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:

  • VarykEnglish
    14·
    1 year ago

    Great thread. I’m just reading and watching stuff this afternoon now

    • cll7793@lemmy.worldOPEnglish
      51·
      1 year ago

      Glad you are enjoying it! Please feel free to share any other channels like Computerphile, Numberphile, Mutual Information, & Veritasium. It’s difficult to find gems nowadays on YT.

      • jantin@lemmy.world
        44·
        1 year ago

        I like Stand-up Maths, usually starts with a real-life situation and escalates into proper math, sometimes also programming shows up.

      • Blyfh@lemmy.world
        2·
        1 year ago

        Well, if you ever want to find some more mathtubers, just browse the #SoMe2 or #SoMe3 hashtags on YouTube. It led me to Morphocular, who does great videos with great visual quality similar to 3B1B. Another great channel is Another Roof with a completely different approach of videomaking. VSauce also has some good videos on math topics, if you like him.

      • SandLight@lemmy.worldEnglish
        1·
        1 year ago

        As mentioned by @Blyfh, 3Blue 1Brown is great.

        I also came across this channel by Freya Holmér recently that does more Long Lecture videos on math for video game programmers. I found the the one on splines to be quite enlightening (as I had recently been doing a lot of spline stuff and struggling with third party packages).

        https://www.youtube.com/@Acegikmo

      • bird@aussie.zone
        1·
        1 year ago

        Late to the party but one channel I came across was Combo Class, who should get more love! I adore his setup and his passion for weird maths stuff.

        Absolutely strange in the most endearing way.