2. In 18th century mathematics is already a modern
science
Large number of new mathematicians are appearing
on stage.
There are many new ideas, solutions added to old
mathematical problems
Researches lead to creating new fields of
mathematics.
Old fields of mathematics are also expanding.
Mathematicians contribute to this expansion.
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4. Leonhard Paul Euler
(1707-1783)
He was a Swiss mathematician
Johann Bernoulli made the biggest influence on Leonhard
In 1727, he went to St Petersburg where he worked in the
mathematics department and became the head of the
department in 1731
In 1741, he went to Berlin and worked in Berlin Academy for
25 years and after that he returned to St Petersburg where
he spent the rest of his life.
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5. 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
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
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6. 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
For any real number x, Euler‟s formula
states that the complex exponential
function satisfies:
EULER’ S FORMULA:
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7. 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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8. GEOMETRY:
Euler (1765) showed that in any triangle, the orthocenter,
circumcenter, centroid, and nine-point center are collinear.
Because of that the line which connects the points above is called
Euler line.8
9. 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 proved that it is not
possible.
This solution is considered to be the first theorem of graph
theory
Seven bridges of Konigsberg
This was old mathematical
problem
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10. He wrote 45 books and over 700 theses.
His main book is Introduction in Analysis of the Infinite.
Euler was very important for further development of mathematics
This 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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12. GABRIEL CRAMER
(1704-1752)
He was a Swiss mathematician
He gave the solution for St. Peterburg paradox
He worked on analysis and determinants
He was most famous by his rule (Cramer‟s rule) which gives a
solution to system of linear equations using determinants.
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14. 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
THOMAS SIMPSON
(1710-1761)
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16. 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
For this he wrote the introduction, and numerous philosophical
and mathematical articles; the best are those on geometry and
on probabilities.
JEAN LE ROND D’ALAMBERT
(1717-1783)
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18. He didn‟t show any interests 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.
JOSEPH LOUIS
LANGRANGE
(1736-1813)
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19. 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.
On 3 April 1813 he was awarded the
Grand Croix of the Ordre Impérial de
la Réunion. He died a week later.
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21. He is a 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 expansion” 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.
PIERRE-SIMON LAPLACE
(1749-1827)
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22. 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
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
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24. French mathematician also known as Comte de Péluse
Monge is considered as 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.
His method, which was one of cleverly representing 3-dimensional
objects by appropriate projections 2-dimensional plane, was
adopted by the military and classified as top secret
GASPARD MONGE
(1746-1818)
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26. 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.
ADRIEN – MARIE
LEGENDRE
(1752-1833)
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28. He is a French mathematician,
physicist and historian
He studied the mathematical theory
of heat conduction.
Fourier established the partial
differential equation governing heat
diffusion and solved in by using
infinite series of trigonometric
functions
JEAN BAPTISTE JOSEPH FOURIER
(1768-1830)
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30. 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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33. 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
He also researched in convergence and divergence of infinite
series, differential equations, determinants, probability and
mathematical physics.
AUGUSTIN LOUIS CAUCHY
(1789-1857)
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34. 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
His last words were:
“Men pass away, but their deeds abide.”
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