Mathematics and Eugene Catalan

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  • Topic: Mathematics, Women mathematicians, Eugène Charles Catalan
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  • Published : February 21, 2011
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Eugene Charles Catalan

The first mathematician I will be writing about is Eugene Charles Catalan. I picked him, because he is one of the top 100 most known mathematicians in the world. Eugene Catalan, was born in Bruges or more commonly known as Belgium, on May 30, 1814. He traveled to Paris where he pursued his mathematical dreams. Later on in 1841, he received his degree in mathematics.

Eugene Catalan studied mathematics and design in a university located in Paris. Eventually, he became an architect, just like his father. At the age of 15, he tutored and taught his fellow students how to solve geometry problems in school. As he grew older, he traveled to attend École Polytechnique due to his outstanding aptitudes in mathematics. In 1833, he was eventually expelled for his political activities. 2 years later, he was able to resume his studies and graduated in 16th place and acquired a post at Collège de Châlons sur Marne. In 1846, Catalan was told to take charge of teaching higher mathematics at the Collège de Charlemagne because of his outstanding skills with numbers and math. Later on in his career, Eugene published books about continued fractions and number theory, which is still used today.

Through all of his hard work, Eugene Catalan is recognized because of his accomplishments. Many people studying math know about “Catalan numbers,” which obviously came from him. Another accomplishment he has made in the mathematical area is being able to dissect a polygon into triangles by means of non-intersecting diagonals. He was not the first to accomplish this, but no one has a more elegant style than he does. The “Catalan minimal surface” is also one of his major accomplishments that he studied around 1855. It relates to another one of his titles called “Catalan's minimal curve.” However, the most famous theory of all is the “Catalan Conjecture” made in 1844 in a letter he sent to one of his friends' journal. It read: I beg you, sir, to please announce in your journal the following theorem that I believe true although I have not yet succeeded in completely proving it; perhaps others will be more successful. Two consecutive whole numbers, other than 8 and 9, cannot be consecutive powers; otherwise said, the equation xm - yn = 1 in which the unknowns are positive integers only admits a single solution. Solving this “conjecture” was awfully slow. In 1850, a man named Victor Lebesgue that no solution existed when n = 2. Catalan also wrote few popular texts that ran in different editions. He wrote: Elements de géométrie (1843); the two volume work Traité élémentaire de géométrie descriptive (1850-52) which ran to 5 editions; Théorèmes et problèmes de géométrie élémentaire (1852) which ran to 6 editions, and many more that are known worldwide. Eugene Catalan made a huge impact in the mathematical world, and contributed with his unbelievable theories and mind puzzling ideas. His accomplishments has helped us today by learning more about his ways of solving numbers and shapes in an “elegant” way.

Pierre Simon de Laplace
I chose Pierre Simon de Laplace as my second mathematician so I can travel way back in history and find out more about mathematics. Laplace was born on the 23rd of March, 1749, and passed away March 5, 1827. Laplace was a famous French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics.

Pierre Simon de Laplace probably made a much larger impact on the world of math than Eugene Catalan did. In his five volume Mécanique Céleste, he translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. Many do not know that the Bayesian interpretation of probability was mainly developed by Laplace. The “Laplacian differential operator” which is widely used in applied mathematics, is also named after him. He was great in the world of mathematics.

However, as an astronomer, he restarted...
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