Curvy Mathematics

Gregory Chaitin

Tribute to Gregory Chaitin

 The Greek alphabet can be found all over the mathematical universe, circle's π, Fibonacci's Φ, etc. Among them resides a not very common one too, the "big O" or as it is called, Omega number (Ω). Turing's halting problem and Gödel's incompleteness theorem are just two igniting inspirations for the discovery of Omega number by a modern iconoclast, Gregory Chaitin.

 During his childhood, his mind was excited by general relativity and quantum mechanics, so his path was foreshadowed/predetermined. Then Gödel's beliefs had a severe impact on him resulting in abandoning his spyglass watching the skies for the peculiar and obscure path leading to the abyss of theoretical mathematics. It is a periculous path contrary to what most people may think about it but the discovery of fundamental facts is an extremely attractive idea. Despite the danger that lurks in these distant regions of the human mind, where the borders of sanity can sometimes easily be crossed, very few brave mathematicians and scientists dare to walk over there and get lavishly repaid! "Sometimes, in mathematics one thinks like God".

 He was no exception in facing difficulties obstructing his way. The toughest part is to realize that one is standing in front of a treasure, not to discover the treasure. Since his twenties, he had already developed the proper toolkit to mathematically study life and evolution but it took him almost a lifetime to completely conceive the potential of his development. Just like everyone, young minds can easily get distracted and attention gets diverted to different objectives. Thankfully, mathematics is indifferent to age.

 It seems that being a good rhetor can be beneficial in all occupations, in all eras throughout human history. Although the ideal scientist should behave as a hero or as an immortal, mortal needs tend to alter human characters even if they are trained to be scientists. "Fields of science are power structures and do not welcome new ideas especially from outsiders." Like the guilds a few centuries ago, nowadays a scientist has to get adopted by a modern scientific team, if one would like some recognition for one's scientific work. In the past, there was only a bunch of scientists and good science was a relatively easy thing to do.

 Mr Chaitin is clear that things have changed - big time: "Science is a big business with a giant administrative bureaucracy" he states. Scientists get paid which means that they have to be productive. "That explains why there have been no fundamental advances in physics since the 1920s. The shut up and calculate dogma has killed physics".

 The current tendency in modern societies is to spend money that one does not possess to buy things which one does not need. Very few are left wondering very basic questions like "Why are we here?", or very few seem to be interested in trying to find an answer to the primordial questions that almost all humans have when they gaze at the night sky during their childhood.

 He considers himself as a very fortunate person as he had the chance to work on many fundamental, philosophical questions which many mathematicians have no interest in anymore. If he could have chosen a different road in life, then becoming a mountain climber or a martian colonist would probably be some of his options. Definitely, he honours the creativity of the human mind, he admires people who use their mental resources in order to advance the understanding of how our universe works instead of spending their time and resources in doing politics and contracting or improving scientific, public relations.

 Just like his hero, Leibniz who created new mathematical fields in order to give an answer to questions which have remained unanswered for countless centuries. Most of Leibniz's precious ideas were discovered after his death among his writings.

 Unfortunately, many scientific advances have been attributed to the wrong people. Dead cannot speak and the truth is extremely difficult to be unveiled. Additionally, too much attention on one's work draws the admiration of non-specialists as well as the envy and hate of one's colleagues. In the end though, science should be above all these mortal and pathetic matters. "Real science is a lonely, solitary pursuit between you and God".

Moderator: Gauss, Overseers.