Millennium Problems: Math’s Million Dollar Bounties

For those not willing to roll the dice that their mathematical discoveries will be important enough to earn one of these large cash rewards, there is good news. There are a number of specific math problems for which there is a cash bounty given to the first person to solve them. The most famous of these are the Millennium Prize Problems, a set of seven math problems worth $1 million each.

#MillenniumProblems #sideprojects

[HeavyMetalMouse]

I love how weird and esoteric, but also how simple to actually express the Riemann Conjecture is.
"There's this special function; it takes inputs and spits out outputs, just like any function. We're interested in what inputs make it spit out zero. The conjecture says that every input that makes the function spit out zero is either a 'trivial' value (one of a well known family of answers), or, if there be any others, they must be found on a very specific line."

It's that latter part that's the hard part to prove or disprove. All the 'hard parts' of the problem are wrapped up in the consequences of what the specific function we're looking at is... the actual function itself is relatively simple to state, but once you start fiddling with it, it ends up falling right into a sort of 'uncanny valley' of mathematical implications that make actually working with it fiendishly hard.

One of two things could be proven: that there exists a non-trivial input that *isn't* on the special line, but that still spits out zero (probably just by finding one); or that it is impossible to find such a counter example (likely by some kind of proof by contradiction).

It isn't immediately obvious from looking at the problem why it's so important or interesting. Weirdly, it turns out that, if we assume the Conjecture is true, it makes a whole *slew* of other extremely important unknown results (many of which involve prime numbers) effectively 'free'. In a sense, it's a lynchpin that could make or break a *bunch* of other really big-deal maths. This is one reason that a lot of people are *pretty* sure it has to be right, though again, it doesn't actually prove it.

[stranger]

I both appreciate and associate with the "I have no idea what I'm talking about" energy in this video.

[aldopacchiano]

Hello. A computer scientist here. Great video! apologies for being pedantic but the correct name is polynomial time not polynominal time.

[ignitionfrn]

3:30 - Chapter 1 - Clay mathematics institute
5:40 - Chapter 2 - P vs NP
8:45 - Chapter 3 - Navier stokes existence & smoothness
10:55 - Chapter 4 - Birch & swinnerton dyer conjecture
12:55 - Chapter 5 - Rieman Hypothesis

[justanoman]

8:37 no, that's not the problem. The problem is that all existing encryption algorithm is NP. If P=NP, that means all of them can be easily cracked and we are all screwed. It's one of the few things that will affect people outside of the math/computer/science fields, it affects everyone.

[gclishe]

The Riemann zeta function is not written correctly at 13:56. The -s for each term should be an exponent

[spinyslasher]

Being a physics major means this is right up my ballpark. And even I have a hard time trying to comprehend just how abstract these stuff can get sometimes.

[sgeskinner]

The partial proof of specific cases of of Birch and Winnerton-Dyer was actually Andrew White solving Fermat as he proved elliptical curves are modular. (Technically he only needed to prove for semi-stable but all elliptical curves are now proved modular)

[EyesOfByes]

Fermat's Theorem is the biggest and best trolling in human history

[Cameron]

Props to Andrew Wiles for the Fermat conjecture proof. I was at a cricket match at university when a math student friend strolled up and said that he'd been at a lecture the previous day where it was delivered. (Yeah it had one problem: thanks Taylor for the fix.) I've read the paper and it sort of makes sense, but the Riemann zeta function is more than my medium brain can cope with. But if you look it up on the wiki machine, there are some lovely colorful graphs, which would make excellent poster gifts for nerds whichever holiday season they observe. (Oh, and read Simon Singh's book.)

[StevenLockey]

"good for you mate"
This is Simon's way of saying his integrity isn't worth 1 million dollars.
He'd even advertise raid shadow legends for that amount!!!

[BuzzKiller]

I picked one hell of an episode to watch while high.

[Hillbilly]

First trip into the Whistlerverse today. Mashed that like button. Cheers.

[buxeessingh]

I know several people who are working on the Riemann Hypothesis and the Navier-Stokes equations. The issue is not the money -- it is the bragging rights.

[pedrorequio]

The issue with P vs NP is that there are NP problems that have very good algorithms that can do it in linear logaritmic time, that is a lot faster than exponential for a great number of samples. One example of such problem is the Fast Fourier Transform(FFT) this makes computation of the fourrier transform almost instante, whereas without this algorithm it is an untractable problem, and this is huge because this is so important in comunication, identification(Think medical exames), it is one of the top algorithms of XX century.

[philhuling]

The statement of the Zeta function didn’t have the requisite exponents and I have always heard it pronounced as “Ree”man

[martinstallard]

3:23 clay mathematics institute
5:33 p versus np
8:41 navier-stokes existence and smoothness
10:48 birch and winnerton-dyer conjecture
12:51 Riemann hypothesis

[RSLT]

Actually, I'm a fan of this channel, but I didn't expect to see this topic featured here. The presentation was impressively simple and provided a good introduction, along with well-researched content.

[y-not]

Maybe you should do a video on all the prizes available for proving the existence of various supernatural things... (which unsurprisingly all go unclaimed 🤔😂)

[Jenx]

That was a fun video; I was one of those crazies that liked math once I was far enough along to study algebra. Unfortunately I’m just not brainy enough to have been good at. I think my differential equations professor let me pass from pity. He was always saying I had creative ideas; a polite way of saying that’s the craziest messed up proof I’ve ever seen