The Shortest Ever Papers - Numberphile
Vložit
- čas přidán 6. 12. 2016
- Audible 30-day free trial: www.audible.com/numberphile (sponsor)
Tony Padilla discusses some of the shortest math papers to be published. From Conway to Nash.
More links & stuff in full description below ↓↓↓
Support us on Patreon: / numberphile
NUMBERPHILE
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9
Numberphile T-Shirts: teespring.com/stores/numberphile
Other merchandise: store.dftba.com/collections/n... - Věda a technologie
the first one is purely savage. one simply doesn't get to fire shots at the king of mathematics like this guy did
Rex Galilae yeah
look up leonard euler. euler = king of maths. the first short paper disproved "euler's conjecture" by stating a counterexample, thus firing a shot at the "king of maths" (awesome comment, as evidenced by 180 likes in around 2 hrs :))
I think I can explain the metaphors he used:
king of mathermatics: Euler
to fire shots at: disproving him (or at least one of his conjectures)
OP is certainly correct in saying that there arent many people who have achieved this in their life
I do not mean to offend you and if I am doing it anyway I am sorry, but you asked *what?* implying you didnt get it, he just wanted to make it clear for you since every evidence up there seemed to mean you didnt get it.
A. L.
You should have used "Wut" LOL
Not a fan of the second paper, they were clearly going out of their way to snipe the record for least words, even going so far as to sacrifice clarity and sensible formatting for that goal. The first paper you showed is far more elegant: it provides all the information anyone could reasonably ask for, and still only takes two sentences to do it.
MrCheeze At least it was a trickshot.
maybe they just did it for the hidden toucan pun (n+2 can)
5JSX5 I believe that would be ntoucan.
+Sen Zen Actually, Conway strikes me as a pretty playful guy. Trying to break the record for shortest paper just for fun seems like something he would do.
Also seems up his alley to publish a paper that doesn't achieve its main goal yet also be insightful
It's like mathematicians spitting one liners and then dropping the mic.
this is one beautiful comment
+
Aditya Khanna +
+
Reminds me of Dr Caulfield lecturing DEs at cambs. He'd often finish the lecture by hitting his pen on the lectern, saying "drops the mic" and then walks out lol
Not mathematical, but when it comes to brevity in communication, the prize goes to Victor Hugo. Hugo went on vacation as Les Miserables was being published. Wanting to know how sales of the book were going, he wrote a letter to his publisher which read simply, "?"
The publisher sent a response to the author which read "!"
Which was the one and only time Victor Hugo achieved brevity
Pity they didn't have emoticons back then.
He was just tired of writing at that point
That's not really brevity. It's just the only question he would ever have asked in that circumstance. Imagine sending a '?' to a random person, and getting a reply of 'what book, I'm not even a publisher'. That what would make sense, if the '?' was actually conveying information succinctly.
@@Hjtrne a large part of conveying information succinctly is know the context, and thus what you could leave out. This just happnes to be a case that you can leave out the whole question and still communicate successfully.
(5:11) "The unsuccessful self-treatment of a case of writer's block" - I laughed so hard. Just brilliant.
+
Someone showed me that paper while I was writing my masters thesis... I was very tempted to squeeze it in as a citation somewhere :-)
I thought the same thing lol. I have a paper i'm working on right now, i think i could squeeze it in somewhere.
Challenge Accepted!
if you look at the article on pubmed, there are tons of medical articles that do!
It is nice to know that you laughed and that you can quote a video with a time stamp, but why does this comment have 464 likes?
I liked the blank "comprehensive overview of chemical-free consumer products". Some people should have to "read" it XD
I mean, if you count software it arguably shouldn't be blank. :V
Software uses ionic compounds and metallically bonded (soldered) materials which are chemicals.
But I thought organic foods don't have chemicals! ( ͡° ͜ʖ ͡°)
Also the silica and plastics used in the supportive structures are chemicals.
And if you're talking about pure software, not even as stored data, then it will still have a chemical effect on your brain.
Software isn't a consumer product, though. When you use software, you don't consume it.
TIL
that "The Effects of Peanut Butter on the Rotation of the Earth", a
study co-authored by hundreds of physicists, is only one sentence long:
"So far as we can determine, peanut butter has no effect on the rotation
of the earth."
Even better; does a decreasing number or pirates cause global warming?
Abstract: The evidence says yes
But this is a classic example or causation and correlation
Dang, and here I was thinking that the added mass would change the effect of gravity on the earth or something and that the conclusion was that if we gathered all of the peanut butter in the world in one spot, we could prolong the inevitable heat death of the earth by a few seconds somehow.
Wtf lol
@@adamspaans8787 Ah, I see you are an enlightened subject of His Holy Noodliness, too. R'amen
That's not a real paper, it's an article in the magazine "Annals of Improbable Research."
Someone should publish
one of these shortest papers
in haiku format.
PhilBagels
Your comment is not
appreciated nearly
enough my dear friend
enough my _dear_ friend*
FTFY
Tanmay Nandanikar You also were wrong
in the middle line, because
it was way too long.
+otto hammar a-ppre-ci-at-ed near-ly count them. There are 7. You're correct about the last line though
Ohhhh I feel like an idiot now. For some reason only your reply and the first one were showing up in the youtube app so I thought you were responding to the first one
I read a bit of John Nash's thesis. I didn't understand a word of it, but I did find a typo. I felt smart. No, wait, I mean... pathetic.
David Mitchell avatar.
Perfect.
Now I'm just imagining David Mitchell saying it. It actually fits pretty well.
You could have told him... in 2015.
lol.
You have 42 thumbs up
I think Riemann's paper "On the Number of Primes Less Than a Given Magnitude" deserves a mention. At 9 or 10 pages, it essentially founded analytic number theory, and states a hypothesis that remains one of the greatest unsolved problem in mathematics
well the "The unsuccessful self-treatment of a case of 'writers block'" one has infinite impact per word, or perhaps an undefined impact
Infinity isn't defined
or zero impact
@@midas8877 correction: it is not well-defined
@@midas8877 it is but okay
Another very short paper with a lot of impact per word is the paper that Watson and Crick wrote describing the structure of DNA--only 2 pages!
Yep. And it is kinda interesting (and easy) to read. Recommend to anyone checking it.
This was the first one that came to mind!
Aditya Khanna
If by "stealing" you mean "acknowledging their sources in the second paragraph and by concluding it is a helix based on the Bessel function pattern that the diffraction pattern suggests, and by drawing the physical consideration that the bases are inside instead of outside", then sure they "stole".
Their last sentence probably has had the greatest impact of any in science: "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material."
Meredith Lee You know. It probably has greater impact. Well done.
1:28 that is the mathematician equivalent of clickbait
I actually heard Alexander Soifer speak and it definitely makes sense that he would write a clickbait paper
There is a short story by Edward Wellen titled If Eve had failed to conceive. It's zero words long.
Xenia Lafleur damn... it's pure genius.
There's another one called If Eve Really Did Conceive:
Endless incest.
+Hi genius!
I should compile a condensed version of Christian scripture including only parts that were true.
It also, would be zero words.
@@amisfitpuivk given 5-10% of Neanderthal DNA, not always an incest.
While it's great to see my fellow West Virginian get recognized for having great short papers, as someone with a biology degree I have to give the impact-to-words-ratio award to Watson's and Crick's "A structure for deoxyribose nucleic acid," arguably the most important paper in the history of the life sciences. It fits on a single double-column page, and toward the end it contains this cute quote written as if the researchers had no idea of the enormity of what they'd discovered:
"It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material."
The urban myth is probably referring to George Dantzig, a statitician who solved previously unanswered problems that he had mistaken for homework.
Isn't this the basis for goodwill hunting? And related to graph theory?
But that's not an urban myth: it actually happened.
@@beeble2003 Yes and no. The story is true, but the PhD thesis was 57 pages long. So it's a 1 pager is the myth part.
@@georgelionon9050 The story is also true in the sense that Danzig's supervisor told him not to worry about his PhD thesis as he could have just put the two papers in a binder and he'd have accepted it
@@bimbogiallo "A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis."
>Poissonian
Something seems fishy about that
In french poisson means fish
@@cptn_n3m012 (that's the joke)
@@cptn_n3m012 he should've made a joke about it, right?
I'm french so I got it but I don't understand why the french word for fish seems to be common knowledge here...
alright Colin
I had a professor who's Ph.D thesis was far shorter than normal. Only 19 or 20 pages. He was worried that his committee wouldn't let him pass his defense because of the unusual length. But they did. Paul Erdos was actually one of the people on the committee, too.
Having tons of information just to meet certain writing criteria is a hugely annoying problem I have with modern sciences, so seeing these was a breath of fresh air.
The writers block one got me so deep in the feels that was amazing
Ikr I cried and shaked when I read that.
I'll just say that a picture is worth a thousand words.
Does that then make it a long paper?
Based on the papers I've read, and with two figures giving it 2000 words, it's still on the short side, just maybe not as impressively short.
If £1 is worth a loaf of bread then does that mean I can make toast out of a £1 coin?
featheredice Now we are asking the real questions
Probably not.
In control theory, there's a paper titled "Guaranteed Margins for LQG Regulators" by John C. Doyle.
Abstract "-There are none."
two short important papers:
E. W. Dijkstra, 'A note on two problems in connexion with graphs', Num. Math. (computer science: canonical shortest path algorithm)
E. Gettier, 'Is true justified belief knowledge?', Analysis (philosophy: refutation of the classical model of knowledge since Plato)
both are about two-and-a-half pages
"Alright class, so for this essay there's no word requirement, just give a complete answer"
"Is it possible to get a one-page paper written in Liberation Serif with font size 65 published in a peer reviewed scientific journal?"
That would fill up a 8.50'' x 11.00'' page with 1.00'' margins.
But the margins will be too small to fit it
Whether it is possible or not would probably depend on your definition of scientific. I don't think it is possible unless there is a disappointingly bad peer reviewed scientific journal, or you have a very broad definition of scientific.
Another short paper is the Abridged Table of Even Primes
Forget about the "Abridged" version, the full paper "Table of Even Primes" is shorter.
The abridged version doesn't include '2' but the the full table obviously does.
But the 2 is still shorter than the word "abridged".
I still feel uncomfortable that 2 is not a prime. But there's reasons... :)
Since when is 2 not a prime? Pretty certain it is! You might be thinking of 1, which is nowadays excluded from the primes by virtue of the fact that many, many theorems would have to be re-stated with 1 as a special case, including the Fundamental Theorem of Arithmetic.
2 isn't a Gaussian prime though, but neither are 5, 13, 17... etc.
get rekt Euler lol xD
too bad Euler wasnt alive anymore in 1966 xD he woulda been like "dang it I'm not perfect"
"Dang, u got me there bro" - Euler, probably.
@@Ostebrix realistically, if euler had still been alive im 1966 (assuming his mental faculties never deteriorated)
First of all, hed have disproven himself a long time ago, second of all, hed probably have proven everything else.
you see... when you respond to someone 2 years late you will very likely get this response:
lol I don't remember watching this video or commenting that soooo whatever man
Thanks, this inspired me to put this much effort into a PhD!!! :D
I kinda hoped Gettier's paper "Is Justified True Belief Knowledge?" made the cut.
12 seconds after being posted and it's in my recommended
Is 1+1=2?
Abstract.
Sometimes.
References
E. Galois, A. Grohendieck, S. Ramanujan
The two expressions are equal, but you have messed up the reference. The correct reference is: Alfred North Whitehead and Bertrand Russell, Principia Mathematica, volume 2, page 86. ("The above proposition is occasionally useful.")
@@MikeRosoftJH 1+1=0 in Z/2Z
@@MikeRosoftJH I found Principia Mathematica vol. 2 but couldn't see 1+1=2. What might I be doing wrong?! Is it definitely on page 86? EDIT - never mind, I see it now. Just looks confusing!
@@duncanw9901 so the correct answer is "depends on the 1 and 2" =)
@@duncanw9901 but then 0=2. The reason it is always true is that 2 is defined as 1+1
1974 seems to have been a hilarious year for papers
Tony Padilla is incredibly interesting to listen to; it’s his enthusiasm about math that’s captivating and inspiring.
I saw this exact comment on another one of his vids. Was that u?
In terms of impact factor per word, I'd like to also suggest Leo Esaki's original paper announcing the creation of the tunnel diode: it is titled 'New Phenomenon in Narrow Germanium p-n Junctions'. It's one page long, has hand drawn bandgap diagrams, and won the Nobel Prize in Physics for it's author!
Task: Write about laziness.
Answer: This is laziness.
He got an A. This is lore from my country.
Here we tell it with "What is risk?" "This is risk."
Task: Name 5 of your biggest flaws
Answer:
1. Laziness
Proof that 1+1=2
First: Sum is defined as moving on the number line b units from a when a+b.
Second: Define the first integers (0, 1, 2, 3, 4... )
By this definition to add a 1 means to move on the number line from a to the next number. By the second definition 2 is the next number after 1.
1+1=2 true
QED
It kinda is, but is true.
Other way of saying it is:
1+1 is defined as being equal to 2
And from then on we can create maths.
And it is actually true, because that's the reason we know 1+1=2 because it's defined as such.
What's the point of mentioning QED when we know 1 is less already (true)
Because I wanted to give it a shoot at my short proof :D
+Ganjanaut that might come off as an anti particle
Grounds control for direction of the pilot
One of the shortest thesis was the thesis by C.N. Yang. His thesis was published as "On the Angular Distribution in Nuclear Reactions and Coincidence Measurements" and was about 30 pages, but apparently, it took his advisor Teller had quite a bit of trouble getting Yang to make his thesis longer. Teller kept asking him to extend his results, although even the original 4 or 5 pages would have been sufficient for a Ph.D. I heard this while doing my Ph.D. at Stony Brook, but I can't confirm it personally.
when you want your P.Hd but you lazy AF
But to be honest. You only need to be more intelligent than the on who could explain your findings.. You just do it and avoid the unnecessary bits.. :D
rkan2 p
As Blaise Pascal probably said (but has since been attributed to all the people these quotes are usually attributed to), "I apologise for writing such a long letter. I would have written a shorter one, but I didn't have the time."
*Ph.D.
Arguably the whole point of mathematics is condensation of information, in an accessible way.
In philosophy there is a three page paper ("Is Justified True Belief Knowledge?" by Edmond Gettier), which had a huuuge impact on the subject.
Came here to comment this.
What's the total KDA? How does it compare to The Communist Manifesto by K.M.?
This is my favorite video of the channel. And it is a tough competition.
The article that revealed to the world the helicoidal structure of our DNA is also very short and concise. I think it has the same impact that Nash paper had, but for the sciences of life
Just needed this after a boring day of school
I do like this guy and his enthusiasm for his subject.
That one on writer's block is brilliant
Oh man, I love the chemistry one. Classic XD
I was always under the impression that it was Gauss's proof of the Fundamental Theorem of Algebra that was the super short one. I looked for but could not find any scan of it or anything to substantiate that.
Very interesting and entertaining! I had a friend whose Ph.D. thesis (UC Berkeley) was 15 pages long. It dealt with a problem in queueing theory. I think that for most of us holding that degree it didn't take long to come to the realization that our thesis was really quite bad.
Haven't watched any Numberphile videos in a while, but chanced upon this one and enjoyed it :P
Okay, here's my shot:
Is the Riemann Hypothesis true?
Probably.
Prove it!
1:25 wait John Conway the game of life guy?
Yes! :) He's been in some of Brady's videos.
ooooooh
Don't let Mr. Conway hear that! He hates when people only take about his game.
My first associations with the name Conway are even more obscure. Chained arrow notation and surreal numbers.
You mean one of the fathers of the ATLAS of finite groups? The discoverer of the Conway group? The man who made a digital computer out of urinal parts?
very nice episode!
Very cool stuff! It would be interesting to try measure the complexity of letters sent out by an organization using a computer program that measures the complexity of words as well as the length of sentences and look to see if there is a connection between the complexity of the letters and the number of people that contact the organization seeking clarification. Essentially is there an optimum length and complexity of a letter?
Now I want to write a paper with the title, "How many theses that end with a question answer that question in the abstract?", and then cite that very paper in the abstract.
Better to go for the paradox with "How many papers whose title is a question _do not_ answer that question in the abstract?"
I love how the first paper just burned Euler with only one page. 👏
Another short paper with great impact is: Marcel Golay. Notes on Digital Coding. Proc. IRE. 37 (1949): 657. It described the error-correcting codes now known as Golay codes, which have proved useful in digital transmission over noisy channels.
one of the only trending videos that isn't an ad
But what were the LONGEST papers/thesis?
Classification of finite simple groups
"The complete list of all integers" by Chuck Norris (2005)
A proof that TREE(3) is finite (which has yet to exist).
dog Then you get to TREE(4) lol
No TREE(4) doesn't need a proof
"Unsuccessful Self-treatment of Writer's Block" - LOL!
What I like about the first example is that it shows a very early example of the use of computing power to produce proofs or disproofs. The CDC 6600 mentioned is an early mainframe. I know many have a natural distaste for any kind of mathematical proof or disproof that heavily involves brute force computing. Well it seems to have a long history dating back to the early computers.
Another nice one, in algebraic geometry, is Beauville-Donagi paper about the Fano variety of lines on a cubic fourfold: 3 pages long and it is one of the most cited papers in the field...
I think the legendary thesis about which you were taking was George Danzig's.
I think you are missing a t in George Dantzig. Do you know which paper exactly?
karatekid You're sure right! My phone autocorrected to Danzig, bit his name was indeed Dantzig. I think the paper was On the Fundamental Lemma of Neyman and Pearson.
Hold me closer George Danzig. Now that I read that attempt at humor, it wasn't as funny as thought it might be
That paper is a mammoth, it is almost full 7 pages long!
U.V. S. Hope that's sarcasm... Poe's Law?
Does P=NP?
No.
-Nataly RAW, 2016
If N=1 or P=0
It's a joke, because the question whether P = NP (which are Complexity Classes, not variables) is still an unsolved problem in Information Technology.
does p=np?
yes.
me, 2016
if that were true, we could instantly forget any algorithm-based encryption.
(Quantum encryption and truly randomized one-time-codes would still work though)
Nataly RAW What is the symbol of the 53rd element of the periodic table?
I.
-ceca siahaan 2016
I love these videos
I also heard that myth about the famous 1-page thesis in school, but didn't think much of it except as a motivation for making your point as concise as possible.
The Chemical-Free paper is hilarious.
The writer's block one is genius.
I'm happy I came across this video. :)
WOW!!!
The video intrigues me to pursue !
wait till you see my first paper haha
Martin Menkyna was that it?
MichaelKingsfordGray it's not gonna be THAT bad .. hopefully :D
MichaelKingsfordGray 😂😂😂😂😂😂😂😂
Did Wittgenstein not submit theTractatus as his PhD thesis? Probably in terms of effortless theses this must be one of the best historical exaples of the 20th c.
The second paper was so well phrased. So short yet so clear..
Tony and Holly are the best subjects / presenters because they’re the sort you’d love to sit down and have a beer with.
The shortest abstract ever was in Physics, and contained no words at all.
E=mc². The paper itself is only four pages long, and although it didn't win Einstein a Nobel (he got two others for Brownian motion and the photoelectric effect), it is the most famous equation in the world.
Which is impressive, considering that, strictly speaking, it is not the correct equation
Tall Troll Unless you understand m as relative mass, as modern physicists take it, and not rest mass.
"Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" is actually three pages long, but it had no abstract. Also, Einstein won only one Nobel Prize, for the photoelectric effect.
The actual shortest story I was told about is this one :
"The last man on Earth sat alone in a room. There was a knock on the door..."
-*Knock*, Fredric Brown, 1948
For sale: baby shoes, never worn
mod prime
I had to think about it twice before understanding it
KNOCK KNOCK.
"Who's there?"
DEATH.
"Death wh-"
sarcastic bowl of cornflakes
"Me
We"
Aniyoyo 良采康 LIGHGHT
Great video, tks.
I think Satoshi Nakamoto's bitcoin whitepaper had the most impact per word.
That's a different kind of impact though. You can't compare a mathematical discovery with an invention. And still, inventing game theory is a way bigger deal than inventing the bitcoin.
Sebi20070 but did any of Nash' papers get libertarian retards to cream themselves over a pyramid scheme?
Einsteins' paper on Mass-energy equivalence i.e. E = mc2 is only 2.5 pages. That's got to be up there?
That paper had one of the shortest abstracts ever. The whole abstract was:
E=mc^2
Isn't Einstein's Special Theory of Relativity only 13 pages long? Surely that would be up there in the #words vs impact section
What an amazing video
these are awesome
My grandfather once got assigned a paper in philosophy class with the prompt: "Why?"
He replied simply, "Why not?"
I think he aced it.
Did he get his Nobel Prize or not?
There was a Numberphile video with James Grim where he talked about a student who was late to a class and misunderstood an assignment. He thought your were suppose to solve the assignment but it was, up until then, not solved. However, he solved it and James said that when he wanted to do a PHD his professor said that he only needed turn in the proof he made. Could that be the short PHD thesis they talk about? Can't remember the video though
Are you talking about A Beautiful Mind movie reference?
Georg Dantzig was the name of the matematician +NaCl on my food
I remember this, but not from a Numberphile video. I found it on TV tropes, in a list of people who did something thought to be impossible because they didn't know it was supposed to be impossible.
Here is the entry from their page "Achievements In Ignorance":
(Quote)In 1939, George Dantzig, a mathematics graduate student, arrived late in class and copied what he thought was homework written on the blackboard. After taking longer than usual to solve the problems, he apologized to his professor for his lateness and turned them in. What he didn't know was that what he copied wasn't homework but two unsolved statistics theorems, the proofs of which he published. To this day, colleges and professors will sometimes place previously unsolved problems like these in with other more mundane problems on "entrance exams" or other evaluative tests, just to see if some brilliant young student who hasn't heard about the problem not being solved yet can find a solution nobody else thought to try.
Dantzig's story eventually morphed into the Urban Legend of the student that was late for an exam and barely completed all the problems on the board only for him to be told that the final problem(s) were "unsolvable" problems and that he made history. The legend can be traced to Reverend Robert Schuller, whom Dantzig once met and told him about the blackboard incident only for Schuller to add the embellishments found in the legend.(End Quote)
It's from the numberphile video about the problem in Will Hunting
@@JannikPitt George, not Georg. He was born in the USA and named after George Bernard Shaw.
wow,i love you Numberphile, you showed me how big can be the math world
Proof by counter example was my favourite!!
Huffman's thesis was 12 pages.
after, or before compression?
klingt net you're not wrong. His famous paper on entropy coding was not his thesis. My mistake.
Yeah, "A Method for the Construction of Minimum-Redundancy Codes" was not his thesis, it was a term paper. :) He was supposed to show optimality of Shannon-Fano codes, which are broadly similar but use a top-down subdivision construction (recursively split the set of symbols trying to keep the weights of both subsets as close as possible). Turns out that's not optimal, but Huffman's bottom-up procedure (repeatedly merge the two lowest-weight subsets) is.
You Sir, has won few internets by this comment :)
but the margin still don't have enough space to contain it
"Unknotting spheres in five dimensions" by EC Zeeman, 1960, is great. It is ~200 words long, including generalising the proof to unknotting n-spheres. It is available as a pdf online.
5:02 I went and checked this papers citations. 51 citations! Mostly theses acknowledgments or little jokes. However, two instances of it being used by accident in text (one published! - Phylogenetic analysis of methionine synthesis genes from Thalassiosira pseudonana.... the others a thesis too: Molecular Doping of Organic Semiconductors), and of course 1 citation where it doesn't actually appear at all: from experiments at CERN - A CVD diamond detector for (n, α) cross-section measurements.
Not a "very" short paper, but Fourier's idea to use... well... Fourier series for solving the heat equation was in a 6 page paper. Here's your winner for influence/content per "words".
Indeed. This drastically changed many fields of physics, as well as mathematics. I mean, who would have thought quantum mechanics would use it?
"The Unsuccessful Self-Treatment Of A Case Of Writer's Block"
... (nothing's written)
Genius
Once in uni I also had a faeces which was short but full of impact
The story mentioned at the end of the video could be that of George Dantzig:
'An event in George Dantzig's life became the origin of a famous story in 1939 while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.'
Those problems formed the basis of his PhD thesis.
Conway's paper doesn't specify constraints on epsilon, so the whole paper is incorrect in the case epsilon > 1.
epsilon ist generally assumed to be
Wouldn't it be >n?
no, for epsilon>1 you would need 2n+1 more. therefore, the statement is false for n>1.
DarkMaple68 I think I'm getting the terminology messed up. I was thinking n was the size of the small triangle, when n is the size of the big triangle.
Ye, the paper was obviously a joke or so. Maybe they made it that short on purpose as a bet or something.
I actually didn't know that triangle thing before. Also, the triangle you started with, the one with length 2 with 4 inside of it, that looked suspiciously like the Triforce from Zelda.
Yes. The triforce has always been very similar in nature to several things. Notably the fractal pattern referred to as 'the Sierpinski triangle'
You do sometimes wonder what influences game designers sometimes...
KuraIthys I have a feeling the triforce was just 3 triangles put together to form a bigger triangle with and upside down triangle between them.
This showed up on my page on April 1. Feels appropriate.
Disproving Euler with a counterexample = Legend mathematician status
is there a Nobel price in economics?
abstract:
no, kinda.
it's not a true Nobel price in economics; it's the riksbank's price in memory of Nobel
watson and crick establishing the shape of dna with 800 words.
Also quite short: E. Nelson wrote a paper "A proof of Liouville's theorem" (Proc. Amer. Math. Soc 12 (1961), 995) consisting of 9 lines of text
A bit longer, but with a very short title: N. G. Meyers & J. Serrin: H=W (Proc. Nat. Aca. Sci. 51 (1964), 1055-1056 )
Every economics PhD student hopes to achieve what Nash did. Short but genius idea using relatively simple maths but achieve greatness (and of course, a nobel prize)
Game theory is still one of the main concepts of Microeconomics, more than 70 years after that famous paper was published. What a beautiful mind.