Yes, it looks as though we really have nailed the problem; Fermat’s Last Theorem may very well be not as esoteric and complicated as experience has wanted us to believe. Please forgive us as we may appear to be blowing our own trumpet – we are not persons of those kind of habits, no, we are merely stating facts as they stand insofar as we can best evaluate them. If our proof stands the test of time and experience – as we strongly believe is going to be the case; then, the immortal words of the great physicist Professor Dr. Albert Einstein (1879-1955) that “Subtle is the Lord. Malicious He is not.” may very well resonate with the truth.
Since the theorem was first set into motion in 1637 by the pre-eminent French Lawyer and amateur mathematician – Pierre de Fermat (1607−1665); in a very notorious marginal note in the copy of book Arithmatica, the note which reads:
``It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.”
Fermat’s so-called ``truly marvellous” proof proved costly and elusive to come by. Fermat had the peculiar habit of writing notes in the margins of his books and most of these notes were theorems he himself had discovered and it was left to the readers of these notes to prove the supposed theorems. For some of the theorems, the proofs were discovered amongst his papers. One stood out, and this theorem, even though its proof was not known, it came to be known as Fermat’s Last Theorem.
Because all of the supposed theorems in the margins had had their proofs found amongst Fermat’s papers and in the case were no papers were found, someone had provided the proof, save for the Last Theorem, everyone was of the idea that this last unproved assertion by Fermat had to be true somehow. So, it gained the title Fermat’s Last Theorem.
Failure after failure, even by the three of the very great mathematicians i.e., Italy’s Leonhard Euler (1707-1783), France’s Pierre-Simon, marquis de Laplace (1749 − 1827), and the celebrated genius and Crown Prince of Mathematics i.e., Germany’s Johann Carl Friedrich Gauss (1777 − 1855); this lead to the yet to be proved theorem gaining, “world-wide, international and historic” notoriety as the hardest mathematical problem known to man. Prior to 1995, this problem was recorded and ranked in the Guinness Book of World Records as one of the “most difficult mathematical problems” known to humanity.
It was not until 358 years later that the English Professor working at the University of Cambridge, Sir Andrew Wiles provided the first definitive proof. His proof spans well over 100 pages of paper and it had two flaws before it was accepted as a final proof. This proof by Sir Professor Andrew Wiles employs so advanced mathematics which is only accessible to the esoteric and the highly advanced mathematical minds. We should say, we ourselves do not have the hope of oneday understanding Sir Professor Andrew Wiles proof. We are not mathematicians but physicists and we only delve into the waters of mathematics on a part-time basis only for mental gymnastics.
The proof by Sir Professor Andrew Wiles employs mathematical tools and methods that were only developed after Fermat. This gave rise to the question that if this proof is so hard, “Did Fermat really have the proof as he claimed?” This question has lead to doubts as to whether or not Fermat actually possessed the correct proof of his conjecture. If he really did, then he must have employed mathematical methods and tools that existed during his day.
If anything, our proof does that, it employs mathematical methods and tools that were present in the days of Fermat. Ours – if only its morass substance is what is to be required, it is a proof that spans not more than 5 pages. To add on to that, it employs mathematical methods and tools that were available in the days of Fermat. This leads one to the strong viewpoint that indeed, Fermat might very well have had the proof as he claimed.
As we anxiously await the World to judge our proof, effort and work, we must --- if this be permitted at this point of closing, say that, we are confident that -- simple as it is or may appear, this proof is flawless, it will stand the test of time and experience. It strongly appears that the great physicist and philosopher -- Albeit Einstein, was probably right in saying that ``Subtle is the Lord. Malicious He is not.” If we are proved correct – as we believe we will, then, we dedicate this success to reducing the complexity of the proof to Fermat’s Last Theorem, to the Education system of our beloved motherland -- Zimbabwe.
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