Math's Fundamental Flaw

there is a hole at the bottom of math a hole that means we will never know everything with certainty there will always be true statements that cannot be proven now no one knows what those statements are exactly but they could be something like the twin prime conjecture twin primes are prime numbers that are separated by just one number like 11 and 13 or 17 and 19. and as you go up the number line primes occur less frequently and twin primes are rarer still but the twin prime conjecture is that there are infinitely many twin primes you never run out as of right now no one has proven this conjecture true or false but the crazy thing is this we may never know because what has been proven is that in any system of mathematics where you can do basic arithmetic there will always be true statements that are impossible to prove that is life specifically this is the game of life created in 1970 by mathematician john conway sadly he passed away in 2020 from covet 19. conway's game of life is played on an infinite grid of square cells each of which is either live or dead and there are only two rules one any dead cell with exactly three neighbors comes to life and two any living cell with less than two or more than three neighbors dies once you've set up the initial arrangement of cells the two rules are applied to create the next generation and then the one after that and the one after that and so on it's totally automatic conway called it a zero player game but even though the rules are simple the game itself can generate a wide variety of behavior some patterns are stable once they arise they never change others oscillate back and forth in a loop a few can travel across the grid forever like this glider here many patterns just fizzle out but a few keep growing forever they keep generating new cells now you would think that given the simple rules of the game you could just look at any pattern and determine what will happen to it will it eventually reach a steady state or will it keep growing without limit but it turns out this question is impossible to answer the ultimate fate of a pattern in conway's game ...