Did Archimedes Write a Problem That Took 2,200 Years to Solve?

[@bensyversen]

There’s one other hypothesis about who wrote this that I found but didn’t mention in the video: Some propose that the original problem can be traced back to Archimedes but the poem itself was written later. Indeed, Archimedes was not much of a poet: some scholars that I read described Archimedes’ use of language as very simple. Suitable for expressing mathematical ideas but not poetry.

[@McBloodFart]

archimedeez nuts

[@NotSomeJustinWithoutAMoustache]

​@@McBloodFartArchimedes if he was a good poet:

[@jaimeduncan6167]

Do you know how old is the oldest manuscript we have? I wonder how fast would the problem run on a modern laptop. Less than 8h in a 1965 computer does not seem large by current standars.

[@bensyversen]

@@jaimeduncan6167 Yeah there are instructions online for how to set up MatLab to solve this problem. I think it could probably be done on an iPhone these days.

[@HorrorMakesUsHappy]

@2:27 when you "multiply by a least common denominator" ... Other than trial and error, was there some way to know to multiply by 891? Also, please do a video describing the geometric method mentioned at @1:19. I wonder if there were geometric methods for the other 3 parts to his riddle.

[@hubertmierzwinski9193]

Archimedes was such a boss that not only he created a math problem for the ages, he also managed to present it in a poem form!

[@Vernand1]

Some of the first ever theories about atoms were also written in poems. I highly recommend you read it, it's interesting what conclusions they drew from what they were able to observe

[@wheedler]

@@Vernand1 Read what?

[@Vernand1]

@@wheedler On the nature of things, by Lucretius

[@zathary564]

I heard math questions between ancient mathematicians were always written in poems. They didn't have a universal algebraic equation model like us, so they wrote it in words and whole sentences.

[@zathary564]

I heard math questions between ancient mathematicians were always written in poems. They didn't have a universal algebraic equation model like us, so they wrote it in words and whole sentences.

[@TeaRiker]

Math problems today: Solve this problem now!! :(( Ancient math problems: If you art diligent and wise, *formulates the problem as a one page long poetry*

[@bensyversen]

Yes indeed 🧐😂

[@SeekingTheLoveThatGodMeans7648]

@@bensyversen It sure took the invention of the early modern computer, with its processing power and storage, to do it. How much time would it take mathematicians in Illinois, working by hand, to crank out such a number? Probably till the sun dies, by a gut guess, and that's if it proceeded mistake-free.

[@antipastamony]

back in high school my friends and I turned in an incredibly dumb word problem that was over a page long for a geometry project. it was entitled “the purposeful porta-potty problem” and while we got an A we were banned from writing long word problems by our teacher, a badge we wore with honor. I’d link it for your amusement, but I’m not sure youtube would like that very much.

[@bensyversen]

@@antipastamony Haha that sounds awesome.

[@Sagitarria]

@@bensyversenit’s perfectly possible to use a modern translation rather then one in archaic English

[@NatetheNerdy]

I just want to point out that the first half of the riddle alone was seen as something that only the greatest minds could solve, and yet it's now a problem we expect our children to learn without pomp or circumstance. There is beauty in thaf fact.

[@bensyversen]

Absolutely true

[@oldvlognewtricks]

Same as circumnavigating the globe. Once a mark of a great adventurer: now as simple as paying for a few plane tickets.

I don't think children solve sets of diophantine equations. Even though this one look easy. It would be a tough riddle for advanced university level of mathematics.

[@rossjennings4755]

In the first half, all the equations are completely linear, and the "diophantine" part doesn't require anything more complicated than multiplying through by a common denominator. A sufficiently dedicated 8th-grader could work out the solution using techniques learned in an algebra class. The second half is much harder though.

[@travisray2934]

I would have zero expectation that a child could work this problem out lol. Certainly on their own. Just the wording is archaic and difficult to understand fully (for me, I'm sure I'll be corrected on how it's actually the simplest thing ever to understand) and that's not even touching the math. I'm sure that there are plenty of 8th graders that can solve these things nowadays but to expect it is crazy to me. More like, "wow, that kid solved this? Bet he/she is fckn brilliant". Albeit I'm a bit of a dope myself. Especially with math 😅

[@SitioLumbia]

Archimedes made " johnny bought 8⁹ bananas " problem to a whole 'nother lever.

[@epigone1796]

I don't know whether "lever" was a typo, or a reference to Archimedes quote "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."

[@SitioLumbia]

@@epigone1796 it's a typo but let it be.

[@Abcdefghijklmnopqrstuvwxyz1024]

134,217,728 bananas! I got it

[@vijay32570]

​@@Abcdefghijklmnopqrstuvwxyz1024 how to?

[@QuickSmasherEXE]

Man, can you believe they fit all those cattle on the island of Sicily?

[@renaatsenechal]

Factory farming has to end

[@life_is_a_myth]

​@@renaatsenechalNo to veganism

[@sandermez3856]

they didn't. those are the children of the cows. s the cows and bulls where on the island but perhaps not children afterwards?

[@pdonettes]

They were very small cattle.

[@DhoklaAboveVadapav]

@@pdonettes I am pretty sure that the smallest of cattles are bigger than atoms.

[@acenutella1196]

Wouldn't it be funny if he actually knew the answer and was the only person to know for 2200 years

[@aceman0000099]

It would be a fucking groundbreaking discovery in the field of human biology to be honest

[@ensiehsafary7633]

Yeah like a super computer brain😂​@@aceman0000099

[@silverseacow]

@@aceman0000099 true

[@locrianphantom3547]

How would he even write that down?

[@_Gam3r]

@@locrianphantom3547 eh, knowing him he probably memorized it in his head

[@aname1190]

Imagine Archimedes’s answer is just “bro that is impossible. There’s no cow of all 4 types” which would fulfill all 4 conditions

[@olegshevchenko5869]

"There's either no cows at all or more cows than there are atoms in the universe. However, since the cows are contained in the said universe, there aren't enough atoms to build them all, so therefore 0 cows is the only correct answer."

[@bensoncheung2801]

@@olegshevchenko5869🧠

[@DellariSafire]

archimedes really just stayed up a few hours too late and decided to make the math version of a shitpost Edit: Dad can you come back with the milk now?

[@Mr-__-Sy]

basically this

[@oz_jones]

More like bullshit post. I'll go.

[@MeltedPancakes]

@@oz_jonesDon’t go that was good

[@epicutmmgamer5366]

@@oz_jonesnonono youre staying

[@kooolainebulger8117]

white boys wildn'

[@nisgreaterthanzero]

Great video! I'd never heard of this problem before. I always thought that not having enough computing power was a modern dilemma. I never knew people were posing problems in ancient Greece that would take supercomputers to solve. Imagine how Archimedes would feel knowing his puzzle survived this long, and the unimaginable tools we used to finally solve it.

[@bensyversen]

Thank you and yes indeed!

[@tcoren1]

It was a supercomputer in 1965, probably a lot of modern fridges have more powerful computers, to say nothing of like, the NES and stuff

[@bensyversen]

Yeah there's a commenter on here somewhere who wrote that his grandfather (who passed away last week at 92) worked on the team that made that supercomputer in 1965 and programmed the software to solve the problem. So cool that he found the video. I asked him if he wanted to share any more about his grandfather but didn't hear back.

[@SeekingTheLoveThatGodMeans7648]

@@tcoren1 It's remarkable to me that we chased a grains of sand scale problem with silicon.

[@SeekingTheLoveThatGodMeans7648]

@@tcoren1 The storage of that much data needs more than a refrigerator controller is equipped with. But, given the storage, which to be honest today might only be as big as a postage stamp, these itty bitty modern processors, also no bigger than a postage stamp, would be well up to the task in a reasonable time.

[@gustavgnoettgen]

How many legs does a cow have? 12 Two in the front, two in the rear, two left, two right, and one on each corner.

[@suhaskanuganti7967]

LMAO true, a human would have 8, 2 in the front, 2 in the back, 1 on the left, 1 on the right and 1 on each corner, LMAO

[@The_Alpha_E]

​@@suhaskanuganti7967No corners

[@Anarchodemsyak]

I don't get this one. Please explain?

[@gustavgnoettgen]

@@Anarchodemsyak Did you expand my comment? The joke is a faulty counting method. A cow indeed has two legs in front, two in the rear, two on each corner... but you don't just add them like that, you keep track of what you counted. Edit: whoops haha ONE on each corner of course.

[@Anarchodemsyak]

@@gustavgnoettgen Ahhh, I get it. I did read it, I was just slow to understand, lol

[@notajalapeno4442]

thats too many cows

[@Sugar3Glider]

50,000,000,000 Lions gonna take the L on this one.

[@50iraqidinar]

Someone had to say it

[@yb3604]

great point

[@JerryCernava]

Serious global warming!😂

[@fanman-sn7po]

never enough

[@huzaifamansoor4068]

Imagine Archimedes watching this video. He'd he proud of your explanation and humanity for finally finding it's solution

[@bensyversen]

I hope so and thank you!

[@supercompooper]

My best friend, Gus German, solveed the Archimedes cattle problem at the university of Waterloo on an old IBM computer (with two others). RIP Gus, miss u man! He also invented RAID.

[@bensyversen]

That is amazing! There is another commenter (whose post I think you found), @ussgordoncaptain, whose grandfather recently passed and also worked on the problem.

[@ric6611]

shadow legends?!

[@CameraMan-it4qz]

He has departed crowned with glory and knowing that he has been adjudged perfect in this species of wisdom.

[@QuickSmasherEXE]

​@@bensyversenFire Emblem LTC player ussgordoncaptain?

[@kshitijsingh2412]

​@@ric6611 bro seriously 🤣

[@BlitzoITA]

I love these kinds of math videos even though I never fully understand what's happening. This one was specifically well done. This should get more views

[@bensyversen]

Thank you!

[@TARINunit9]

Now remember one of the Twelve Labors of Hercules was to clean up after all these cows

[@FRANCIS4117.]

ouch he must have been mad

[@sonofcronos7831]

It was not these cows in Sicily, but other cows in Elis

[@shadowseek27]

​@@sonofcronos7831Myths change and evolve. I'm down to change it to this

[@redstocat5455]

I don't think he could do that

[@FelixNothus]

Wasn't it horses?

[@Markfr0mCanada]

As a Canadian, I'm very happy to hear that it was my country men who achieved something noteworthy in this video, even if it means that they got trolled by a 2000 year old shitpost.

[@JordanBeagle]

11:40 I love that over 2,200 years ago they were still having beef with each other solving math problems

[@bensyversen]

Hey thanks for watching my video and leaving these comments! I’m glad you enjoyed it.

[@rahevar3626]

The answer could also be zero. The only potential issue is that the problem states the number of bulls in each herd is "mighty." However, since "mighty" is not a standard term and is a relative property, this should not be held against it.

[@Dunkle0steus]

This video has the quality of a channel with 1 million subs. Congrats, man.

[@bensyversen]

Thanks!

[@adam17tt]

The construction of this question alone is already incredible. The question itself is simple, but the solution is incalculable!

[@Quincy_Morris]

Question ain’t simple.

[@shanetwomey5273]

Mate that was a great video! you are definitely going to blow up. Looking forward to watching whatever you upload next!

[@bensyversen]

Thank you so much! Glad you enjoyed it.

[@alvoi4379]

Great video. I already knew the problem and the story, but you were so good at explaining it that I still watched the full video! My compliments

[@bensyversen]

Thank you! I was hoping to make it entertaining enough to satisfy those who already know the story

[@AdrianCruz_]

Stuff like this that involves math and history always fascinates me. Unknown to them in the past whether we would be still working on and using the problems to test computers. Imagine what the future may bring us

[@TeaRiker]

wtf, i thought this video had 200k views or something

[@bensyversen]

Thanks :)

[@fundowakin]

True, I thought the same

[@Thisone95]

It certainly deserves more than the 3k it has right now.

[@Guitareben]

It will!

[@kodirovsshik]

Wait, it doesn't???

[@ZMacZ]

Archimedes of Syracuse is one of the greatest scientists ever, if not the greatest. Basically a walking logic machine. If he were alive today he'd still be great.

[@gamerx3071]

idk if even he can understand quantum physics tho

[@FelixNothus]

Greatest huh? I want to see Archimedes 1v1 Da Vinci to be sure.

[@MAATsBud]

What I'm worried about is that all of those cows and bulls that where in Sicily 0:55

[@Onaneehsyu9286]

And I thought my Math teachers were 'terrors' for their Math problems.

[@rodri882]

I thought this was a viral video and then I looked at the views... This video is highly well done and definitely deserves more views, keep it up!

[@Iv_john_vI]

A bug in the algorithm allowed an interesting video to pass to it's viewers!

[@travisray2934]

Literally 3 seconds into the problem and I'm already at, " yeah fck math, dude."

[@bensyversen]

Aww. Thanks for taking the time to give it a try anyway

[@noahway13]

01:22 I'm tapping out.

[@bensyversen]

Fair enough

[@hedgehog3180]

Archemides was really like “oh you think you're so smart? Well prove the Riemann Hypothesis”.

[@BeneluxMapperr]

Bro, this video is criminally underrated

[@bensyversen]

Thank you!

[@MaGaO]

I'm doing a bit liking it

[@2394098234509]

I like this video a lot. Really good exposition. It's at exactly the right level of detail where you can go through it carefully if you want and check all the details, or you can ignore them and just follow along at a high level. And the animations are on point too.

[@bensyversen]

Thank you! That's exactly what I was going for so I'm happy to hear that it worked for you.

[@sunfline]

What an amazing video! Never knew about this problem, and you were so good at explaining it. It's a question of time, when your channel will get its much deserved subscribers and attention!

[@bensyversen]

Thank you!

[@The_Original_Default_Username]

I had no idea there was this much documented history about Archimedes. If math courses in school had been taught to me this way, I would have probably latched on to mathematics. This was an informative and interesting video, even as a person who's not competent in advanced math. Thanks!

[@bensyversen]

He is truly fascinating. Very little is known about Archimedes the person, but the mathematical writings that he left behind tell quite a story.

[@presidentofallfoodnice8113]

You probably wouldn't though would you

[@soumajitsen1395]

I have no idea why the algorithm recommended this to me, but I am glad it did. Liked, subscribed and shared! :D

[@bensyversen]

Awesome, thank you!

[@deepseapenguin]

I have to be honest this is probably one of the best math video I've ever watched He use a funny, humour way to explain the question to you, I had a little giggle while watching the intro, it's immediately grab my attention and i feel like i must continue watch When he actually start explaining the problem part by part, the background music + the way he explain makes me feel like im in an adventure with him, together looking at an ancient problem. Slowly getting out the answer and finding the result. I'm now regret that i never study my English well to express my feelings for this video.

[@bensyversen]

Thank you!

[@Paplu-i5t]

Whoever it was that wrote that poem was aware of the profoundity of the solution. Hence he wrote that whoever can get it is the one who is wise among all men. In an age when people often challenged each other on who is greater - this was one way of a declaration pointing to oneself.

[@chaddrshiftjobro]

I've been interested in this problem for years, and this is a great explanation.

[@bensyversen]

Thank you, I’m very happy to hear that!

[@andrzejsamorzewski146]

The problem with this is that assuming one cow takes only 0.5 square meter, on the whole isle of Sicily you could barely squeeze 51422000000 of cows. Archimedes busted.

[@swausgebouwen143]

0:16 spore galaxy assets?

[@bensyversen]

The milky way animation is from Envato Elements

[@clownymoosebean]

I like how you play epic music whenever the cows are on screen. Really keeps me engaged, as someone who isn't good at math, and normally isn't interested in it.

[@jodofe4879]

Iimagining having to do this without calculator makes my head hurt more than imagining the number of cattle does. Ancient mathematicians were something else.

[@samueljoseph7]

Your channel is gonna blow up! nice work mate.

[@bensyversen]

Thank you!

[@Nukepositive]

Time traveler goes back 2,200 years. Achimedes: So, have you attained the wisdom of the ages? Time traveler: Oh, yeah. We solved it in less than 8 hours. We use it as a training ground to find out how to solve problems FASTER.

[@hughcrawford7403]

There is a point you can reach in the quality of educational KZbin videos, where the size of your channel and the number of views is primarily dictated by time and luck. It's where your videos are indistinguishable in quality to the greats in your field. It feels like one is watching Numberphile, 3B1B, or Stand Up Maths. The video is so indistinguishable from that of a larger channel, they people think they've somehow missed one of the biggest KZbinrs in their area of interest. The comments are filled with "How does this not have more views?" Once you reach this point, you must simply wait until the algorithm blesses you, and hope it does so eventually. Welcome to the ranks mate, can't wait to see more of your content 🙂

[@bensyversen]

Thank you! Yes now I just have to work on making more videos. They take me a really long time but I’m getting better at it!

[@Medic_TFTwo]

He really is a smart bird.

[@Ninjasaucetoothbrush]

Not a very clean one though...

[@ussgordoncaptain]

10:26 Hey! my grandfather was one of the people who worked on that supercomputer he actually wrote the software to solve it. So what you call a supercomputer back then is worse than your laptop you could probably do the computation in way way less time than it took them.

[@bensyversen]

Wow that is so cool! Is your grandfather still around?

[@ussgordoncaptain]

@@bensyversen he died last week. It happens when you're 92.

[@bensyversen]

I’m sorry for your loss. If it would be something you’d like or find meaningful, I’d love to hear a little more about your grandfather (and I could share it with the audience in tribute)

[@supercompooper]

​@@bensyversengoogle Archimedes cattle problem gus German. Three students did it. Zarnke and Williams too!

[@bensyversen]

@@supercompooper So cool! I wonder which one was this guy's grandfather. It looks like Gus German died in 2022.

[@idk01123]

Calling it now, this channel’s gonna make it big.

[@scoutgaming737]

Amazing video. Really underrated channel

[@bensyversen]

I appreciate that!

[@reidflemingworldstoughestm1394]

Well get on the stick. Rate it highly, before it's too late!

[@zaxtonhong3958]

“If you took every atom in the universe and made it its own universe, then the number of atoms in all of those universes” This is a cool way of saying atoms in the universe squared

[@captaincole4511]

This video is ridiculously underrated, fantastic video

[@bensyversen]

Thank you!

[@reidflemingworldstoughestm1394]

Then get out there and rate it highly. What are you waiting for?!

[@nosoysospechoso7951]

Not much of a math person myself, this video was really entertaining and fun. You deserve 1 like for each cow. Alas, I can only give you one. Good job.

[@bensyversen]

Thanks for watching! I'm glad you enjoyed it.

[@amazinggrapes3045]

Why, Archimedes? Just why??

[@Ariya037]

They didn't have social media back then

[@StorytellingSpot]

Archimedes Write a Problem That Took 2,200 Years to Solve... ... and we are in year 2024 GIGACHAD IMPRESIVE

[@fantasyphilosophy3261]

This video should easily have 100x the views. I hope it gets it soon

[@bensyversen]

Thanks!

[@jackhandma1011]

Mathematicians are doing a little trolling sometimes. Fermat: I have a marvelous proof of this but this margin is too narrow to contain it. Archimedes: If thou art diligent and wise, O stranger...

[@Alex-cw3rz]

Eratosthenes : calculates the circumference of the earth using two sticks and their shadows and is only a few percent out. Archimedes : does the equalivant of when you sre bored and typing as many numbers as possible into a calculator. Wow Archimedes is the best mathematian of his age

[@bensyversen]

Hahaha that’s hilarious. In fairness, Archimedes did a lot of other stuff that’s far more significant than the cattle problem, but I thought this was a fun story.

[@somal5827]

This story probably describes one of the first written records of shitposting in history. Archimedes was so fed up with someone that he decided to construct a really difficult math problem just to shut him up for a long time.

[@robertl4522]

Helios *got milk* .

[@soberhippie]

I bet it was a trick question. I bet the correct answer would have been "You can't fit that many cattle onto Sicily" or something irritating like that

[@Alex-ik8pr]

I was thinking that 😂

[@UniDocs_Mahapushpa_Cyavana]

I think it was a weird dream. The writer just did not say, because it makes him look smarter if people assume he came up with it. I *always* ♾ find dreams have *inferable, hidden information* 🕵🕵🕵 that is *not directly perceived* 🤐🤐🤐 about *the dream world* 🌍🌍🌍. E.g. Character 👤🪞 motivations ❓, modus/modi operandi 🛣🛣🛣, the validity ✅❌ of a statement 📑 within the dream, etc. Dreams 💤 are primarily logic 🤔 puzzles 🧩🧩🧩. So the solution is that Helios has *a lot* of cows. Too many to fit on just this world. And the cattle herd had been moved to somewhere else in the universe 🌌 to fit, while technically having grazed in Sicily at one.

[@PGG-o6r]

0:24 By the way, a beautiful interior painting

[@Potatoman-zu6db]

That map at 0:57 was one of the most interesting parts of this video

[@bensyversen]

It's here if you want to take a closer look: etc.usf.edu/maps/pages/10400/10489/10489.htm

[@sakkoyaba4482]

​@@bensyversenbruh this dude prolly didnt even understand anything else😂😂

[@enderknight39]

This deserves way more views.

[@bensyversen]

Thanks!

[@JordanBeagle]

8:45 Buddy guy created a riddle so hard no you could solve it... well until very recently

[@Arochishi]

The english was harder to understand

[@jaif7327]

It does make me wonder if writing math problems in poems and generally easier ways to process makes the questions much more widely understood? As in that one superpermutations issue which was solved when someone rephrased it as watching an anime series in some specific orders.

[@scaevolaludens679]

cool video, but the use of AI pictures is pretty shite

[@bensyversen]

Fair enough. I know that not everyone likes those

[@Mr_PotatoMaster]

@@bensyversenthey kinda take away from the video :/ there are a couple of free sources of drawings and pics that can substitute the use of AI

[@bensyversen]

I’d be curious to know if there were certain images in particular that bothered you, or if it was just a general sense. I’m still working out the best way to approach videos like this which require filling a lot of screen time with imagery of some sort

[@kjh23gk]

@@bensyversen The main problem people have with AI art is that it sidesteps illustrators/artists.

[@bensyversen]

For sure. I’m sympathetic to that (former musician here), but it does also create capabilities for somebody like me who doesn’t have the budget to commission bespoke art to make things to spec. I subscribe to some stock image services as well but often can’t find what I need. I know this won’t satisfy everybody, but I do keep certain guardrails, such as never prompting for the style of a specific artist’s work.

[@rickestofthericks6067]

He would have received a letter back saying wrong number....

[@WinWitWon]

Amazing, and interesting the whole time, you probably hear this a lot, but im suprised at how few subs you have. Keep putting out bangers like this, and I bet you will go exponential!

[@bensyversen]

Thanks!

[@fundowakin]

Wtf, I wasn't expecting that this video only has ≈300 views. Well done, deserved my like❤

[@bensyversen]

Thank you!

[@sinx2247]

Woah you're right! I finished the video fully expecting it to have at least 10K views

[@sideeggunnecessary]

Mary had a little lamb, whose fleece was white as snow, and every where that Mary went, that lamb was sure to be equal to 1/5 + 1/7 of the dappled lamb plus the yellow lamb.

[@CL2K]

I wonder how fast the auctioneers gotta rap to be able to sell off all that cattle!

[@Gribbo9999]

I just use the method I always use. Count the legs and divide by 4.

[@tennysonmathew7019]

Lets assume that a cow 'C' exists and is continuous and differentiable over the period of length L=0 to L=Lc, where Lc is the length of the cow, then the derivative dC/dx that exists for any point 'p', (0 < p < Lc) is known as the '*steak*' of the Cow C at point p. -Butchers theorem

[@gidget330]

This Video is definitely about to blow up. Amazing video btw, loved the visuals❤❤

[@bensyversen]

Thank you!

[@hsuyaarchives2526]

It must be an Indian problem, Archimedes wanted to solve. After all most of the ancient maths problems of Indian mathematicians have been written like poetry and you know Indians' love for cows. No offense to his genius...

[@geenoix2357]

imagine Archemedies ghost appears to tell you you're wrong

[@Clock_Man_2763]

Archimedes pulling out a long 2200 year long sick social experiment to many mathematicians with this one 😂

[@dwaynemontgomery1851]

Reminds me of when a friend kept bragging about how he was smarter than everyone else so i took a book i knew had a looping ending and some chapters marked out of order, encrypted it using a pretty basic cypher, but gave it to him with all the chapters out of order and left out the page that tells you why some chapters are out of order along with the correct order

[@uncreativename9833]

This video is about to blow up

[@HORRIOR1]

Forget cow level Archimedes figured a cow multiverse.

[@aramisortsbottcher8201]

I love the choice of music.

[@bensyversen]

Excellent. I am happy to hear that 😀

[@jimsackmanbusinesscoaching1344]

Stupid question. Why did you take the number of cows from Part 2 and use it to calculate the number of bulls in Part 3 and Part 4? Just to be 100% for those that did not grow up on a dairy farm like I did, cows are female and bulls are male. If you were calculating cows or cattle in Parts 3 & 4, I can see it. But using the cows seems irrelevant to the number of bulls in those parts.

[@bensyversen]

If I’m understanding your question right, it’s because the numbers for the second part involves both the cows and the bulls…once those conditions are set then the numbers are interrelated going forward and the value for the whole herd needs to be multiplied together to preserve the earlier relationships each time you bring in a new constraint.

[@jimsackmanbusinesscoaching1344]

@@bensyversen Okay, well...when I listened to your version both Part 3 and Part 4 say bulls. You determined the number of bulls in part 1 to be about 7K. The number of cows was about 10M (perhaps you meant cattle). Given that the number of bulls was established in Part 1, my confusion is why you would then use the number of cattle in Parts 3 and 4. The 3rd and 4th parts talk about the geometry of the bulls in your reading and says nothing about the cows. That was my confusion.

[@bensyversen]

Hey thanks for following up. This is a good question that highlights one of the key ideas to this method of solving the problem, and it’s something that I could have articulated more clearly. The basic idea is that in each part, we’re finding the *smallest * possible solution that meets all the criteria so far. As we add new criteria, the values for all of the cattle in the herd needs to be multiplied by the same amount to preserve the original proportions. Here’s a less complicated example that illustrates what I mean: Let’s say we have a similar problem but with just cows and bulls (color doesn’t matter). Maybe step 1 says that there are 3 times as many bulls as cows. At that point, we could set # of cows = 1 and # of bulls = 3. But maybe the next step says that the # of bulls needs to be a perfect square. We could multiply the # of bulls by 3 to reach 9, which is a perfect square. BUT we would also need to multiply the number of cows by the same amount, because if we don’t then the ratio between the cows and the bulls would no longer be 1 to 3 as specified in part 1. So every time we multiply some portion of the herd by a number to satisfy a new requirement, we have to multiply ALL of the cattle in the herd by that same amount, even if they’re not specifically mentioned again. Does that make sense?

[@jimsackmanbusinesscoaching1344]

@@bensyversen I was my hearing your description of the problem that was wrong. I missed your repeated use of the word herd in part 2. That creates a relationship between the number of cows and the number of bulls. When I was listening to the video, you were saying herd and I was hearing cows.

[@bensyversen]

Aha! Glad we got to the bottom of it. 😀

[@chemoorestry6298]

4:59 about the test of a square number by looking at its prime factors is a bit misleading as it implies it's the only way. A square number will have all its prime factors with an even power, e.g. 10'000 = 2^4 x 5^4 = (2^2)^2 x (5^2)^2 = 4^2 x 25^2 = (4 x 25)^2 = 100^2. I get you were going for the smallest real solution but just to clarify for anyone interested.

[@bensyversen]

Thank you for clarifying, but yes the goal was to find the smallest square

[@d.lawrencemiller5755]

I came here to say this too and am delighted someone else noticed

[@sammy_trix]

It simply shows that Archimedes can post a problem, and it took so long in the present with our technology to solve. They were such smart and wise back then. Loved your videos. We need educational and inspiring videos like this more!

[@bensyversen]

Thank you!

[@dominiqueubersfeld2282]

Yet another problem written by Archimedes and not solved: "How much wood would a woodchuck chuck if a woodchuck could chuck wood?"

[@MaladyKayjo]

I think that he did this just to give a hypothetical massive number is that anybody smart enough would be able to realize how absurd it was

[@conorpillay4315]

I am certain this video will get a lot of traction soon, which it wholeheartedly deserves!

[@atismoke]

Commenting to help with the algorithm, hope this channel gets recomended to other people!

[@bensyversen]

Thanks!

[@bhatkrishnakishor]

Wow! Love your story telling. Subscribed for more of these types of videos.

[@bensyversen]

Thank you!

[@ethribin4188]

I FEEL so much how Archimedes must have felt. I LOVE playing around with numbers just for fun ^-^ Not even sarcastically. Theres something so satisfieing in having loads of numbers, and finding relations and new numbers. Its a lot of fun.

[@bensyversen]

I completely agree!

[@irfanjaafar3570]

It's fascinating how the ancient Greeks understood "one-half and one-fifth of a cow" instead of "70% of a cow." Edit: this is some kind of veritasium-level stuff. Keep it coming and you'll get millions of subs.

[@bensyversen]

Thank you! Yes, I believe that fractions would have had a more clear geometric interpretation for the ancient Greeks than percents. Remember that they did not have the same number/decimal system that we have today.

[@Iv_john_vI]

I am sure Archimedes knew there is a solution and we don't know his method!

[@stefanhuber7357]

You are reminding me too much from the college math classes I’ve been trying to forget for years now 😢

[@ionuto.1906]

This was a great video! I am a first year university student(cs) and can't help but be amazed every time my calculus teacher traces back a certain idea or concept back to Archimedes. Had he lived in our times, he may very well have been able to move even the sun from its orbit!

[@bensyversen]

Yes indeed!

[@hashimnameer1308]

ummm, I think you are missing a crucial point here, the place of this herd, it is in sicily, if the numbers are too large, it will be illogical to contain them all in sicily, so it is better to calculate the area of the island, and the area the that a cow/bull occupies, you get the rest i believe. in this you will need to consider few more variables, like the varying size/area of a cow and a bull or a baby cow, also considering all the ratios that you got and applying it to the different areas those cattle take up, the actual area of the island, since there are trees, houses, .. that would be illogical to not estimate and deduct it from the area. maybe Archamedes just wanted to know how his fellow mathematician thinks, more logically or more numbery/pure math.

[@this-statement-is-cats]

This is very underrated, i thought this was numberphile

[@bensyversen]

Thank you!

[@clarencejohncabahug5466]

This is like a version of 10 trillion lions vs the sun. But this time, the sheer amount of cattle can actually dwarf the sun.