equation and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published. 
While still in his teens, was able to obtain a prestigious teaching post after Cardano 
resigned from it and recommended him. 
Retired young (only 42) and quite rich. 
Moved back to his home town to take up a professorship of mathematics in 1565. 
Shortly thereafter, he died of white arsenic poisoning, allegedly murdered by his sister.


<H2>Bombelli </H2>

Biography in Dictionary of Scientific Biography
<br/>
Crater Bombelli

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Bombelli.html">
MACTUTOR<a/>. 
NAME
<br/>
Born: Jan 1526 in Bologna, Italy
<br/>
Died: 1572 in (probably) Rome, Italy
<br>
Summary: 
Rafael Bombelli was an Italian mathematician who wrote an influencial algebra text and made free use of both negative numbers and complex numbers.

<p/>
<a href="http://en.wikipedia.org/wiki/Bombelli">
WIKI<a/>.
Rafael Bombelli (1526–1573) born in Bologna.
<br/>
Summary: 
Italian mathematician.
Author of a treatise on algebra.
A central figure in the understanding of imaginary numbers. 

<p/>
<a href="http://galileo.rice.edu/Catalog/NewFiles/bombelli.html">
The Galileo Project<a/>. 

<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Bombelli.jpeg"
height=
"350" />


<H1>Cossic Artists</H1>

<H2>Nicolas Chuquet </H2>

Biography in Dictionary of Scientific Biography
<br/>
Paris street: Rue Nicolas Chuquet (17th Arrondissement)

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Chuquet.html">
MACTUTOR<a/>. 
NAME
<br/>
Born: 1445 in Paris, France
<br/>
Died: 1488 in Lyon, France
<br>
Summary: 
Nicolas Chuquet was a French mathematician who wrote the earliest French algebra book.

<p/>
<a href="http://en.wikipedia.org/wiki/Nicolas_Chuquet">
WIKI<a/>.
Nicolas Chuquet (born 1445 (some sources say c. 1455) in Paris, France; died 1488 (some sources say c. 1500) in Lyon, France)
<br/>
Summary: 
French mathematician.
His great work, <i>Triparty en la science des nombres</i>, unpublished in his lifetime. 
Most of it, however, was copied without attribution by Estienne de La Roche in his 1520 textbook, <i>Larismetique</i>. 
In the 1870s, scholar A Aristide Marre discovered Chuquet's manuscript and published it in 1880. 
The manuscript contained notes in de la Roche's handwriting.
Chuquet's thinking was brilliant and far ahead of its time. 
He invented his own notation for algebraic concepts and exponentiation. 
May have been the first mathematician to recognize zero and negative numbers as exponents.

<H2>Pacioli </H2>

Biography in Dictionary of Scientific Biography

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Pacioli.html">
MACTUTOR<a/>. 
Luca Pacioli
<br/>
Born: 1445 in Sansepolcro, Italy
<br/>
Died: 1517 in Sansepolcro, Italy
<br>
Summary: 
Italian mathematician.
Published the influential book 
<i>Suma</i> in 1494 giving a summary of all the mathematics known at that time.


<p/>
<a href="http://en.wikipedia.org/wiki/Pacioli">
WIKI<a/>.
Luca Pacioli
<br/>
Fra Luca Bartolomeo de Pacioli (sometimes Paciolo) (1445–1514 or 1517) 
<br/>
He was also called Luca di Borgo after his birthplace, Borgo Santo Sepolcro, Tuscany.
<br/>
Summary: 
Italian mathematician and Franciscan friar.
Collaborator with Leonardo da Vinci.
Seminal contributor to the field now known as accounting.  


<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Pacioli.jpeg"
height="250"/>

<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Pacioli_2.jpeg"
height="250"/>

<p/>
<img src="http://upload.wikimedia.org/wikipedia/commons/2/2a/Pacioli.jpg"
height="550"/>

<p/>
The painting <i>Ritratto di Frà Luca Pacioli</i> (1495) now in Naples.
Painter unknown (perhaps Jacopo de' Barbari).
In the painting Pacioli is demonstrating a theorem by Euclid.
Table  with
geomerical tools: slate, chalk, compass, a dodecahedron.
A rhombicuboctahedron half-filed with water is hanging to his right.

<p/>
<img src="http://upload.wikimedia.org/wikipedia/commons/1/18/Leonardo_polyhedra.png"
height="450"/>
<p/>
Woodcut 
by Leonardo da Vinci for <i>the Divina Proportione</i> by Luca Pacioli 1509.
A rhombicuboctahedron, 
an 
Archimedean solid. F=26, E=48, V=24.
<p/>
<img src="http://upload.wikimedia.org/wikipedia/commons/9/9e/Divina_proportione.png"
height="450"/>
<p/>
Woodcut 
from <i>the Divina Proportione</i> by Luca Pacioli 1509.
The divine proportion applied  to the human face.


<H2>Johannes Widman </H2>

Biography in Dictionary of Scientific Biography

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Widman.html">
MACTUTOR<a/>. 
Johannes Widman
<br/>
Born: 1462 in Eger, Bohemia (now Cheb, Czech Republic)
<br/>
Died: 1498 in Leipzig, Germany
<br>
Summary: 
Johannes Widman was a German mathematician who is best remembered for an early 
German arithmetic book (1489, reprinted until 1526)
which contains the first appearance of + and - signs.
This book was printed. It had more examples and a wider range
of examples than many others.
Graduated from University of Leipzig in 1482.
Later taught here. Taught the fundamentals of arithmetic and algebra.
First ever algebra lecture in Germany (1486).
Used Cossist notation as was usual at that time. 
Considered computation with irrational numbers and polynomials to be part of algebra.
His book popular until those of Adam Ries and others appeared.


<H2>Michael Stifel </H2>

Biography in Dictionary of Scientific Biography


<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Stifel.html">
MACTUTOR<a/>. 
Michael Stifel
<br/>
Born: 1487 in Esslingen, Germany
<br/>
Died: 19 April 1567 in Jena, Germany
<br>
Summary: 
German mathematician who invented logarithms independently of Napier using a totally different approach.

<p/>
<a href="http://en.wikipedia.org/wiki/Michael_stifel">
WIKI<a/>.
Michael Stifel (1487 - April 19, 1567) 
<br/>
Summary: 
A German mathematician. 
Discovered logarithms and invented an early form of logarithm tables decades before John Napier. 
Published "Arithmetica integra" in 1544.
Attempted to use the Bible to predict the apocalypse. 
Predicted that Judgement Day would occur on October 19, 1533 at 8:00 AM. 
When this prediction failed, he did not make any other predictions.


<H2>Adam Ries </H2>

Biography in Dictionary of Scientific Biography

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Ries.html">
MACTUTOR<a/>. 
Adam Ries
<br/>
Born: 1492 in Staffelstein (near Bamberg), Upper Franconia (now Germany)
<br/>
Died: 30 March 1559 in Annaberg, Saxony (now Annaberg-Buchholz, Germany)
<br>
Summary: 
Adam Ries was a German mathematician who published one of the first widely available arithmetic texts.

<p/>
<a href="http://en.wikipedia.org/wiki/Adam_Ries">
WIKI<a/>.
Adam Ries (March 27, 1492 – March 30, 1559)
better known by the name Adam Riese
<br/>
Summary: 
German mathematician. 
Adam Ries did not publish his books in Latin, the usual practice at the time, but in German. This way he reached a wider audience and, like Martin Luther, contributed to the unification of the German language.

<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Ries_3.jpeg"
height="300"/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Ries.jpeg"
height="300"/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Ries_2.jpeg"
height="300"/>


<H2>Pedro Nunes </H2>

Biography in Dictionary of Scientific Biography

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Nunes.html">
MACTUTOR<a/>. 
Pedro Nunes or Nunez. In full: Pedro Nunes Salaciense
<br/>
Born: 1502 in Alcácer do Sal, Portugal
<br/>
Died: 11 Aug 1578 in Coimbra, Portugal
<br>
Summary: 
Portuguese scholar.
Worked in geometry, spherical trigonometry, algebra as well as geography, physics, and cosmology.

<p/>
<a href="http://galileo.rice.edu/Catalog/NewFiles/nunez.html">
The Galileo Project<a/>

<p/>
<a href="http://en.wikipedia.org/wiki/Pedro_Nunes">
WIKI<a/>.


<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Nunes.jpeg"
height=
"200" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Nunes_2.jpeg"
height=
"200" />

<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Nunes_3.jpeg"
height=
"200" />


<H2>Robert Recorde </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9062911">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9062911">Academic Edition<a/>,
requires campus password)

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Recorde.html">
MACTUTOR<a/>. 
Robert Recorde
<br/>
Born: 1510 in Tenby, Wales
<br/>
Died: 1558 in London, England
<br>
Summary: 
Recorde was a Welsh doctor and mathematician who invented the "equals" symbol '=' which appears in his book The Whetstone of Witte (1557).

<p/>
<a href="http://www.britannica.com/eb/article-9062911">
BRITANNICA<a/>. 
Robert Recorde
<br/>
Born: c. 1510, Tenby, Pembrokeshire, Wales
<br/>
Died: June 1558, London, England
<br/>
Summary:
Physician, mathematician, and author of introductory mathematics textbooks.

<p/>
<a href="http://en.wikipedia.org/wiki/Robert_Recorde">
WIKI<a/>.
Robert Recorde (c. 1510 – 1558)
<br/>
Summary: 
Welsh physician and mathematician. 
Introduced the "equals" sign (=) in 1557.
It appears that he acted as physician to King Edward VI and to Queen Mary, to whom some of his books are dedicated. 
Also controller of the Royal Mint. 
After being sued for defamation by a political enemy, 
was arrested for debt and died in the King's Bench prison, Southwark, in 1558.


<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Recorde.jpeg"
height="250"/>


<H1>Later Developments</H1>


<H2>Viète </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9075315">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9075315">Academic Edition<a/>,
requires campus password)
<br/>
Crater Vieta
<br/>
Paris street name: Rue Viète (17th Arrondissement)

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Viete.html">
MACTUTOR<a/>. 
François Viète
<br/>
Born: 1540 in Fontenay-le-Comte, Poitou (now Vendée), France
<br/>
Died: 13 Dec 1603 in Paris, France
<br>
Summary: 
French amateur mathematician and astronomer.
Introduced the first systematic algebraic notation in his book 
<i/>In artem analyticam isagoge</i>. 
He was also involved in deciphering codes.


<p/>
<a href="http://www.britannica.com/eb/article-9075315">
BRITANNICA<a/>. 
François Viète, seigneur de la Bigotiere
<br/>
Born: 1540, Fontenay-le-Comte, France
<br/>
Died: Dec. 13, 1603, Paris
<br/>
Note:
Seigneur = lord. Latin  Franciscus Vieta.
<br/>
Summary:
Mathematician.
Introduced the first systematic algebraic notation.
Contributed to the theory of equations.

<p/>
<a href="http://en.wikipedia.org/wiki/Viete">
WIKI<a/>.
François Viète (or Vieta), seigneur de la Bigotière (1540 - February 13, 1603)
<br/>
Generally known as Franciscus Vieta.
<br/>
Summary: 
French mathematician.

<p/>
<a href="http://galileo.rice.edu/Catalog/NewFiles/viete.html">
The Galileo Project<a/>. 

<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Viete.jpeg"
height=
"360" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Viete_2.jpeg"
height=
"360" />


<H2>Thomas Harriot </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9039337">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9039337">Academic Edition<a/>,
requires campus password)
<br/>
Crater Harriot
<br/>

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Harriot.html">
MACTUTOR<a/>. 
Thomas Harriot
<br/>
Born: 1560 in Oxford, England
<br/>
Died: 2 July 1621 in London, England
<br>
Summary: 
English mathematician.
Did outstanding work on the solution of equations.
Recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution.

<p/>
<a href="http://www.britannica.com/eb/article-9039337">
BRITANNICA<a/>. 
Thomas Harriot
<br/>
Born: 1560, Oxford, England
<br/>
Died: July 2, 1621, London
<br/>
also spelled  Hariot 
<br/>
Summary:
Mathematician, astronomer, and investigator of the natural world.

<p/>
<a href="http://galileo.rice.edu/Catalog/NewFiles/harriot.html">
The Galileo Project<a/>

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Obits2/Harriot_Aubrey.html">
Aubrey's Brief Lives<a/>

<p/>
<a href="http://en.wikipedia.org/wiki/Thomas_harriot">
WIKI<a/>.

<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Harriot.jpeg"
height=
"250" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Harriot_2.jpeg"
height=
"250" />


<H2>Descartes </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9108563">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9108563">Academic Edition<a/>,
requires campus password)
<br/>
Crater Descartes
<br/>
Paris street name: Rue Descartes ( 5th Arrondissement)

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Descartes.html">
MACTUTOR<a/>. 
René Descartes
<br/>
Born: 31 March 1596 in La Haye (now Descartes),Touraine, France
<br/>
Died: 11 Feb 1650 in Stockholm, Sweden
<br>
Summary: 
French philosopher.
La géométrie includes his application of algebra to geometry from which we now have Cartesian geometry. A great influence on both mathematicians and philosophers.

<p/>
<a href="http://www.britannica.com/eb/article-9108563">
BRITANNICA<a/>. 
Descartes, René
<br/>
Born: March 31, 1596, La Haye, Touraine, France
<br/>
Died: February 11, 1650, Stockholm, Sweden
<br/>
Summary:
French mathematician, scientist, and philosopher. 
One of the first to abandon scholastic Aristotelianism.
Formulated the first modern version of mind-body dualism.
Promoted the development of a new science grounded in observation and experiment.
For these reasons,
has been called the father of modern philosophy. 
Applying an original system of methodical doubt, he dismissed apparent knowledge derived from authority, the senses, and reason.
Erected new epistemic foundations ( “Cogito, ergo sum”).

<p/>
<a href="http://galileo.rice.edu/Catalog/NewFiles/descarts.html">
The Galileo Project<a/>


<p/>
<a href="http://plato.stanford.edu/entries/descartes-works/">
STANFORD<a/>

<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Obits2/Descartes_Aubrey.html">
Aubrey's Brief Lives<a/>

<p/>
<a href="http://en.wikipedia.org/wiki/Descartes">
WIKI<a/>

<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes.jpeg"
height=
"300" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_2.jpeg"
height=
"300" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_11.jpeg"
height=
"300" />


<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_10.jpeg"
height=
"130" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_7.jpeg"
height=
"130" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_12.jpeg"
height=
"130" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_8.jpeg"
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<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Descartes_4.jpeg"
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<H2>Fermat </H2>

Biography in Dictionary of Scientific Biography
<br/>
<a href="http://www.britannica.com/eb/article-9034048">Encyclopaedia Britannica<a/>
(also: 
<a href="http://search.eb.com.ezproxy.csusm.edu/eb/article-9034048">Academic Edition<a/>,
requires campus password)
<br/>
Crater Fermat
<br/>
Paris street name: Passage Fermat and Rue Fermat (14th Arrondissement)


<p/>
<a href="http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Fermat.html">
MACTUTOR<a/>. 
Pierre de Fermat
<br/>
Born: 17 Aug 1601 in Beaumont-de-Lomagne, France
<br/>
Died: 12 Jan 1665 in Castres, France
<br>
Summary: 
French lawyer and government official.
Most remembered for his work in number theory; in particular for Fermat's Last Theorem. 
Also important in the foundations of the calculus.

<p/>
<a href="http://www.britannica.com/eb/article-9034048">
BRITANNICA<a/>. 
Fermat, Pierre de
<br/>
Born: August 17, 1601, Beaumont-de-Lomagne, France
<br/>
Died: January 12, 1665, Castres
<br/>
also
<br/>
Summary:
French mathematician.
Founder of the modern theory of numbers. 
Together with Descartes,  leading mathematicians of the first half of the 17th century. 
Discovered independently the fundamental principle of analytic geometry. 
Methods for finding tangents to curves and their maximum and minimum points.
Through his correspondence with Blaise Pascal, a co-founder of the theory of probability.

<p/>
<a href="http://galileo.rice.edu/Catalog/NewFiles/fermat.html">
The Galileo Project<a/>


<p/>
<a href="http://en.wikipedia.org/wiki/Fermat">
WIKI<a/>

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<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Fermat.jpeg"
height=
"400" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Fermat_3.jpeg"
height=
"400" />
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<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Fermat_4.jpeg"
height=
"400" />
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Fermat_5.jpeg"
height=
"400" />
<p/>
<img src="http://www-gap.dcs.st-and.ac.uk/~history/BigPictures/Fermat_6.jpeg"
height=
"300" />


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