Essay The 's Last Theorem, By Michael Hutchings

Essay The 's Last Theorem, By Michael Hutchings

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Fermat’s Last Theorem--which states that an + bn = cn is untrue for any circumstance in which a, b, c are not three positive integers and n is an integer greater than two—has long resided with the collection of other seemingly impossible proofs. Such a characterization seems distant and ill-informed, seeing as today’s smartphones and gadgets have far surpassed the computing capabilities of even the most powerful computers some decades ago. This renaissance of technology has not, however, eased this process by any means. By remembering the concept of infinite numbers, it quickly becomes apparent that even if a computer tests the first ten million numbers, there would still be an infinite number of numbers left untested, ultimately resulting in the futility of this attempt. The only way to solve this mathematic impossibility, therefore, would be to create a mathematic proof by applying the work of previous mathematicians and scholars.
A mathematic proof, as defined by Michael Hutchings of University of California-Berkley, is simply “an argument which convinces other people that something is true [through mathematical reasoning]” (Hutchings 1). This definition, however, severely simplifies the steps that much be taken in order to move a mathematical claim into truth; in extension to the previous definition, it must be recognized that the steps with which truth is revealed include largely the jumping between bodies of established knowledge and conclusive principles to back up the central claim—acting as a string of sorts that yield the cohesive argument at the end of the process. Therefore, when proofs are mentioned in this paper, the definition used will be that of Hutchings in addition to the idea of mandating evidence chains.
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...ives of students nor does it particularly resonant due to its low appeal and interest. To completely dive into the stigma of an apathetic high school student, does it matter whatsoever whether or not a solution can be found to an + bn = cn? What practical or academic repercussions are there? No and none. In terms of practical, pragmatic use, little evidence can be found that Wiles’s work substantially impacted any mathematical work of substance since the proof to Fermat’s Last Theorem has long been hailed as “one of the hardest mathematical puzzles,” not as one of the most fundamentally important or urgent questions for the math community. This may sound harsh and reductive of the seven years work that Wiles dedicated to pursuing his passion, but the central argument is not that Wiles’s work was useless to him, but that it is useless to the great majority of people.

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