Collatz Conjecture (extra footage) - Numberphile

lots of problems like this don't succumb until they're surrounded by other problems so people have said what's a what are similar problems that we could play with that would be like this maybe we'd get some information for instance why 3n plus 1 why not 3 and minus 1 Brady let's try a 3n minus 1 just over 7 let's try 7 again ok now we're going to change our idea we're going to instead go from when it's when it's even again we're going to divide by 2 just as before but when it's odd we're going to make a tiny change instead of going from n to 3n plus 1 we're going to go to 3n minus 1 big deal must be the same kind of thing well let's try 7 again why not 7 3 and minus 1 that's 20 that's even goes down to 10 goes down to 5 3 and minus 1 that's 14 whoops goes down to 7 it will never get to 1 never so we solved that problem we now know the answer we did 3n minus 1 maybe they're all easy except 3n plus 1 so one of the weird things people have done or beautiful things really is to say well let's think of any rule like this let's think of a n plus B and maybe we could have a machine that would tell us you give me a and B and I'll tell you this as the machine whether it'll end or not and people have proved that's an undecidable problem that's as hard as the whole thing problem in computer science which your readers probably know about your listeners so that's an undecidable so people have explored this in various ways looking for ways to connect it to a deeper mathematical fabric after which you might get a hint as to how the sonnet but nobody has succeeded professor I can imagine there are lots of problems that are simple to conceive and difficult to solve why is the Collatz conjecture why is this one so famous why is this one captured the imagination is it because famous people tried it or certainly famous people notice there got interested in there's another phenomenon here which is the advent of the personal computer and 1970 as when this began to get popular and people were just having access to computers that could do this really fast and do a lot more than you can do by hand before then it was a kind of curiosity people knew some examples coops himself I believe the date is 1937 when he claims to have first put this forward though there's some controversy over who really did it first my own feeling is that something that's simple and and cute is this must have been discovered many times by many people different places some of the big famous problems in mathematics that we know the name of have prizes attached to them million dollars although all these things we hear about vision doesn't have a big prize attached has a little prize but from someone whom you would like to win a prize from I would anyway air dish offered $500 for this prize although in other places he says you know it's completely hopeless so why only $500 I don't know he was being conservative that day what why does this one not have a millennium prize if so many big mathematicians find it interesting and it's so hard why doesn't this have a million dollars attached to it it's a good question the Millennium prizes and the things which are famous like the Riemann hypothesis or the problem of fluid flow those are problems that are deeply connected with many other areas of mathematics but one of the things that makes Rakow lots problem hard is that as a kind of isolated peak you see it in the distance well there are people who really want to go up and climb that mountain if they see in the distance and other people who say well you know there's a lake nearby there's a nice hill over here some green grass why don't I just play in this area I'll learn more and I'll do more that's interesting shouldn't we be encouraging mathematicians to go for the isolated peak though because of all the things they'll invent to get up there well yes that's a good thing to do if there are things to invent so far people have tried a lot of techniques on Co Lots but I I don't know that it's led to that my new mathematics the the Fermo problem was a real classic that was solved really only when it suddenly became connected to deep mathematics there was an early period where it was connected to the development of basic algebraic number theory through the 19th century fantastic developments came out of it then there was a kind of dry period I think when not much really fundamental came out of it then suddenly it became through the work of Frey I guess connected with a theory of elliptic curves and then Ribit did stuff and then while saw that he could really get somewhere so it was when it it kind of got engaged when the gears began to mesh that it was really became a hot item and was solved and that's when it became important so if the Collatz conjecture is proven yeah it is possible the person who does it will win prizes and money just a pony I do it I think that's right I think that's right though it's so famous now I think they'll be celebrated whether or not they get big big money from it the big money chases prizes slightly randomly I'm afraid I don't know that it really inspires much mathematical work but it does make good publicity no paper Riemann did precisely that he explained how to extend the dysfunction to all possible values except for one so there's only one value where there is nothing you can do that somehow it will be undefined

Channel: Numberphile2

Views: 343,691

Rating: 4.9792366 out of 5

Keywords: collatz conjecture, fermats last theorem, riemann hypothesis

Id: O2_h3z1YgEU

Length: 6min 1sec (361 seconds)

Published: Tue Aug 09 2016