Leonhard Euler (1707-1783) was a prolific mathematician and physicist born in Basel, Switzerland. He made seminal contributions to graph theory, number theory, and mathematical analysis. Some of his most important works included establishing foundational concepts like the modern mathematical function f(x), the use of the Greek letter π and e, and Euler's identity relating the most important mathematical constants. He spent much of his career in St. Petersburg, Russia, where he worked at the Imperial Academy of Sciences and established himself as one of the preeminent mathematicians of the 18th century.

1. Leonhard Euler
(1707-1783)

2. Introduction
→ Introduction
→ His life
→ His most important works
→ Conclusion

3. His life
Born in Basel in 1707
At 16 : Master of Philosophy
Received lessons from Bernouilli
In 1727 he went to St Petersburg

4. His life
1731 : professor of physics
1733 : head of the mathematics department
1741 : he went to Berlin Academy
1766 : came back in St Petersburg
He died in 1783

5. Mathematical notations
The concept of a function, notation f(x)
The letter e ''Euler's number'' use to define the
Exponential function : ex
The greek letter Ʃ for summations
The famous greek letter π
The letter i to denote the imaginary unit

6. Analysis
n
x ∞ x
e =∑ n =0 n !
∞
1 ²
∑ n2 = 6 '' The Basel Problem ''
n=1
i
e =cos i sin  '' The Euler's formula ''
i
e 1=0 '' The Euler's identity ''

7. Number Theory
The infinitude of prime numbers
The sum of the reciprocals of the primes diverges
The totient function : φ(n)
The Euler's theorem
231 − 1 = 2,147,483,647 is a Mersenne prime

8. Euler's circle

9. Euler's line

10. Graph theory
V–E+F=1

11. Conclusion

12. http://scienceworld.wolfram.com/biography/Euler.html
http://www.maths.tcd.ie/pub/HistMath/People/Euler/Ro
http://www.pdmi.ras.ru/EIMI/EulerBio.html
http://www-history.mcs.st-
and.ac.uk/Biographies/Euler.html
http://en.wikipedia.org/wiki/Leonhard_Euler