Running time of the Euclidean Algorithm

**Pierre-Joseph-Étienne Finck** was born October 15, 1797, and died July 27, 1870. Finck’s most significant mathematical contribution appears to have been his analysis of the running time of the Euclidean Algorithm, which he published in 1841.

One wonders if his own life experiences contributed to his interest in recursive algorithms. Upon graduating from the École Polytechnique in 1817, he was admitted to the Artillery School. However, he wasn’t satisfied with his studies there, and applied ( in March 1818 ) to transfer to the Royal Guard cavalry. **Request denied**.

4 months later, he applied to the cavalry again, this time saying that he would resign if his request was not honored. **Request denied**.

So he resigned from Artillery School…. But by early 1819 he had second thoughts, and applied for reinstatement to the Artillery School. **Request denied**.

At this point, he changed tactics, and began studying mathematics at the University of Strasbourg. He completed his doctoral dissertation (on movements of the terrestrial equator) in 1829. Ironically, by that time, he had been appointed as a mathematics instructor at the Artillery School of Strasbourg.

I suppose Finck’s life might provide a valuable lesson in the importance of sticking to your guns.

Source: Mactutor History of Math archive

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