Joseph-Louis Lagrange
Born: 25 Jan 1736 in Turin, Sardinia-Piedmont (now
Italy)
Died: 10 April 1813 in Paris, France
Joseph-Louis Lagrange is usually considered to be a
French mathematician, but the Italian Encyclopaedia [40] refers to him as an
Italian mathematician. They certainly have some justification in this claim
since Lagrange was born in Turin and baptised in the name of Giuseppe Lodovico
Lagrangia. Lagrange's father was Giuseppe Francesco Lodovico Lagrangia who was
Treasurer of the Office of Public Works and Fortifications in Turin, while his
mother Teresa Grosso was the only daughter of a medical doctor from Cambiano
near Turin. Lagrange was the eldest of their 11 children but one of only two to
live to adulthood.
Turin had been the capital of the duchy of Savoy, but
become the capital of the kingdom of Sardinia in 1720, sixteen years before
Lagrange's birth. Lagrange's family had French connections on his father's
side, his great-grandfather being a French cavalry captain who left France to
work for the Duke of Savoy. Lagrange always leant towards his French ancestry,
for as a youth he would sign himself Lodovico LaGrange or Luigi Lagrange, using
the French form of his family name.
Despite the fact that Lagrange's father held a
position of some importance in the service of the king of Sardinia, the family
were not wealthy since Lagrange's father had lost large sums of money in
unsuccessful financial speculation. A career as a lawyer was planned out for
Lagrange by his father, and certainly Lagrange seems to have accepted this
willingly. He studied at the College of Turin and his favourite subject was
classical Latin. At first he had no great enthusiasm for mathematics, finding
Greek geometry rather dull.
Lagrange's interest in mathematics began when he read
a copy of Halley's 1693 work on the use
of algebra in optics. He was also attracted to physics by the excellent
teaching of Beccaria at the College of Turin and he decided to make a career
for himself in mathematics. Perhaps the world of mathematics has to thank
Lagrange's father for his unsound financial speculation, for Lagrange later
claimed: -
If I had been rich, I probably would not have devoted
myself to mathematics.
He certainly did devote himself to mathematics, but
largely he was self taught and did not have the benefit of studying with
leading mathematicians. On 23 July 1754 he published his first mathematical
work which took the form of a letter written in Italian to Giulio Fagnano. Perhaps most surprising was
the name under which Lagrange wrote this paper, namely Luigi De la Grange
Tournier. This work was no masterpiece and showed to some extent the fact that
Lagrange was working alone without the advice of a mathematical supervisor. The
paper draws an analogy between the
binomial theorem and the successive derivatives of the product of
functions.
Before writing the paper in Italian for publication,
Lagrange had sent the results to Euler,
who at this time was working in Berlin, in a letter written in Latin. The month
after the paper was published, however, Lagrange found that the results
appeared in correspondence between
Johann Bernoulli and Leibniz.
Lagrange was greatly upset by this discovery since he feared being branded a
cheat who copied the results of others. However this less than outstanding
beginning did nothing more than make Lagrange redouble his efforts to produce
results of real merit in mathematics. He began working on the tautochrone, the curve on which a weighted
particle will always arrive at a fixed point in the same time independent of
its initial position. By the end of
1754 he had made some important discoveries on the tautochrone which would
contribute substantially to the new subject of the calculus of variations (which mathematicians were beginning to
study but which did not receive the name 'calculus of variations' before Euler called it that in 1766).
Lagrange sent Euler his results on the tautochrone containing his method of
maxima and minima. His letter was written on 12 August 1755 and Euler replied on 6 September saying how
impressed he was with Lagrange's new ideas. Although he was still only 19 years
old, Lagrange was appointed professor of mathematics at the Royal Artillery
School in Turin on 28 September 1755. It was well deserved for the young man
had already shown the world of mathematics the originality of his thinking and
the depth of his great talents.
In 1756 Lagrange sent
Euler results that he had obtained on applying the calculus of
variations to mechanics. These results generalised results which Euler had himself obtained and Euler consulted Maupertuis, the president of the Academy, about this remarkable
young mathematician. Not only was Lagrange an outstanding mathematician but he
was also a strong advocate for the principle of least action so Maupertuis had no hesitation but to try to
entice Lagrange to a position in Prussia. He arranged with Euler that he would let Lagrange know that
the new position would be considerably more prestigious than the one he held in
Turin. However, Lagrange did not seek greatness, he only wanted to be able to
devote his time to mathematics, and so he shyly but politely refused the
position.
Euler also
proposed Lagrange for election to the Berlin Academy and he was duly elected on
2 September 1756. The following year Lagrange was a founding member of a
scientific society in Turin, which was to become the Royal Academy of Science
of Turin. One of the major roles of this new Society was to publish a
scientific journal the M
