A Magic Square Breakthrough - Numberphile

NUMBERPHILE

Videos by Brady Haran

Special mention to Debbie Chakour and Michael Colognori, eagle-eyed fact checkers from the Numberphile Society!

[Living_Murphys_Law]

Let's go, Numberphile main plot progression

[tremapar]

The $10k promised Parker prize should be a check for like $9998.50

[arrozbyanyothername]

2:26 I enjoy the running joke Matt Parker has on this channel of pretending he's recalling something and instead is just reading it off

[StephenLawlessOLCS]

The 8x8 magic square featured at 3:22 is all the more impressive when you see that it contains the digits 1-64 once each. No gaps, no repeats.

[unvergebeneid]

I love how Matt subtlety tries to redefine "Parker Square" to mean "a 3×3 magic square of square numbers" instead of _almost but not quite_ that. I see you Matt! Nice try!

[connoranastasio]

Magic Squares getting an update patch in 2025 is wild

[denelson]

For the not keen-eyed among you, you'll notice that the Pfefferman square has the added property that it contains every natural number from 1 to n² exactly once.

[parzh]

12:58 "We now have a breakthrough that's answered all our questions except for «Does a 3-by-3 magic square of squares exist?»"

One might say that that's a Parker breakthrough

[katherinek]

That is the best mathematical result ever. It answers all of our questions, but leaves just a finite space of unknown to work out as a treat.

[youarentreadingthisareyou]

They secretly solved it, but they're gonna wait until Matt's 45th birthday in December to finally reveal the magic square of squares.

[superjez]

Closer and closer for Parker to be famous in some obscure mathematical book with the papers kinda stemming from the classic numberphile video.

[cykkm]

A square of much smaller square numbers with the same defect as the winning solution is in Lee Sallows, The lost theorem, The Mathematical Intelligencer, 19(1997), n°4, 51-54. All rows, columns and _one_ diagonal sum up to the square number 147²=21609. I don't know Parker's definition of "nice and small" numbers; this reference may be irrelevant.

127² 46² 58²
2² 113² 94²
74² 82² 97²

[MDA.]

The first square also works in modular arithmetic. Actually for every square where there are two different sums it should be possible to find a modulus in which the square is correct. The first square works in mod 3, 9, 11, 27, 33, 99, 297, 349, 1047, 3141, 3839, 9423, 11517, 34551, 103653.

[jbomber]

yknow, this episode made me realize that we really are the same mathemeticians of old. In the sense that we are just putting our open problems out there for other people to collaborate on - the only difference is that we're doing it through the medium of these YouTube videos instead of putting them in journals or newspapers. And I think this channel is really amazing for getting us all to participate in that.

[rahulkumar-hfjz]

We got Parker Square Update before GTA 6 😭

[SeanCMonahan]

[[1]] is a magic square of squares. It's a magic square of every integer power, actually. It has the bonus that every possible diagonal sums to the same number, including the ones that wrap around at the edges.

[Awkwerp]

My first thought near the beginning when you showed the bigger squares was "I wonder if they have a minimum size required for each power- like maybe squares minimum is four, and cubes minimum is 7, etc". Really cool to see that end up being exactly whats being studied.

[mazza]

gosh it was eight year ago….. time really does feel like its flying at times

[joehopfield]

The vast power of the collective maths genius at Matt‘s disposal truly boggles the mind. As long as he uses it for good and not evil.

[IceMetalPunk]

So the paper has proven upper bounds on the possible lower bounds of square sizes?

Honestly, my favorite part of this is that it's actual newly discovered maths brought on by a YouTube channel. If it weren't for the original video, and Tony's video, and then Brady's questioning, and then a viewer's watching it and pondering it... the new maths wouldn't have happened. I love the impact you guys are having on the world at large!