Read Euler, read Euler. He is the master of us all. Laplace

Leonard Euler was born near Basel, Switzerland. He was a precocious youth, blessed with a gift for languages and an extraordinary memory. Euler eventually carried in his head an assortment of curious information, including orations, poems, and lists of prime powers. He also was a fabulous mental calculator, able to perform intricate arithmetical computations without benefit of pencil and paper. These uncommon talents would serve him well later in life.

After entering the University of Basel at age 14, Leonard encountered his most famous professor, Johann Bernoulli. Not Euler's teacher in a modern sense of the term, Bernoulli instead became a guide for the young scholar, suggesting mathematical readings and making him available to discuss those points that seemed especially difficult.

At university, Euler's education was not limited to mathematics. He spoke on the subject of temperance, wrote on the history of law, and eventually completed a master's degree in philosophy.

Ultimately, the call of mathematics was stronger than anything. His progress was rapid. He had many scientific outputs and proofs related to number theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry, combinatorics and graph theory. Some mathematicians argue that his mathematics was not as precise as of today's and he had sometimes proceeded heuristically. However, one can question whether modern mathematics would exist without him.

His grave is in St Petersburg.

*Dunham, W. Euler: The Master of Us All, The Mathematical Association of America, Washington (1999). The Dolciani Mathematical Expositions, 22. *

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence. Keith Devlin, as quoted in Dr. Euler's Fabulous Formula : Cures Many Mathematical Ills (2006)

Theorem: For any real $x,{e}^{ix}=\mathrm{cos}x+i\mathrm{sin}x.$

Proof:

$\begin{array}{l}{e}^{x}=1+x+\frac{{x}^{2}}{2!}+\frac{{x}^{3}}{3!}+\frac{{x}^{4}}{4!}+\mathrm{...}\\ {e}^{ix}=1+ix+\frac{{(ix)}^{2}}{2!}+\frac{{(ix)}^{3}}{3!}+\frac{{(ix)}^{4}}{4!}+\mathrm{...}\\ {e}^{ix}=1+ix-\frac{{x}^{2}}{2!}-\frac{i{x}^{3}}{3!}+\frac{{x}^{4}}{4!}+\frac{i{x}^{5}}{5!}-\frac{{x}^{6}}{6!}-\mathrm{...}\\ {e}^{ix}=(1-\frac{{x}^{2}}{2!}+\frac{{x}^{4}}{4!}-\frac{{x}^{6}}{6!}+\frac{{x}^{8}}{8!}-\mathrm{...})+i(x-\frac{{x}^{3}}{3!}+\frac{{x}^{5}}{5!}-\frac{{x}^{7}}{7!}+\mathrm{...})\\ {e}^{ix}=(\mathrm{cos}x)+i(\mathrm{sin}x)\\ {e}^{i\pi}=(\mathrm{cos}\pi )+i(\mathrm{sin}\pi )\\ {e}^{i\pi}+1=0\end{array}$

"Euler's Identity" video from Youtube