True to His Standards in Politics, Religion, and Math

 Augustin Louis Cauchy

Aug. 21, 1789-May 23, 1857

In Abstract Algebra we work with permutations a lot. What is a permutation you may ask? A permutation is essentially when you have a set of items and you change the order of the items, you then have created a permutation. In an earlier blog post we worked with permutations of a square. Here is a more specific definition of permutations from my text book, Contemporary Abstract Algebra by Joseph A. Gallian-

    "A permutation of a set $A$ is a function from $A$ to $A$ that is both one-to-one and onto. A permutation group of a set $A$ is a set of permutations of $A$ that forms a group under function composition."

Why am I interested in permutations? Well first off they are super cool, secondly, it is because this guy, Augustin Cauchy was interested in permutations too! Cauchy was one of the pioneers of analysis and the theory of permutation groups. He, like many mathematicians, added to several different areas of mathematics and physics including studying differential equations, infinite series and their convergence and divergence, determinants, calculus, probability, and optics.

Cauchy lived through the French Revaluation and when he was very young his parents feared for their safety and health as they had very little food and resources. However things got better as time passed. Laplace and Lagrange both visited Cauchy's home and encouraged his studies. In 1807 he graduated from the Ecole Polytechnique. He then attended an engineering school and eventually, in 1810, worked as an engineer for Napoleons' English invasion fleet at Cherbourg while continuing to do mathematical research on the side.

Around 1813 Laplace and Lagrange had convinced Cauchy to focus solely on mathematics. He came back to Paris and spent time teaching and doing research for years. Though Cauchy produced many important papers for mathematics, he had a way of offending his colleagues... he was very Catholic and came off as self-righteous and judgmental. Even poor, kind Mr. Abel was offended by this man! Abel exclaimed-"Cauchy is mad, and there is no way of being on good terms with him, although at present he is the only man who knows how mathematics should be treated. What he does is excellent, but very confused…"

In 1830 when Charles X was exiled and Louis-Philippe took the throne, Cauchy also went into exile since he refused to take an oath of allegiance. Because of this he lost all of his positions and chairs that he held in Paris. He began to teach in Turin and eventually attempted to teach the grandson of Charles X. This was an interesting experience I'm sure... Most articles reveal that the grandson was not the best of students and Cauchy was not the best of teachers, so the two made a less than stellar pair to say the least. 

Finally, in 1838 Cauchy returned to Paris and gained back his seat at the Academy, the Ecole Polytechnique, but was not allowed to teach as he still refused to take the oath of allegiance. By 1848 when Louis-Philippe was overthrown, Cauchy regained his chair at Sorbonne and held that position till he died. Some of his last words were, "Men pass away, but their deeds abide." Cauchy's works certainly abide today, and we are so thankful for that.


    Thanks bunches,

      -Haylee Jo Lau


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