Numberphile's Square-Sum Problem was solved! #SoME2

Comments · 387

• EV

  @evansaschow · 3 years ago · pinned

  The terminology “ninja pair” has gotta be named after the Ninja Report from How I Met Your Mother, right?

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• CI

  @cienciandre · 4 years ago

  Imagine the people involved in this just casually writing a proof by induction with 49 base cases lol

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• IS

  @IsYitzach · 4 years ago

  I must say, putting Matt Parker's face in the thumbnail was genius marketing. I thought it was a Numberphile video. I watched the whole thing because math.

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• MO

  @moosewhisker8072 · 4 years ago

  I remember working on this problem in summer 2018. We used different methods to show that a solution exists for all integers of the form 8n^2+8n using regular sequences consisting of all integers from 2k^2-2 to 2(k+2)^2-2. You can stitch them together using graph theory to make a really nice honeycomb pattern which is easy to find hamilton paths on (which is equivalent to finding regular sequences)

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• LE

  @lexinwonderland5741 · 4 years ago

  3B1B's SoME is probably the best thing for math education since the first YouTube math channels like OG Numberphile. It has brought out so many fascinating areas of math I had never thought about, and encouraged so many fantastic educators to produce videos like this. Absolutely fantastic job and I'm glad I discovered your channel, and I can't wait to see more content from you!

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• PE

  @pearceburns2787 · 4 years ago

  I can't say this is the most accessible maths video for non-maths people, but it does feel exactly like reading a maths paper, and I'd like more content like this!

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• VB

  @vbregier · 4 years ago (edited)

  <a href="https://www.youtube.com/watch?v=-vxW42R47bc&amp;t=188">3:08</a> I would argue that 1 should be ticked...<br>There is one ordering, and it does satisfy the property, as there are no two consecutive numbers, we can say that the statement is true for this ordering. all the sums of two consecutive numbers are squares.<br><br>(which is also confirmed later by « any subsequence of a regular sequence is regular ».)

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• DR

  @drchaffee · 4 years ago

  This is a beautiful, well-crafted example of how a recreational problem generates lines of reasoning; proof construction; and computational techniques - all essential tools for math writ large.

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• OM

  @omegaminusfour · 4 years ago

  For the Dutch IMO selection test, a solution for a particular number was needed was needed for the fourth problem. I instantly knew that there was an easy solution. Although I spended a lot of time on the problem (at least, more than necessary), I managed to solve the problem with 7 points.

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• VE

  @vekyll · 4 years ago (edited)

  A beautiful example of what we can do when humans and computers join forces, and everyone does what they are the best at. Obviously, neither humans alone nor computers alone couldn&apos;t come up with this solution all by themselves.

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• -.

  @-.._.-_...-_.._-..__..._.-.-.- · 4 years ago

  Maybe I&apos;m dumb, but I never knew square numbers could be represented like this, as literal squares. This is kinda mind blowing, because now I&apos;m realizing that cubes are the same way but literal cubes. I had no idea! I just thought those were the names we gave them because a square is 2D space while a cube is 3D space. I never realize these numbers actually formed perfect squares and cubes and that&apos;s why we call them that. Now, I&apos;m feeling a little angry that this somehow got passed me.

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• CA

  @canaDavid1 · 4 years ago

  <a href="https://www.youtube.com/watch?v=-vxW42R47bc&amp;t=180">3:00</a> shouldn&apos;t 1 be possible? (As there are no pairs of numbers, every has a sum of a square)

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