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What are the most mindblowing things in mathematics? (lemmy.world)

submitted 1 year ago* (last edited 1 year ago) by [email protected] to c/[email protected]

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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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[–] [email protected] 16 points 1 year ago (1 children)

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

[–] [email protected] 4 points 1 year ago

I suspect this holds true to any base x numbering where you take the highest valued digit and multiply it by any number. Try it with base 2 (1), 4 (3), 16 (F) or whatever.