In 18th century mathematics is
already a modern science
 Mathematics begins to develop very
fast because of introducing it to
schools
 Therefore everyone have a chance to
learn the basic learnings of
mathematics
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Thanks to that, large number of new
mathematicians appear on stage
 There are many new ideas, solutions
to old mathematical
problems,researches which lead to
creating new fields of mathematics.
 Old fields of mathematics are also
expanding.
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FAMOUS
MATHEMATICIANS
LEONHARD EULER
Leonhard Paul Euler
(1707-1783)
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He was a Swiss mathematician
Johann Bernoulli made the biggest
influence on Leonhard
1727 he went to St Petersburg where he
worked in the mathematics department
and became in 1731 the head of this
department
1741 went in Berlin and worked in Berlin
Academy for 25 years and after that he
returned in St Ptersburg where he spent
the rest of his life.
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Euler worked in almost all areas of mathematics:
geometry, calculus, trigonometry, algebra,applied
mathematics, graph theory and number theory,
as well as , lunar theory, optics and other areas
of physics.
He introduced several notational conventions in
mathematics
Concept of a function as we use today was
introduced by him;he was the first mathematician
to write f(x) to denote function
He also introduced the modern notation for the
trigonometric functions, the letter e for the base
of the natural logarithm (now also known as
Euler’s number), the Greek letter Σ for
summations and the letter i to denote the
imaginary unit
He wrote 45 books an over 700
theses.
 His main book is Introduction in
Analisyis of the Infinite.
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Analysis
He discovered ways to express
various logarithmic functions using
power series, and he successfully
defined logarithms for negative and
complex numbers
 He also defined the exponential
function for complex numbers, and
discovered its relation to the
trigonometric functions
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EULER’ S FORMULA
For any real number x,
Euler’s formula states
that the complex
exponential function
satisfies
Number theory
He contributed significantly to the
theory of perfect numbers, which
had fascinated mathematicians since
Euclid.
 His prime number theorem and the
law of quadratic reciprocity are
regarded as fundamental theorems
of number theory.
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Geometry
Euler (1765) showed that in any
triangle, the orthocenter,
circumcenter, centroid, and ninepoint center are collinear.
 Because of that the line which
connects the points above is
called Euler line.
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Seven bridges of Konigsberg
Seven bridges of Konigsberg
Seven bridges of Konigsberg
Seven bridges of Konigsberg
This was old mathematical problem.
 The problem was to decide whether
it is possible to follow a path that
crosses each bridge exactly once and
returns to the starting point.
 1736 Euler solved this problem, and
prooved that it is not possible.
 This solution is considered to be the
first theorem of graph theory
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Euler was very importnat for further
development of mathematics
 Next quotation tells enough about his
importance:
 “Lisez Euler, lisez Euler, c'est notre
maître à tous ”(Read Euler, read
Euler, he is the master of us all.)
Pierre-Simon Laplace
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GABRIEL CRAMER
GABRIEL CRAMER
(1704-1752)
Swiss mathematician
 He give the solution of St. Peterburg
paradox
 He worked on analysis and
determinants
 He is the most famous by his rule
(Cramer’s rule) which gives a
solution of a system of linear
equations using determinants.
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THOMAS SIMPSON
THOMAS SIMPSON
(1710-1761)
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He received little formal education and
taught himself mathematics while he was
working like a weaver.
Soon he became one of the most
distinguished members of the English
school
Simpson is best remembered for his work
on interpolation and numerical methods of
integration.
He wrote books Algebra, Geometry,
Trigonometry, Fluxions, Laws of Chance,
and others
JEAN LE ROND D’ALAMBERT
JEAN LE ROND D’ALAMBERT
(1717-1783)
He dealt with problems of dinamics
and fluids and especially with
problem of vibrating string which
leads to solving partial diferential
equations
 During his second part of life, he was
mainly occupied with the great
French encyclopedia
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For this he wrote the introduction,
and numerous philosophical and
mathematical articles; the best are
those on geometry and on
probabilities.
JOSEPH LOUIS LANGRANGE
JOSEPH LOUIS LANGRANGE
(1736-1813)
He didn’t show any intersts for
mathematics untill his 17.
 From his 17, he alone threw himself
into mathematical studies
 Already with 19, he wrote a letter to
Euler in which he solved the
isoperimetrical problem which for
more than half a century had been a
subject of discussion.
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Lagrange established a society known
as Turing Academy, and published
Miscellanea Taurinesia, his work in
which he corrects mistakes made by
some of great mathematicians
 He was studing problems of analytical
geometry, algebra, theory of numbers,
differential eqations, mechanics,
astronomy, and many other...
 Napoleon named Lagrange to the
Legion of Honour and made him the
Count of the Empire in 1808.
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On 3 April 1813 he was awarded the
Grand Croix of the Ordre Impérial de la
Réunion. He died a week later.
PIERRE SIMON LAPLACE
PIERRE-SIMON LAPLACE
(1749-1827)
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French mathematician and astronomer
His most known works are Traite de
mecanique celeste and Theory analytique
des probabiliteis
His name is also connected with the
“Laplace transform” and with the “Laplace
ex pansion” of a determint
He is one of the first scientists to postulate
the existence of black holes.
He is one of only seventy-two people to
have their name engraved on Eiffel Tower.
It is also interesting to say the
difference between Laplace and
Lagrange
 For Laplace, mathematics was merely
a kit of tools used to explain nature
 To Lagrange, mathematics was a
sublime art and was its own excuse
for being
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He is remembered
as one of the
greatest scientists
of all time,
sometimes referred
to as a French
Newton or Newton
of France
He became a count
of the First French
Empire in 1806
and was named a
marquis in 1817
GASPARD MONGE
GASPARD MONGE
(1746-1818)
French mathematician also known as
Comte de Péluse
 Monge is considered the father of
differential geometry because of his
work Application de l'analyse à la
géométrie where he introduced the
concept of lines of curvature of a
surface in 3-space.
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His method, which was one of
cleverly representing 3-dimensional
objects by appropriate projections 2dimensional plane, was adopted by
the military and classified as top
secret
ADRIEN – MARIE LEGENDRE
ADRIEN – MARIE LEGENDRE
(1752-1833)
He made important contributions to
statistics, number theory, abstract
algebra and mathematical analysis.
 Legendre is known in the history of
elementary methematics principially
for his very popular Elements de
geometrie
 He gave a simple proof that π(pi) is
irrational as well as the first proof
that π2(pi squared) is irrational.
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JEAN BAPTISTE JOSEPH
FOURIER
JEAN BAPTISTE JOSEPH FOURIER
(1768-1830)
French mathematician, physicist
and historian
 He studied the mathematical
theory of heat conduction.
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Fourier established the
partial differential
equation governing heat
diffusion and solved in by
using infinite series of
trigonometric functions
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JOHANN CARL FRIEDRICH GAUSS
JOHANN CARL FRIEDRICH GAUSS
(1777 – 1855)
He worked in a wide variety of fields
in both mathematics and physics
incuding number theory, analysis,
differential geometry, geodesy,
magnetism, astronomy and optics.
 “Mathematics is the queen of the
sciences and number theory is the
queen of mathematics.”
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AUGUSTIN LOUIS CAUCHY
AUGUSTIN LOUIS CAUCHY
(1789-1857)
Cauchy started the project of
formulating and proving the teorems
of calculus in a rigorous manner and
was thus an early pioneer of analysis
 He also gave several important
theorems in complex analysis and
initiated the study of permutation
groups
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He also researched in convergence
and divergence of infinite series,
differential equations, determinants,
probability and mathematical
physics.
 He was first to prove Taylor’s
theorem, he brought a whole new
set of teorems and definitions, he
dealed with mechanics, optics,
elasticity and many other problems
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His last words were:
“Men pass away, but their
deeds abide.”
Anela Bocor
Mateja Jelušić
Ivan Jelić
Vojislav Đuračković
Boris Dokić