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François Viète (1540-1603)

In his excellent book Mathematics for the Non-mathematician, Professor Morris Kline writes,

The remarkable fact about Viète is that he was a lawyer who worked for the kings of France.  Mathematics was just a hobby to him, but one at which he “worked” extensively. 

Mathematics for the Non-mathematician, page 118

François Viète was born in the French countryside in 1540.  His father, a successful lawyer and notary, sent François to study law at the University of Poitiers.  After completing his studies, Viète quickly established himself in the legal profession, handling civil disputes involving the king’s land and overseeing the interests of Mary, Queen of Scots.

Eventually, Viète would be chosen to serve as a privy councilor for both Henry III and Henry IV.

However, it was in mathematics, not law, where Viète would make his most lasting contributions–most notably the introduction of letters to represent variables in algebraic equations.

In his Introduction to the Analytic Arts, published in 1591, Viète suggested the use of vowels to represent unknown numbers and consonants to represent known numbers.  This concept, later revised by Descartes, allowed mathematicians to work with complex equations with far more ease and thus greatly facilitated advances in the field.

Writing on Viète’s system, mathematics historian Dirk J. Struik states

The improvement in [mathematical] technique was a result of the improvement in notation.  The new results show clearly that it is incorrect to say that men like Viète “merely” improved notation.  Such a statement discards the profound relation between content and form.  New results have often become possible only because of a new mode of writing…An adequate notation reflects reality better than a poor one, and as such appears endowed with a life of its own which in turn creates new life.

A Concise History of Mathematics, page 88

Pierre de Fermat (1607-65)

Fermat’s entry in the Oxford Concise Dictionary of Mathematics states,

Professionally he was a lawyer in Toulouse, and so he was considered the “Prince of Amateurs.”

Oxford Concise Dictionary of Mathematics  Page 150

This “Prince of Amateurs” was born in the French commune of Beaumont-de-Lomagne in 1607.  Fermat earned a law degree from the University of Orleans before beginning his legal profession in Toulouse.

 He’s best known for his contributions to number theory and for several notable publications which include Tangents of Curves (1629) and Methods of Investigating Maxima and Minima (1637).  Struik writes that

there are places in [Fermat’s writings] which are as beautiful as Horace or Emerson.

A Concise History of Mathematics, page 2

A close friend of philosopher and mathematician Rene Descartes, Fermat helped develop Cartesian coordinates—unifying, to some extent, algebra and geometry.  According to Morris Kline,

Descartes and Fermat made possible the algebraic representation and the study by algebraic means of the various objects and paths of interest to scientists.  In addition, algebra supplies quantitative knowledge.  This method of working with curves and surfaces is so basic in science that Descartes and Fermat may very well be called the founders of mathematical physics.

  Mathematics for the Non-mathematician, page 278

Fermat’s work on tangents also inspired Isaac Newton in his development of calculus. 

Fermat once noted, I have found a very great number of exceedingly beautiful theorems.

Among these “beautiful theorems” are Fermat’s Little Theorem, Fermat’s Two Squares Theorem, and Fermat’s Last Theorem.

Gottfried Leibniz (1646-1716)

Gottfried Leibniz was born into a family of German academics in the mid 1600s.  His father was a professor of moral philosophy and his maternal grandfather taught law.  Leibniz attended the University of Leipzig where he studied philosophy and law, earning multiple degrees. 

His first job was as legal advisor to the Elector of Mainz.  After the Elector’s death in 1673, Leibniz became the librarian to the Duke of Brunswick, a position that allowed him pursue his interests in science and mathematics. 

Today Leibniz is best known for developing the mathematical field of calculus.  In England, Isaac Newton developed his own version of calculus and the men would later quarrel bitterly over who should be recognized as the discipline’s founder. 

According to one source,

Newton’s discovery of differential calculus was perhaps ten years earlier than Leibniz’s, but Leibniz was the first to publish his account, written independently of Newton, in 1684.

Oxford Concise Dictionary of Mathematics  Page 237

Joseph-Louis Lagrange (1736-1813)

The son of a well-to-do lawyer, Lagrange attended the University of Turin in northern Italy where he studied law and showed little interest initially in mathematics. 

It was not until he read the works of British astronomer Edmond Halley that Lagrange, then aged 17, took it upon himself to learn all he could of mathematics.

He became, according to the Oxford Dictionary of Mathematics,

Arguably the greatest, alongside Euler, of 18th century mathematicians.

Oxford Concise Dictionary of Mathematics 231

In fact, he and Euler would become close friends with Euler helping Lagrange obtain the directorship of mathematics at the Berlin Academy.  From there, Lagrange moved to the Académie de Science in Paris.  He managed to survive the French Revolution and its terror and eventually died in Paris in 1813 aged 77.

His key written works include Reflections on the Algebraic Resolution of Equations (1771), Analytical Mechanics (1788), and Theory of Analytic Functions (1797).