Chaitin, best known for Chaitin’s unknowable number, thinks it depends on the math:
Gregory Chaitin: Deep philosophical questions have many answers, sometimes contradictory answers even, that different people believe in. Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics — papers that fill in much-needed gaps because somebody has to publish. So you take some problem, you change the wording of the mathematical problem a little bit, then you solve it, and then you write a paper.
But other mathematics does seem to be discovered. That’s when you find some really deep, fundamental mathematical idea, and there it really looks inevitable. If you hadn’t discovered it somebody else would have discovered it.
One idea is that mathematics is in the mind of God or in the Platonic world of ideas. It’s all there, and all we do is discover it. But I think there’s a distinction. A famous mathematician, Henri Poincaré, said (it sounds better in French than in English) “There are problems that we pose and problems that pose themselves.”News, “Mathematics: Did we invent it or did we merely discover it?” at Mind Matters News
What does it say about our universe if the deeper mathematics has always been there for us to find, if we can?
You may also enjoy:
rom the transcripts of the second podcast: Hard math can be entertaining — with the right musical score! Gregory Chaitin discusses with Robert J. Marks the fun side of solving hard math problems, some of which come with million-dollar prizes. The musical Fermat’s Last Tango features the ghost of mathematician Pierre de Fermat trying to frustrate the math nerd who solved his unfinished Last Conjecture.
Also, Chaitin’s discovery of a way of describing true randomness. He found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data. So, Chaitin on randomness: The simplest theory is best; if no theory is simpler than the data you are trying to explain, then the data is random.
How did Ray Solomonoff kickstart algorithmic information theory? He started off the long pursuit of the shortest effective string of information that describes an object. Gregory Chaitin reminisces on his interactions with Ray Solomonoff and Marvin Minsky, fellow founders of Algorithmic Information Theory.
Here are the stories, with links, to an earlier recent podcast discussion with Gregory Chaitin:
Gregory Chaitin’s “almost” meeting with Kurt Gödel. This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius. Chaitin recalls, based on this and other episodes, “There was a surreal quality to Gödel and to communicating with Gödel.”
Gregory Chaitin on the great mathematicians, East and West: Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out. Chaitin discusses the almost supernatural awareness some mathematicians have had of the foundations of our shared reality in the mathematics of the universe.
How Kurt Gödel destroyed a popular form of atheism. We don’t hear much about logical positivism now but it was very fashionable in the early twentieth century. Gödel’s incompleteness theorems showed that we cannot devise a complete set of axioms that accounts for all of reality — bad news for positivist atheism.
You may also wish to read: Things exist that are unknowable: A tutorial on Chaitin’s number (Robert J. Marks)
Five surprising facts about famous scientists we bet you never knew: How about juggling, riding a unicycle, and playing bongo? Or catching criminals or cracking safes? Or believing devoutly in God… (Robert J. Marks)