(Brady: There you go.)
(You're wearing it. [laughs])
I'm wearing it. Yep.
(Brady: Tell me the news.)
We found 42.
(Brady: All right.)
Do you want to see what it is?
(Brady: Yep. All right.)
You ready?
-80538......
...all cubed. Plus
804......5, cubed,
plus 126......31, cubed.
(Brady: All right. There we go. And why is this significant?)
(Why is 42 a bit of a milestone in this field of endeavour?)
So this started a computer search from way back in 1954.
They were looking for the numbers up to 100 to see which of them could be represented as a sum of 3 cubes
and we've now just answered that,
65 years later.
(Brady: So this is it. This was the last one?)
This was the last one. Yep.
It takes 17 digit numbers to get there.
That's why - of course they had no hope of ever finding it in 1954.
(Brady: I saw you recently when you'd found 33,)
(and you used a big computer not far from here at the University of Bristol.)
That's right.
(Brady: Was this one found by computer - the same computer?)
No, this is actually much bigger.
So we had to go another order of magnitude beyond what I did for 33, to find this.
So I actually think the most interesting aspects this time around were sociological rather than mathematical.
After the 33 news, I got lots of offers of help.
Had to turn most of them down, actually.
The first thing I did was go straight to Drew Sutherland at MIT,
he's a world expert at this sort of thing.
We teamed up and you know, modified the code to make it run in a much bigger scale.
The other thing was, we got a big offer of help from Charity Engine.
So they harness the power of millions of volunteer PCs. Okay, and they gave us a computing platform,
that's you know, massively larger than anything I could get as an academic.
And that's how we found it.
(Brady: So some of the people watching this video, if they're involved with Charity Engine, may have been involved with the discovery?)
That's right, yeah.
(Brady: Okay.)
(How did you find out? How did you find out that there had been the breakthrough?)
(What - how did the news get to you?)
Oh, the Charity Engine guys emailed us with the solution.
(Brady: Right. )
(Did they - did the e-mail say "great news! This is amazing!" or was it a really perfunctory email? Or - ?)
Just said we have a solution.
Here it is.
(Brady: Can I see the email?)
[laughs] Sure, it'll take me a minute to dig up.
(Brady: How did that feel when you saw that? Were you just like "yeah,")
(or were you like "yeah!" and jumped up and down in your underpants?)
I didn't do a jump for joy this time, but... [laughs]
Yeah, it was pretty satisfying to solve something, you know that's been out there for decades.
We're not finished, of course.
Okay, so the next number after 42 with no known representations is 114.
That doesn't have quite the same ring to it.
But there's actually another number that we care about more, and that's three.
K equals three.
So the reason this gets ignored is there's a couple of small solutions.
Actually, you want to have a go?
All right. 
- (Brady: For three?)
Yeah, three.
(Okay.)
(Well one cubed plus one - or do they have to be unique?)
No.
(So, one cubed plus one cubed plus one cubed?)
Yeah, very good.
Okay, and if you play around for a little longer, there's another one you can find.
Umm, and it's four cubed plus four cubed plus negative five cubed.
So 4 cubed is 64, another 64 is 128, takeaway 125 is 3.
A mathematician called Mordell asked in 1953 "if these are the only two solutions",
and we still don't know.
That's kind of what kicked this whole thing off.
That's why in '54 they started looking,
they were hoping to find a solution for three.
We're gonna throw everything we have at it, and we'll see.
But, you know, with this kind of thing, you never know.
It's a once in a generation kind of thing, so.
(Brady: Are you gonna throw any resources at 114, or is it just getting silly constantly going up and up and up?)
Yeah, so there's another 10 below 1000 which would be the next milestone,
I think I'm ready to hang up the hat after we have a go at 3. Yeah.
(Brady: So you'd rather get a different solution for 3 than the first solution for 114?)
Thats right yeah.
(Brady: There are 10 numbers below 1000 that you haven't got?)
That's right. 
- (Only 10!) 
- Yep. That's right.
So there were 13 when I started this;
I found 33 and then 795,
and we've just done 42.
(Brady: Well, congratulations.)
(Are you gonna celebrate? You doing anything to celebrate?)
It's my wife's birthday today. So, yeah.
(Brady: You got her a nice present. That's her present, is it?)
[laughs]
(I think she's gonna want more than that. Flowers, maybe.)
I think so. Yeah.
[both laugh]
[Preview of more videos] And so if we just look at the numbers up to 100.
So let me say k less than or equal to 100...
...The interesting thing is for k less than 100,
we now only have two more numbers to worry about.
Who knows? It may well be that if you just look up to 10 to the 16, you'll find a solution.
