A tribute to Euler

Among the greatest of mathematicians is Leonhard Euler (1707-1783), whose insight, industry, and ingenuity are unsurpassed in the long history of mathematics. In this talk we sketch Euler’s life, describe the quantity and quality of his mathematical output, and discuss a few of his discoveries from the realms of number theory, geometry, analysis, and combinatorics. We then look at a specific theorem: his proof, using integral calculus (!), of what is known as “Euler’s Identity” -i.e., exp(ix)=cos(x)+isin(x). We should thereby get a sense of Euler’s genius and see why he is rightly known as “the Master of Us All.” NOTE: This talk should be accessible to any student who has seen calculus.