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What are the most mindblowing things in mathematics? (lemmy.world)
submitted 1 year ago* (last edited 1 year ago) by cll7793@lemmy.world to c/nostupidquestions@lemmy.world
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What concepts or facts do you know from math that is mind blowing, 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 mind blowing 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) > 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10 (10s are stacked on each other)
  • Σ(17) > Graham's Number
  • Σ(27) If you can compute this function the Goldbach conjecture is false.
  • Σ(744) If you can compute this function the Riemann hypothesis is false.

Sources:

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[-] Artisian@lemmy.world 113 points 1 year ago* (last edited 1 year ago)

For the uninitiated, the monty Hall problem is a good one.

Start with 3 closed doors, and an announcer who knows what's behind each. The announcer says that behind 2 of the doors is a goat, and behind the third door is ~~a car~~ student debt relief, but doesn't tell you which door leads to which. They then let you pick a door, and you will get what's behind the door. Before you open it, they open a different door than your choice and reveal a goat. Then the announcer says you are allowed to change your choice.

So should you switch?

The answer turns out to be yes. 2/3rds of the time you are better off switching. But even famous mathematicians didn't believe it at first.

[-] Ethalis@jlai.lu 12 points 1 year ago

I know it to be true, I've heard it dozens of times, but my dumb brain still refuses to accept the solution everytime. It's kind of crazy really

[-] emokidforever@lemmy.world 1 points 1 year ago

This explanation really helped me make sense of it: Monty Hall Problem (best explanation) - Numberphile

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this post was submitted on 03 Aug 2023
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