The Mystery of 42 is Solved - Numberphile

42 was the last remaining number below 100 which could not be expressed as the sum of three cubes (*) - UNTIL NOW
More links & stuff in full description below ↓↓↓

(*) barring numbers for which this known to be IMPOSSIBLE - see previous videos.

NUMBERPHILE

Videos by Brady Haran

[neilgerace]

"I told you you weren't going to like it."

[N.I.R.A.T.I.A.S.]

Drew Sutherland looks like he could be any age between 25 and 55.

[Varinrumpai]

Fun fact. 42 (forty-two) is the natural number that succeeds 41 and precedes 43.

[bestserg]

Born too late to explore the earth,
Born too early to explore the galaxy,
Born just in time to witness the answer to the Ultimate Question being found.

[greenredblue]

“How did you accomplish this amazing achievement!?!”

“We had a computer do it. But we are very proud of the algorithm.”

“Oh.. and how did you know that you were getting close? Were you excited?”

“The computer emailed me the solution. And no.”

“...Oh. Well still, this is a very important day all the same!”

“Actually it is! How did you know it was my wife’s birthday?”

[nsxdarin]

also the only number that can be written as the product of 6 and 7

[HonkeyKongLive]

This has been the kind of long term drama I come to YouTube for.

[chromeAKs]

When the secrets of the Universe are figured out, it will immediately be replaced with another one

[workwithnature]

42 = 7x6 took me a while to figure out.

[nekogod]

This feels so satisfying, I remember watching the first video where 33, 42 and 74 were missing, and it's so nice to have it come full circle!

[ffggddss]

The numbers marked "impossible" are all ≡ ±4 (mod 9).
All such integers are impossible, because every cube is ≡ {0, ±1} (mod 9), so all possible sums of 3 of them, must be ≡ {0, ±[1, 2, 3]} (mod 9) – IOW, anything but ±4.

Fred

[mananself]

It’s amazing that the third solution for 3 has been found already.

[yusuf-]

Brady: You must be really excited; tell us how you're feeling.
Andrew: Yes.

[crisdekker]

I'm assuming you called the computer that found this "Deep thought".

[jblen]

Fun fact: 42 is ASCII for *, which in programming means 'all', so 42 is the meaning of everything.

[ceruchi]

Aw, one of the best things about being a longtime Numberphile viewer is getting to watch math breakthroughs in real time. These updates always make me tear up!!

[stevemonkey]

We now have an answer to 42. Oh well, that's it, that's now the end of the universe.

[kinyutaka]

I've noticed something. If you sum consecutive cubes it equals the sum of the numbers squared.

1³+2³+3³=6², 1³+2³+3³+4³=10², 1³+2³+3³+4³+5³=15², etc.

That means that the difference between the squares of triangular numbers (n² and (n-1)²) is going to be equal to n³

[santiagomontoya]

This truly makes me happy, I had been thinking about this since the 33 video. Congrats to Andrew

[ThePetaaaaaa]

I can't believe how excited I just was when I saw the thumbnail