42 was the last remaining number below 100 which could not be expressed as the sum of three cubes - until now

[Wanderfound]

@cepheus42

can someone tell me why it matters? What does it do for us that we can now describe all numbers below 100 as the “sum of three cubes?”

To pure mathematics! May it never be of any use to anyone!

— Henry John Stephen Smith

[cepheus42]

I can totally agree with that sentiment. Things are beautiful because they are.

[anon62577920]

[Wally]

Aaaaaaaaand, that’s Numberwang!

[Uniq]

Have they proven that certain numbers have only one possible solution or are there infinitely many possible (just unrealistic to find?). For example, are there potentially other 3 number combos that could be cubed and summed up to 42?

[Wally]

I’m flattered, but frankly, I haven’t got a clue. All I can think of is recursively trying a bunch of other combinations?

[tuhu]

@Uniq

For example, are there potentially other 3 number combos that could be cubed and summed up to 42?

There are potential other combos… the theory is that there are infinite sets of three for each*, not just one for each. (That’s why it’s interesting where we couldn’t even find one. The other sets could also approach being infinitely large numbers too, but there’d be an infinite number of those sets…)

Also, 42 is just the last of the ones under 100; there’s still 10 under 1000 that haven’t had a set found yet.

* for every whole number that’s not of the form 9𝑘+4 or 9𝑘+5…

[philbin1]

42: The answer to life, the universe and everything