Research Paper On Leonhard Euler

Noah Kokkinos

Mrs. Dreyer

Roots of Thought Honors

1 March 2016

The Blind Mathematician In the time of the Enlightenment, mathematics was in for a big change in the way it functioned. At this time, mathematics in Europe had the best of the best working together in academies to conjecture and prove theorems and advance mathematics. Being a mathematician in this era meant solving long, grueling problems that would usually plague all but one person who could solve it and free their friends from the insanity of the challenge. The major thing that stumped the mathematicians in some of these problems was that they were too hard to calculate when there was a repeated equation used over and over again. Leonhard Euler, one of the most prolific mathematicians

The history of e actually dates back to before Euler though. Before it was given a name, this term appeared almost 100 years before Euler in logarithms being done by a mathematician named Napier. (O’Connor) Slowly after that,this term began popping up in other places without anyone really knowing what it was. It took until Euler investigated the term for it to finally be given a name and exact value. The Euler-Mascheroni constant, or gamma, was discovered by Euler in a much different but yet similar way. This constant was not surfacing in any other person’s work until Euler discovered it in his own equations. Once he found the constant he exchanged letter with another mathematician named Mascheroni, hence the name of the constant. Anyway, those two exchanged letters to find out more about this term. The two eventually figured out what this number was and then began seeing appear in many other problems from other scientists. They especially saw it appear in what is known as the Taylor problems and the digamma function. (Weistein) Euler in his work and discoveries of e and gamma would set a basis for mathematicians around the

What makes this problem so difficult is that to solve one of them, someone must do a repetitive series of multiplying with the factorials of fractions to find the answer. This compound-interest number, created by Euler, is labeled as e because it is irrational. Without its label, people would have to recite all of its digits over and over again. So, instead of doing repetitive multiplication, mathematicians use this e to stand for all of this multiplication and unneeded digits. (Stapel) The discovery of this number also allows mathematicians to take on more difficult problems because it takes away the trouble of