The Problem with 7825 - Numberphile

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James Grime on a proof involving Pythagorean Triples.
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Опубликовано:

26 сен 2024

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Комментарии : 1,4 тыс.

@Qba116 6 лет назад

I love these classic Numberphile videos where James Grime talks about one particular number

@numberphile 6 лет назад

So do we.

@oldcowbb 6 лет назад

make a table of video of every real number like periodic video

@revenevan11 4 года назад

Can we add the sequence of numbers that numberphile has covered in the order they made the videos to the integer sequence database?

@Taquilou 2 года назад

@@numberphile I only watch videos where James appear.

@Kirkezz Год назад

@@revenevan11 numberphile numbers

@dominicsaavedra5113 6 лет назад

Probably my favorite guy on Numberphile.

@conoroneill8067 6 лет назад

He has his own channel as well, where he posts similar stuff (it's called singingbanana, though I don't know why). It's pretty inactive, but you can binge on some of his older videos if you haven't seen them.

@edwardteach841 6 лет назад

i dont think i could ever like anyone more than i like cliff stoll

@superoctave 6 лет назад

James Grime and Matt Parker are my favorites!

@muizzsiddique 6 лет назад

"Singing banana" captures his personality very well.

@christophgrun5636 6 лет назад

I think they are all very likable - and with very different personalities - but there is something very special about James :)

@victor3582 6 лет назад

I can feel 7825. When I go somewhere where everyone is having a good time, everything stops when I get there.

@emadgergis6710 4 года назад

100th like I know you don't care.

@searchwithin1414 3 года назад

OMG... that is hilarious!!!

@brendawilliams8062 3 года назад

Especially when the address says 78125 and you are lost

@thorodinson6649 3 года назад

@@brendawilliams8062 bad take

@brendawilliams8062 3 года назад

@@thorodinson6649 look Thor grab 1001035 and let’s trash the place

@lewkforce 6 лет назад

Interesting how 7, 8, 2, and 5 were the digits for 7,825 which also gave you the original issue in a+b=c.

@IanJeffray 6 лет назад

That blue pen appears rather green

@dvoraj20 6 лет назад

It is an optical illusion caused by rather specific lighting condition. It is the same effect that occasionally makes the light from a row from four lightbulbs occasionally appear to be concentrated in a row of five point sources instead.

@chaosme1ster 6 лет назад

Parker pen

@alexanderf8451 6 лет назад

Oh no its another controversy

@user-rh8hi4ph4b 6 лет назад

Jan Dvořák It's not an optical illusion, i checked with a color picker. Its hue in HSL format is 159 which is pretty much green (a little bit on the turquoise side, but still objectively green).

@fatsquirrel75 6 лет назад

Can't help but picture Picard: "There ... are ... four .... lights !!!"

@nigellafarage7323 6 лет назад

*_lol blue and red makes purple, so 7825 is purple, silly mathematicians_*

@CraftQueenJr 6 лет назад

I know!

@brcoutme 6 лет назад

James Grime said it wrong though, it doesn't need to be red and blue. It needs to be neither red nor blue... so 7825 is obviously yellow, but that leads back to his question at the end of the video of what if their were 3 or more colors would it inevitably still reach a point when it no longer works (assuming a finite number of colors).

@superherothijs12321 6 лет назад

with my experience of mixing multiple colors I bet you 7825 will be brown

@bibasik7 6 лет назад

7825 is purple? I didn't know a number could be comfortable! And don't you wind up about powder. The powder is harmless.

@加州猫主席 6 лет назад

Thijs van Dijk I mean, it's a sort of splitting-the-difference-between-purple-and-brown sort of color.

@dothemaths1256 6 лет назад

I always get excited when James grime is on numberphile

@FlightGearUser 6 лет назад

I have to do some calculus exercises... Me: "Okay, right now I'm absolutely not in the 'math-mood', let's just do other things first." *Numberphile just uploaded a video* Also me: Let's just watch this...

@leonthethird7494 6 лет назад

what is the derivative of an inverse function

@AuroraNora3 6 лет назад

depends

@FlightGearUser 6 лет назад

Maybe use that (f^(-1))' (y) = 1/f'(x) as long as f'(x) =/= 0 and assuming that f is differentiable? :)

@AuroraNora3 6 лет назад

pentix I think you mean f'(x)≠0

@FlightGearUser 6 лет назад

Thanks, obviously it shouldn't have a pole at x=0, therefore f'(x) ≠0 :)

@littlebigcomrade 6 лет назад

Ramsay theory : The formula to find lamb sauce.

@bcdm999 6 лет назад

Expressed by the notation LS=f*ck

@badhbhchadh 5 лет назад

* Ramsey

@clovermx1472 5 лет назад

Badhbhchadh no. It is ramsay

@prithvip6360 4 года назад

Its bland.

@lunaros4209 3 года назад

If you don't understand it, you're a sack of yankee dankee doodle shite.

@maxpeeters8688 6 лет назад

Absolutely loves James Grime, always a pleasure to see him featured on Numberphile again.

@Willzp360 6 лет назад

Fine example of a Parker Grid at 2:31 there James

@soulsilversnorlax1336 6 лет назад

Will Price Ah, yes. The Parker Grid, the ideal space for containing a Parker Square.

@Leyrann 4 года назад

Except he already knew he was going to fail.

@themeeman 6 лет назад

I bet I could do this for a^3 + b^3 = c^3

@mathpin 6 лет назад

Clingfilm Productions that would be very interesting to see XD! But will your proof fit in the margin of a book?

@nivolord 6 лет назад

I can do it with one colour.

@blackmagic3286 6 лет назад

that's a joke about Fermat last theorem.

@dlevi67 6 лет назад

Clingfilm Productions Indeed, o man full of wiles. I'll raise you one and bet I can do a^4 + b^4 = c^4 in about the same time as you do the cubes.

@elzian4975 6 лет назад

I might be able to do for both a^3 + b^3 = c^3 and a^4 + b^4 = c^4 at the same time, although you need to give me some time.

@darmstadtschaa 6 лет назад

"imagine all supercomputers in the world checking all the posibilities since the dawn of time you still wont be able to check all the posibilities ... so they used some clever mathematics to reduce the number they had to check, and it took them about 2 days" i snorted when i heard this, but this is actually great!

@midiphy 6 лет назад

...and those two days of supercomputation probably cost more than 100$ :)

@Ridgwaycer 6 лет назад

That's what grant money is for.

@dockmeister8480 6 лет назад

I think the check itself is worth more than 100$, so its even.

@ObjectsInMotion 6 лет назад

The university pays for the electricity.

@tonyennis3008 6 лет назад

WE pay for the electricity.

@djjimmaster8261 6 лет назад

FOR SCIENCE!

@numera8892 6 лет назад

James Grime appears in my subscription box: instant view.

@numberphile 6 лет назад

That’s what we like to hear.

@assiddiq7360 3 года назад

"The number 7825 must be both red and blue, which it can't" Superposition: "Bonjour"

@졸지마 3 года назад

well actually, 7825 must be none of red and blue.

@KnakuanaRka 3 года назад

Actually, it has to be neither or red or blue; if it’s either color, there is a trip,e of one color.

@alexandermcclure6185 5 месяцев назад

It is in the superposition |R>|B>|R'>|B'>! (did I get the notation right?)

@hOREP245 6 лет назад

it doesn't look blue because it's on brown paper.

@SashaFierceBadass 6 лет назад

If you draw on it with a yellow marker it would look orange.

@gabydewilde 6 лет назад

but thats a story for a different video

@zetacon4 6 лет назад

I thought the reason was video coloration problems. Having experience with that very thing, that is my first guess. If someone can prove me wrong, that would be interesting also.

@NondescriptMammal 6 лет назад

that makes sense, neutral browns are basically dark shades of yellow

@razzpup7961 5 лет назад

It’s looks green

@psyched1639 6 лет назад

This is probably the least click-baity title I've ever seen. That's something I really like about this channel.

@kasturi-725 6 лет назад

Whenever there are videos with James in it, I never hesitate to see it at that instant.

@erickvillegas8327 6 лет назад

Cool! I just learned how to come up with pythagorean triples. One of the side affects of watching numberphile: you might accidently learn something.

@almightyhydra 6 лет назад

For the a + b = c case, there are really only 3 options, not 512 - either 1 and 2 are (say) red and 3 blue, or 1 and 2 are different colours and 3 is red or blue. The other colours are derived from there until it becomes impossible.

@grahamrich9956 5 лет назад

almightyhydra Hence why he said that it was easy to convince yourself it was true instead of simply checking every possible combination of red and blue for every space.

@ragnkja Год назад

Four options, actually, because if 1 and 2 are the same colour, 4 can be the same colour as either 1 or 3.

@Muhahahahaz Год назад

There are exactly 512 ways to assign the colors. Whether those colors actually follow the rules or not is up for you to decide Yes, you can reduce this space through logic. This is the kind of work mathematicians do all the time, but it’s not always so trivial to do so :)

@farisakmal2722 6 лет назад

this problem reminds me of the 17 sudoku clues problem

@ikchess 6 лет назад

Always enthusiastic, always interesting. So glad James Grime does these.

@zappawoman5183 6 лет назад

I have synaesthesia only where numbers are concerned. As a child, I was trying to find a way to make the numbers add up in such a way that their respective colours would blend to give me the correct colour for their total. I quickly ran into the same problem you guys did.

@ciarfah 6 лет назад

Interesting!

@cubethesquid3919 6 лет назад

That's interesting! I wonder if I have synaesthesia, except with feelings. I have certain emotions associated with numbers, and often, based only on how I feel about a given number, I can tell if it is prime. For example, 167. It feels sharp, and makes me feel edgy. One day, I was talking to my mom about my "synaesthesia", and threw out that number because it felt prime. Then, a few minutes later I looked it up, and sure enough! 167 is prime.

@captapraelium1591 6 лет назад

The trick to making this work is to assign numbers to colours in a balanced fashion, rather than linear. As in, red = 1 orange = 2 .....violet = 7, won't work. It would need to be arranged like the Chinese Bagua, where the opposing number was actually opposed on the spectrum. Of course, with synaesthesia, you don't get to choose the assignments so whether it works would depend on your particular individual affliction. Sorry to hear you lucked out :( That would have been really frustrating!

@ianw8479 6 лет назад

Cube the Squid I def have some version of this as well lol

@Tumbolisu 6 лет назад

Colors are a three dimensional thing to our brains. This means you will always need three numbers to represent a color in a unique way. Single numbers just won't cut it.

@princevegeta5907 4 года назад

*625² + 7800² = 7825²* *5180² + 5865² = 7825²* WTH, how will we construct a right triangle with this?

@sadkritx6200 3 года назад

It's possible. The two right triangles are different. Using inverse trig functions the first one has angles 90, 85.42(approx) and 4.58(approx) The second right triangle has angles 90, 48.55(approx) and 41.45(approx) In fact I think this type of triangle seems to be rare in this case since we're using whole numbers. Otherwise we would have infinitely many such right triangles having same hypotenuse. Suppose we have a constant hypotenuse 'x' unit. The other sides are a and b. So, a=root(x^2-b2). Since x constant you can choose infinite values of b to get infinite values of a. Just make sure 0

@adraedin 3 года назад

I know this is an old post but someone else might stumble here... It's the Pythagorean theorem (using really big numbers). The theorem states that "in a right triangle a² + b² = c². Where side c is the side opposite the right angle." In other words, if there were a right angled triangle with side (a) being 3 units long, side (b) being 4 units and you were looking for side (c)... c² = a² + b² c² = 3² + 4² c² = 9 + 16 c² = 25 c = (sqrt) 25 (*sqrt 25 to remove the exponent from c) c = 5 Using this formula and some trig, so long as you know the length of 2 sides and that the triangle has a 90 degree angle, you can find the length of the remaining side and the other 2 angles. (That's what Sadman did above.) In the case of 7825 being c, there are two ways to form a right angled triangle and either option they choose of the two won't allow them to color the chart correctly to meet the other requirements and it ends their little game.

@princevegeta5907 3 года назад

@@adraedin Thanks a lot. That's very helpful

@KnakuanaRka 3 года назад

That’s saying that if you construct a triangle with sides 625-7800-7825 or 5180-5865-7825, one of the angles of the triangle (the one opposite the 7825) is a right angle.

@snoopdogg2912 5 лет назад

5:30 Actually Ramsays theory allows you to solve for the location of the lamb sauce .

@andrjsjan4231 4 года назад

Where you referring your joke to the famous chef gordon Ramsay??.

@thinebeatingstick 4 года назад

@@andrjsjan4231 what does it look like

@andrjsjan4231 4 года назад

Michael Sowierszenko like your mom opssss by the way I didn’t understand your joke?

@driptcg 6 лет назад

I laughed so hard when he so calmly said "so they reduced the number of scenarios they had to check to about 3 Trillion" XDD

@wasabiwon6037 5 лет назад

I don’t know what this man is saying but his excitement sells me every time.

@anacarolinaclauss3105 6 лет назад

how he is amazed about what he's talking about, it's contagious :)

@garrettducat5769 6 лет назад

If everyone had a teacher/professor as excited about Math as James then everyone would be a mathematician.

@wanderingrandomer 6 лет назад

That blue pen didn't look very blue to me

@matejcataric2259 6 лет назад

Agree ahahahah

@H0tdogCat 6 лет назад

probably the yellow-ish paper mixing to make it look green!

@aminulhuda4025 6 лет назад

Nelson Goodman says hi to you

@АлмазэтоСадыковблин 6 лет назад

WanderingRandomer perfect amount of blue in the video

@dvoraj20 6 лет назад

@nouche 4 года назад

Number: **exists** Numberphile: Do you have a problem?

@jasmin7168 6 лет назад

Aaaaahh! I've missed seeing James!! 🤗🤗

@davidschneide5422 4 года назад

These videos have no expiration date. Enthusiasm for mathematics is everlasting.

@Ajax-322 6 лет назад

I almost never understand this channel, but I love it anyway

@ThatsWhatTheManWants 6 лет назад

Shout out to the nail and gear in the background!

@numberphile 6 лет назад

The Mighty Nail and Gear.

@WilcoVerhoef 3 года назад

@@numberphile I wonder where it is now

@FinetalPies 6 лет назад

Great video, love that we're discussing a specific number

@maureenbailey6532 2 года назад

Love watching your channel! It’s the never ending pursuit of beauty!

@igt3928 6 лет назад

What, a new Internet Comment Etiquette AND a new Numberphile video at the same time? is it Christmas already??''

@imveryangryitsnotbutter 6 лет назад

But it's not even July!

@styloyt 6 лет назад

Aleatorio can’t wait for the collaboration

@grill-surf-bust 6 лет назад

stylo big money salvia here bouncing on my boy's number?

@MilChamp1 6 лет назад

imagine the venn diagram of the fans of both channels

@faith3174 6 лет назад

Bush did 9/11 (_)(_)::::::::::::::::::D~~~~~~~~~~~@tedcruz~~~~~

@smergthedargon8974 3 года назад

2:50 He turns into Michael Rosen for a split second when saying "twelve".

@YYHoe 5 лет назад

7825 should be either: 1. In a superposition of red and blue 2. Purple or violet

@ijpete98 3 года назад

Not only is 7825 the sum of two distinct combinations of two perfect squares, but oddly enough, it's the difference of two perfect fourth powers: 13^4 - 12^4 = 28561 - 20736 = 7825

@badlydrawnturtle8484 6 лет назад

The time estimate for a brute force approach is a bit off, because you don't have to check all of the possibilities. As soon as you come across a contradiction, you can stop and go on to the next set. Similarly, you only actually have to check 4 of the “512” combinations for the introductory problem to prove it never works (and indeed if you expanded the introductory problem to an arbitrary number of integers, you would never have to check more than those 4).

@KpxUrz5745 3 года назад

He is just fantastic. Loves numbers. Loves math. Is completely consumed by his wonderful passion. And does his very best to spread the thrill and excitement.

@HorrorGamesITA 3 года назад

"It can't be red and blue at the same time" Violet: bonjour

@alexandermcclure6185 5 месяцев назад

Did you mean: *Purple*

@seanspartan2023 6 лет назад

Ramsey theory has always fascinated me. Thank you so much for this video!

@hammer5064 6 лет назад

Then proving that, for n colors, there will always be a perfect square which can be written as the sum of n other perfect squares and that those pairs must be the same color will prove the conjecture?

@hammer5064 6 лет назад

That would probably be ridiculous to prove, though

@adolfodef 6 лет назад

Everybody knows *42* is the base number system used by the computronium running our reality [actually, it is _Quadragesimal_ (40) plus an independent "C.R.C." on _Binary_ (2)]. -> Knowing that *7825* is part of the equation leading to the "seed" used on this _particular run_ on the multiverse will get us closer to formulate the ultimate question.

@steliostoulis1875 6 лет назад

I missed you Professor Grime 💕

@laju 6 лет назад

They tried to fit the second part of the truly marvelous proof in the margin, but it was too narrow to contain it.

@a-blivvy-yus 6 лет назад

If there is always a number you'll reach where these equations break once you count high enough, wouldn't this calculation reflect entropy? With entropy, systems lose organisation over time. With these patterns, the number you reach before being forced into a 3-of-a-kind pattern gets higher as you add more colours. So wouldn't it be possible that this equation could end up having relevance to the concept of entropy if and when we solve it?

@Muhahahahaz Год назад

It’s actually kind of the opposite. If more related numbers have the same color, then that represents more structure, which is to say less entropy (The reason they are playing this specific game, avoiding 3 numbers of the same color, is that they want to see how *big* the system has to be before structure is forced to appear) Thus Ramsey Theory says that large mathematical objects often have some inherent structure, or emergent properties, which actually act against entropy! I feel like this connects to the structure of matter and the Universe in some way - Some matter/energy arrangements are just far more stable/favorable! Especially when moving towards larger scales (Yes, over long time scales, eventually all order will disappear as entropy increases. But in the meantime, it’s truly remarkable how organized and structured everything seems to be)

@darreljones8645 5 лет назад

It turns out 9 is the smallest number for which the "a+b=c" coloring described at the start of the video is impossible. Here's one that works for 1 through 8: Color 1, 2, 4, and 8 red; color 3, 5, 6, and 7 blue.

@sunshine_tidings6983 6 лет назад

"I didn't do it. I failed." So this is a Grime Square™?

@boudewijnj.m.kegels5198 3 года назад

I’d love to live at that squareat nr. 7825.

@charlottedarroch 6 лет назад

If you extend the case of sums of first powers to 3 colours (so we're excluding monochromatic triples (a,b,a+b), where a and b are distinct), then you can go at least as far as 22, using colour classes {1,2,4,8,11,16,22}, {3,5,6,10,12,19,20,21} and {7,9,13,14,15,17,18}.

@markphc99 6 лет назад

Furthermore, I notice that Mr Heule has been working on Polymath 16 (the Hadwiger-Nelson problem) and just broken his own record for the smallest unit-distance graph with chromatic number 5.This follows the recent breakthrough by Aubrey de Grey, although I imagine this record may not hold for very long, considering the great progress now being made in this area.It's not so difficult to explain .. so maybe a future numberphile video please?

@SimonClarkstone 6 лет назад

Related trivia: Ramsey Theory you mentioned and a vaguely similar problem about graph colouring is where we got the gigantic Graham's Number from.

@davidnacin7777 6 лет назад

Great video, though I'd mention that the Babylonians were making lists of Pythagorean triples long before the Greeks!

@zetacon4 6 лет назад

This was a fun video. I saw immediately that 1 thru 9 was impossible to not duplicate the same color. It happened for me when he showed the number 9 would be red. Bingo! That did it. Then, when he was discussing the 7825 number, I knew it was too large to ever examine every possibility. That somebody narrowed just a subset to 1 trillion was amazing, and then took 2 days to run the sets, was also thrilling to me. This sort of problem is what makes math so wonderful and inviting to me.

@AlexKing-tg9hl 5 лет назад

Who else is here just because it has James Grime in it?

@indian_scouser_ynwa 6 лет назад

Always happy to see James on numberphile😄

@mstrainjr 5 лет назад

7:52 - That's okay, you just have to defragment it and that will make the red go away. Or am I misunderstanding the problem?

@jaythompson7149 6 лет назад

Where have you been James?! My favorite numberphile guy! Glad to see you back! J

@gabeyk9 5 лет назад

8:52 3.6 x 10^2355, for the record.

@bradensorensen966 5 лет назад

The 1-9 “a+b=c” problem is EASILY disproved simply because ever number can be used to equal 9, meaning that you would need a third color to at the very least be 9 in order to prevent a match with a, b and c.

@gamemeister27 6 лет назад

It does strike me as a potentially useful step in understanding why this is the case in that having a brute force example may help mathematicians identify patterns that hadn't been tangible before.

@pierrestober3423 6 лет назад

one color->5 two colors ->7825 Not a very useful pattern (though I understand what you mean to say )

@mnikhk 6 лет назад

We'll that's what they do lot of times

@pierrestober3423 6 лет назад

mnikhk what ?

@HostileLemons 5 лет назад

My brain exploded about a quarter the way through this...

@ryanstevens199 6 лет назад

Gotta love how briskly and casually he goes through the method of creating a Pythagorean triple. That could be its own whole video!

@xavierglorot2582 6 лет назад

"...this kind of proof does not increase our understanding of why..." I would soften this statement, the tricks used to reduce the number of possibilities to check can reveal some interesting structures of the problem.

@michaeleveritt3472 6 лет назад

CGP gray print could not be unnoticed

@alandanielestradamartinez1722 6 лет назад

I had to scroll way too far to find this comment

@jeffxgoodman67 5 лет назад

My aspie ears can’t stand the sound of marker on paper, but I love these videos!

@detectivejonesw 6 лет назад

whats the name of the generalized version of this problem

@DDvargas123 6 лет назад

Maybe what you are looking for is Ramsey Theory?

@kennethgee2004 6 лет назад

well this problem is also connected to fermat's last theorem as anything in the form a^n+b^n=c^n is part of the theory. If you noticed thought he addition of 1 to 9 also add the same issue as 7825. There are two sets of possible additions for 5 and 8 that break down the rules. 9 is another example of two pairs that are in opposite colors, so not matter what is chosen the coloring breaks. we might want to stick to the addition to understand this problem. multiplying is only causing us greater amount of work.

@gruntslayer3524 6 лет назад

Wait so is 7825 the first time there is a c in two Pythagorean tripled that have to be of opposite colors

@henryD9363 6 лет назад

Spencer Schmidt -- I'm confused as well. Yes for 7824, no for 7825. But what about lower (and higher?) no's?

@gordslater 6 лет назад

I'm a C shell user so consequently not the best person to ask, but I'm assuming it's more of a C++ thing. I feel old. Again

@samhill1660 6 лет назад

I love Dr. Grime's enthusiasm.

@omarsamraxyz 6 лет назад

Even tho I'm a tenth grader, and sometimes I don't decipher completely what numberphile's guests are explaining, but I still love this chanel😍.

@alexvolute7454 5 лет назад

For those wondering, 2^7825 is 3.62840x10²³⁵⁵

@Triumvirate888 6 лет назад

I wonder if this has something to do with the built-in limitations in DNA.

@newkid9807 5 лет назад

I wonder how you were dropped as a kid SAD!

@angelmendez-rivera351 4 года назад

New Kid WTF is wrong with you

@valthiriansunstrider2540 4 года назад

That's a neat idea, maybe there's something to that

@PC_Simo 2 года назад

I sure hope the 100$ prize covered the cost of whatever computer program the guy used to solve the problem 🤔.

@poorman-trending 6 лет назад

Can you talk about other patterns showing in the image? I see a lot of vertical lines.

@KaitouKaiju 6 лет назад

That's just a consequence of the size of the grid they used

@Patrik6920 2 года назад

this is lovely, it in a way reminds me of how sir Isac newton showed how to calculated pi accurately down to 50 decimals in a matter of hours...when it previously had taken 30 years get to 16 decimals, it also raisees important questions, if we ignor the failure at 7825..and continue...at the next failure, we note the failure and continue..and so on...each point where it fails...what r the pattern?, can we calculate wher it fails..resonable fast?..ofc with some thinking we can rduce the problem to a=(m^-n^)^, b=4mn, c=(m^+n^)^ and solve to se if c has sevral roots...still it will take time calculate...there must be a more elegant way...what if we use a different base instead of Base10?...or a fractionalBase?...

@beekeeperhoneymoon8179 6 лет назад

Nail&Gear in the background

@PhilBoswell 6 лет назад

So I take it that there's more going on here than "7825 is the smallest number that is the largest number in more than one Pythagorean Triple"?

@boltingmouse8262 5 лет назад

The symbol in the picture in the background looks like CGP grey’s logo

@thomvandijk9535 6 лет назад

Why do I always watch your videos when I am drunk

@MMrandomdude12 6 лет назад

We may not understand why it's true, but knowing that 7825 has this property is surely a stepping stone towards finding an analytical proof?

@dlevi67 6 лет назад

Or maybe not. I haven't looked at the paper, but I suspect (given the size of the problem) that they stopped at the first "failure"; what if there are infinite others? Or demonstrably finite others?

@Tumbolisu 6 лет назад

dlevi67 The first failure is the only failure. Finding another failure would mean that you have to skip 7825. What if it's actually part of another triplet, in the same way that 5 is part of two triplets? What would you do at this point?

@dlevi67 6 лет назад

Tumbolisu The first failure is sufficient to declare failure over N. You (or as far as I know anyone) haven't demonstrated that there is/isn't a partition of the numbers _above_ 7825 (or above an arbitrary number greater than 7825). The number of triples that 7825 belongs to is neither here nor there, though it's clearly got to be more than one.

@mitchellsteindler 6 лет назад

dlevi67 I think you entirely missed the point. Analytical proofs are useful

@dlevi67 6 лет назад

Mitchell Steinder I never said otherwise; quite the opposite. All I'm saying is that 7825 by itself may not be particularly useful on the way to an analytical solution, just like 2, as the first prime, isn't particularly useful to generalise about primes.

@AlonsoRules 6 лет назад

Makes Andrew Wiles & Fermat look like the infamous margin proof that Fermat claimed

@xephren6557 6 лет назад

nice nail and gear on the shelf

@kartoffelmozart 6 лет назад

Man I love this guy. Now I totally wanna study on stampede uni!

@adrianomeis4924 6 лет назад

Man I'm early....it's my first time i can't look in the comments for explanation for what I just saw :(

@twanwilting3770 6 лет назад

You did not even see the entire video before commenting ...

@TommoCarroll 6 лет назад

Haha we know what you mean!

@PuzzleQodec 6 лет назад

Huh? The comments give better explanations than James? If that's true then I'm in comment heaven.

@mvl71 6 лет назад

As far as I understand it, he heard "Laurel"

@rafaellisboa8493 6 лет назад

I wish I could go back like 40 years in time when they could only have megabytes long data and never have done any proof by computer before and say "yeah in 2018 we have proofs literally hundreds of terabytes long" and watch people bang their heads against the wall.

@hellishemo 6 лет назад

I found a pattern where a^2+b^2=(b+p)^2 made pythagorean triples if p was a factor of a. (lowest factor being 2 if a is even) I noticed in the video that for 7825; the two triples that make it up one of the two follow this pattern, and the other does not.. Namely 5180^2+5865^2=(5865+1960)^2 .. obviously 1960 is not a factor of 5180 in this case whereas 625^2+7800^2=(7800+25)^2 is. It could be nothing, but.. This was the first time I've come across a case where the a pythagorean triple exists that doesn't fit the above format. (p not being a factor of a). Perhaps this is why?

@dlevi67 6 лет назад

Um, 7, 24, 25?

@yondaime500 6 лет назад

If you expand (b+p)² and cancel out b², you're left with a² = p(2b + p). So p (which is c - b) being a factor of a² is a necessary but not sufficient condition for a Pythagorean triple. I don't know how often it turns out that p is a factor of a, but I see quite a few examples on Wikipedia where this condition is not verified, regardless of which number you pick as a: (20, 21, 29), (33, 56, 65), (48, 55, 73), (65, 72, 97) etc.

@TheEclecticity 2 года назад

@@yondaime500 more like a commonplace but not necessary condition. Let's move away from the cliché "necessary but not sufficient" which is tired, over-used and has become beyond vague.

@aereoelvis 6 лет назад

I genuinely wish I cared as much about ANYTHING as he does about 7825. I'm sad now....

@versailles3891 5 лет назад

I noticed that the difference between 7800 and 7825 was 25, and that the multiple of 7800 squared was 25 to the fourth, squared. Why is that?

@pelerflyp5398 6 лет назад

4:32 omg I tried to find this for such a long time thank you!

@drzl 6 лет назад

Am I colorblind or is that blue green??

@yondaime500 6 лет назад

I think it's halfway between Battery charged blue and Deep green-cyan turquoise.

@trupalcanada 8 месяцев назад

blue on yellowish brown paper appears green

@pjbarnestx 4 года назад

I found a solution for "primitive" triples: odd = red, even = blue odd^2 + even^2 = odd^2 always. This solution only fails for: even^2 + even^2 = even^2 But those triples are non-primitive triples like 6-8-10, which can be reduced to 3-4-5.

@all8273 6 лет назад

These things are interesting, but what I would like to see in these videos is more explanation of why it matters.I know he talks about not knowing why it is true, but I want to know why it matters at all. Why does it matter if you can or can't color in numbers a certain color in a formula?

@anlumo1 6 лет назад

That's probably outside the scope of mathematics. For example, another similar problem is the graph coloring theorem. This actually is important in practice when you draw country maps, because it says that you will never need more than four colors (I think there's an older Numberphile video about this specifically). Maybe there's some similar application for this, but that's not the concern of mathematicians.

@Nickname006 6 лет назад

That is not something mathematicians worry about. Physicists and engineers care about the use of these things. But first comes the discovery, then the application.

@Shoonoonoo 6 лет назад

I think the question of why it matters isn't a question for mathematics, it's a personal question. Because clearly it matters to him much more than it does to me, and maybe to you. He has a passion for math and for numbers, and passion is one of those things that the more you try to justify it to someone else, the muddier it gets. That isn't to say you can't share your passion with someone. But the more intense your interest in a field, the more alone you'll be. I think the reason this matters to this guy and to the people who did the research is because they like numbers and think this kind of thing is fun. With $100 at stake they're not in it for the money! Cheers!

@Benimation 6 лет назад

It's hard to tell what's going to be useful in the future..

@alexpotts6520 6 лет назад

I'm reminded of the following quote: Reporter: Mr Mallory, why do you want to climb Mt Everest? George Mallory: Because it is there. Mathematicians are like George Mallory. They don't care about whether doing something is useful, only whether it can be done at all, and how.