Gödel's First Incompleteness Theorem:
This theorem states that in any consistent formal mathematical system that is expressive enough to formulate basic arithmetic, there exist true mathematical statements that cannot be proven within the system. In other words, there are truths within mathematics that cannot be deduced or demonstrated using the rules and axioms of that particular mathematical system.
It implies that there will always be mathematical truths that lie beyond the reach of formal proof within a given system.
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Hello guys, thanks for all the instructive comments. I initially wanted this market to be a questioning about very fundamental notions of maths, but maybe not as fundamental as directly arguing the validity of the concept of a theorem. My initial goal was more to question the broadness of our current math knowledge and the possibility that we could discover and maybe switch to another arithmetic/logic framework in the coming years of the singularity that would be better and more « dense », more fundamentally complete and that would be more powerful, let me try to rephrase my question for a possibly clearer market :
Is there a world where mathematics appear to be disrupted by a more complete framework, with better usability and capabilities, maybe refuting part or all of our current knowledge about maths, and allowing new discoveries and comprehensions.
The hope of this market was to measure the temperature regarding this possibility of a wider versions of what we call mathematics today that would come in the future.
The fact it tuned to be interesting to bet on for you is fun I guess, but also it seems like some people could be interested by this rephrasing.
But overall I admit that the current phrasing is quite poor. I hope this can turn into a better and clearer market later, as I found this very thought provoquant because, as an engineer, I always felt like maths is lacking something to grasp about the world we live in, like if there was big holes in the field and that we could found a much more « compact » version of all this, allowing much more consistent writing, calculation and logical manipulation.
Thanks everyone, If you could help me turn this into a less contradictory/incorrect phrasing that would be awesome, if not, no problem, I still got some fun trying to explain myself here haha
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