Augustin Cauchy

Augustin Cauchy,  Many mathematicians of the day believe that your largest accomplishments were in the field of complex functions. You are known for your book that you mentioned in your second letter called Cours d'Analyse, where you stress the importance of "rigor" in analysis. It is in this book where you defined Cauchy's Criterion for Convergence. Since your book is written in French, I will recite a translated version. It states, "[it] is that a necessary and sufficient condition for convergence of a sequence {x n } is that it be a Cauchy sequence, where a Cauchy sequence is defined to be for each  e > 0, there is a positive integer N such that | x n  - x m  | < e for all m > N and all n > N." (Cauchy). It is extremely difficult to find what value N the series converges to, and you realized that it is not necessary to find the best or most exact value for N. You need only find any value that works. You were not the first mathematician...

Dear Augustin Cauchy,  Your mathematical accomplishments have had an enormous impact in the fields of math and science. More concepts and theorems have been named after you than any other mathematician alone, and to this day, you have written the second largest number of papers of any mathematician, only second to Leonard Euler. Some areas you have had influence in are complex functions, optics, elasticity, group theory, mathematical physics and astronomy, hydrodynamics, and differential equations. Even though you are not most well-known for your work in algebra, I first heard of you in an Abstract Algebra course. In the field of algebra, your early work is the basis of group theory, and you have contributed to finding the inverse of a matrix, creating theorems on determinants formed by subdeterminants, and you proved a generalization of one of Ruffini's theorems. Even though it took some time after you for abstract group theory to form and for it to move alway from the term subs...

Dear future mathematicians,  When I returned to Paris in 1813, my old friends Lagrange and Laplace persuaded me to spend the entirety of my time studying mathematics. The debilitating nature of my depression was short lived, so I was supposed to return to Cherbourg later in the year when my health had improved, but this was not compatible with my mathematical ambitions. At this time, I found myself completely absorbed in the subject and did not want to return to engineering. I applied to be a professor at the École des Ponts et Chaussées but was turned down. With no other leads on jobs, I decided to work as an engineer on the Ourcq Canal project instead of returning to Cherbourg, so I could continue my work. I still strongly wanted an academic career but was turned down for more positions on numerous occasions. I first applied for a position in the Bureau des Longitudes and was not hired. Legendre, another mathematician, was appointed instead. I also lost a position to Po...