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To solve complex problems, it is sometimes possible to reduce its complexity with special methods, for example, one method is to add a new dimension to the problem. For example, to prove the Pythagorean theorem, which is an area problem, a simpler proof can be provided by converting it into a volume problem.
According to Shannon's theory, entropy has been added or information has been added by adding a dimension.
Can this idea lead to a new proof of Fermat's Last Theorem, which has already been solved with a very complicated proof by the British mathematician Andrew Wiles?
The idea of adding a new dimension or utilizing different perspectives to solve complex problems is indeed a common approach in mathematics and problem-solving in general. However, it's important to note that Fermat's Last Theorem has already been proven by Andrew Wiles in 1994, and his proof is considered to be valid and complete.
Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than 2. Andrew Wiles' proof of this theorem involved a deep understanding of advanced mathematical concepts, particularly in the field of elliptic curves and modular forms. His proof spanned over 100 pages and utilized sophisticated techniques from various branches of mathematics, including algebraic geometry and number theory.
While it is possible to approach problems from different angles and use alternative methods, it is highly unlikely that adding a new dimension or changing the problem's formulation would lead to a fundamentally different and simpler proof of Fermat's Last Theorem. The mathematical community has extensively reviewed and accepted Wiles' proof as a valid and rigorous solution to the problem.
It's worth noting that even though the original proof of Fermat's Last Theorem was complex, the techniques and insights developed during the process have had significant impacts on other areas of mathematics. The proof opened up new avenues of research and contributed to the development of mathematical concepts and tools that have found applications in various fields.
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