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) > 101010101010101010101010101010 (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:

  • Nfamwap@lemmy.world
    1·
    1 year ago

    11 X 11 = 121

    111 X 111 = 12321

    1111 X 1111 = 1234321

    11111 X 11111 = 123454321

    111111 X 1111111 = 12345654321

  • aggelalex@lemmy.world
    1·
    1 year ago

    The Fourier series. Musicians may not know about it, but everything music related, even harmony, boils down to this.

  • timeisart@lemmy.world
    1·
    1 year ago

    Multiply 9 times any number and it always “reduces” back down to 9 (add up the individual numbers in the result)

    For example: 9 x 872 = 7848, so you take 7848 and split it into 7 + 8 + 4 + 8 = 27, then do it again 2 + 7 = 9 and we’re back to 9

    It can be a huge number and it still works:

    9 x 987345734 = 8886111606

    8+8+8+6+1+1+1+6+0+6 = 45

    4+5 = 9

    Also here’s a cool video about some more mind blowing math facts

  • mookulator@lemmy.worldEnglish
    1·
    1 year ago

    The four-color theorem is pretty cool.

    You can take any map of anything and color it in using only four colors so that no adjacent “countries” are the same color. Often it can be done with three!

    Maybe not the most mind blowing but it’s neat.