Albert Girard () (11 October 1595 in

Saint-Mihiel Saint-Mihiel () is a commune in the Meuse department in the Grand Est region in Northeastern France. Geography Saint-Mihiel lies on the banks of the river Meuse. History A Benedictine abbey was established here in 708 or 709 by Count Wulfoalde ...

, France − 8 December 1632 in

Leiden Leiden ( ; ; in English language, English and Archaism, archaic Dutch language, Dutch also Leyden) is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the Provinces of the Nethe ...

Dutch Republic The United Provinces of the Netherlands, commonly referred to in historiography as the Dutch Republic, was a confederation that existed from 1579 until the Batavian Revolution in 1795. It was a predecessor state of the present-day Netherlands ...

) was a French-born mathematician. He studied at the

University of Leiden Leiden University (abbreviated as ''LEI''; ) is a public research university in Leiden, Netherlands. Established in 1575 by William, Prince of Orange as a Protestant institution, it holds the distinction of being the oldest university in the Neth ...

. He "had early thoughts on the

fundamental theorem of algebra The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant polynomial, constant single-variable polynomial with Complex number, complex coefficients has at least one comp ...

" and gave the inductive definition for the

Fibonacci number In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

s. He was the first to use the abbreviations 'sin', 'cos' and 'tan' for the

trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...

in a treatise. Girard was the first to state, in 1625, that each prime of the form 1 mod 4 is the sum of two squares. (See

Fermat's theorem on sums of two squares In additive number theory, Pierre de Fermat, Fermat's theorem on sums of two squares states that an Even and odd numbers, odd prime number, prime ''p'' can be expressed as: :p = x^2 + y^2, with ''x'' and ''y'' integers, if and only if :p \equiv ...

.) It was said that he was quiet-natured and, unlike most mathematicians, did not keep a journal for his personal life. In the opinion of

Charles Hutton Charles Hutton FRS FRSE LLD (14 August 1737 – 27 January 1823) was an English mathematician and surveyor. He was professor of mathematics at the Royal Military Academy, Woolwich from 1773 to 1807. He is remembered for his calculation of th ...

, Girard was

...the first person who understood the general doctrine of the formation of the coefficients of the powers from the sum of the roots and their products. He was the first who discovered the rules for summing the powers of the roots of any equation.

This had previously been given by

François Viète François Viète (; 1540 – 23 February 1603), known in Latin as Franciscus Vieta, was a French people, French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as par ...

for ''positive'' roots, and is today called

Vieta's formulas In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (1540-1603), more commonly referred to by the Latinised form of his name, "Franciscus Vieta." Basi ...

, but Viète did not give these for general roots. In his paper, Funkhouser locates the work of Girard in the history of the study of equations using

symmetric function In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f\ ...

s. In his work on the

theory of equations In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equation (mathematics), equations defined by a polynomial. The main problem of the theory of equations was to know when an al ...

Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiagroup theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

Cauchy Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real a ...

, Galois and others. Girard also showed how the area of a spherical triangle depends on its interior angles. The result is called Girard's theorem. He also was a

lute A lute ( or ) is any plucked string instrument with a neck (music), neck and a deep round back enclosing a hollow cavity, usually with a sound hole or opening in the body. It may be either fretted or unfretted. More specifically, the term "lu ...

nist and mentioned having written a treatise on music, though this was never published.

References

{{DEFAULTSORT:Girard, Albert 1595 births 1632 deaths People from Saint-Mihiel Dutch people of French descent 17th-century French mathematicians 17th-century Dutch mathematicians Leiden University alumni French lutenists Dutch lutenists French emigrants Immigrants to the Dutch Republic