... one of - if not the most famous proof in all of mathematics - admired for its elegance - simplicity and profundity is Euclid's Proof of Infinite Primes - mathematical rigor currently enjoys an unprecedented historical resurgence over its long history - yet to this author - it seems the strength of the deep-learned analysis and logical arguments used in ancient Greek proof somehow remains missing in contemporary mathematics - to address this - the author does not follow conventional research protocol and abandons research into all prior knowledge on the elusive proof of the long-standing Twin Prime Conjecture - rather - a rare summit attempt is made from first principals alone - equipped with little more than the definition of a twin prime - this Canadian mathematician begins a six year mathematical solo research expedition into unravelling the chaos that is the twin primes - always in search of patterns - the nature of the of twin primes has led several mathematicians to conclude that the exhibited random pattern is chaotic - no discernible pattern exists - under such conditions we cannot predict anything about how twin primes behave nor attempt to count them over increasingly large - infinite domains - lacking a proof akin to Euclid's - that outcome places twin primes outside the harmonious mathematics of the ancient Greeks - a world that we mathematicians have always sought to retain - such incongruity and disharmony is jarring and harsh for any mathematician to accept - after undergoing my transformation into a mathematical alpinist - the expedition strategy was to focus not on the (twin) primes but rather their theoretical complement - the odd composites - it was conjectured by the author that a deeper understanding of these simplistic mathematical entities would indirectly reveal how twin primes are constructed - to summit one of the highest unclimbed mathematical peaks - required new innovative techniques - bold daring thoughts and inexhaustible patience and persistence - if you continue to climb and gain altitude you must - eventually - reach the summit - one painful step at a time - lastly - having reached the summit - by far the most daunting task was to collate and present the argument in such a manner that others would not only understand it but be convinced of the result in the same manner that those who read Euclid's proof are - with elegance - simplicity and profundity ...
... this long-awaited Proof of the Twin Prime Conjecture rescues the harmonious nature of mathematics out of chaos ... it was an exhilarating unforgettable intellectual mathematical alpine expedition ... more than once I felt at the brink of physical and mental exhaustion and had to take a brief walk away simply to recover from the task - too often any discussion of the hard intellectual struggles are omitted from the discourse and too often the final result alone is presented as if it was the initial effort and attempt - when the truth involved so much more ...