What are the most mindblowing fact in mathematics? - Lemmy.world

What concepts or facts do you know from math that is mindblowing, awesome, or simply fascinating? Here are some I would like to share: - Gödel’s incompleteness theorems: There are some problems in math so difficult that it can never be solved no matter how much time you put into it. - Halting problem: It is impossible to write a program that can figure out whether or not any input program loops forever or finishes running. (Undecidablity) The Busy Beaver function Now this is the mindblowing one. What is the largest non-infinite number you know? Graham’s Number? TREE(3)? TREE(TREE(3))? This one will beat it easily. - The Busy Beaver function produces the fastest growing number that is theoretically possible. These numbers are so large we don’t even know if you can compute the function to get the value even with an infinitely powerful PC. - In fact, just the mere act of being able to compute the value would mean solving the hardest problems in mathematics. - Σ(1) = 1 - Σ(4) = 13 - Σ(6) > 101010101010101010101010101010 - Σ(17) > Graham’s Number - Σ(27) If you can compute this function the Goldbach’s conjecture is false. - Σ(744) If you can compute this function the Riemann hypothesis is false. Sources: - YouTube - Gödel’s incompleteness Theorem by Veritasium [https://piped.video/watch?v=HeQX2HjkcNo] - Wikipedia - Gödel’s incompleteness theorems [https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems] - YouTube - Halting Problem by Computerphile [https://piped.video/watch?v=macM_MtS_w4] - Wikipedia - Halting Problem [https://en.wikipedia.org/wiki/Halting_problem] - YouTube - The Busy Beaver function by Mutual Information [https://piped.video/watch?v=kmAc1nDizu0] - Wikipedia - Busy Beaver [https://en.wikipedia.org/wiki/Busy_beaver]