LEONHARD EULER

Leonhard Euler (1707-1783) was a Swiss mathematician and physicist who is considered one of the greatest mathematicians in history. Euler made fundamental contributions to many areas of mathematics, including number theory, geometry, trigonometry, physics, and astronomy.

Life and career

Euler was born in Basel, Switzerland, on April 15, 1707. He studied at the University of Basel, where he received his doctorate in 1726. In 1727, Euler joined the Academy of Sciences in Saint Petersburg, Russia, where he worked for 14 years. In 1741, Euler moved to Berlin, Germany, where he worked at the Prussian Academy of Sciences. Euler returned to Saint Petersburg in 1766 and remained there until his death on September 18, 1783.

Contributions

Euler made fundamental contributions in many areas of mathematics, including:

1. *Number theory*: Euler worked on number theory, especially congruence theory and zeta function theory.
2. *Geometry*: Euler made important contributions in geometry, especially in the theory of curves and surfaces.
3. *Trigonometry*: Euler developed the theory of trigonometric functions and introduced the current notation for the sine, cosine and tangent functions.
4. *Physics*: Euler worked in physics, especially in the theory of mechanics and the theory of optics.
5. *Astronomy*: Euler made important contributions in astronomy, especially in the theory of planetary orbit.

Legacy

Euler is considered one of the greatest mathematicians in history. His contributions have had a profound impact on mathematics and physics. Euler's notation and terminology are still used today in many areas of mathematics and physics.

Some of Euler's most important concepts and results include:

- Euler's formula for the exponential function: e^(ix) = cos(x) + i sin(x)
- Euler's formula for the sum of a geometric series: 1 + r + r^2 + ... = 1 / (1 - r)
- Euler's number: e = 2.71828...
- The Euler-Mascheroni constant: γ = 0.57721...

In short, Leonhard Euler was a Swiss mathematician and physicist who made fundamental contributions to many areas of mathematics and physics. His legacy is enormous and his results and notations are still used today in many areas of science.