Paul Erdős: The Man Who Loved Only Numbers [1998]

Oh I'm very pleased to be able to introduce our lecturer Paul Hoffman who's going to talk to us about the mathematician Paul Erdos Hoffman first met Erdos in 1986 and interviewed him over the last 10 years of his life even follow him on his mathematical sod Jones Hoffman's 1987 profile of air - in the Atlantic Monthly won the National Magazine Award for feature writing the most prestigious award in American magazine publishing in their criterion the judges proclaimed it a minor classic written with amazing clarity and width ah then after air dodge had died in 1996 Hoffman wrote a biography of him entitled the man who loved only numbers published by the Fourth Estate and for this he was awarded the 1999 Aventis prize for science books until recently Hoffman was publisher of Encyclopedia Brittanica and editor-in-chief of Discover Magazine an experienced broadcaster he's the author of 10 books including Archimedes revenge and is currently writing his eleventh the wings of madness about the history of flying machines before the Wright brothers we both live in Woodstock he lives in Woodstock New York and I live in Woodstock Oxford so thank you very much hope your kind audience I'm a little under the weather today I've actually had the flu so this could be the most eventful talk that you've ever seen but luckily there's a door for me to run out if there's any problems I love old things I wrote about a man who was quite old and they'll come to that in a moment so it's wonderful to be at one of the most respected and oldest institutions in the world I've been slowly moving back in time I ran Encyclopedia Britannica which was formed just down the road in Edinburgh in 1768 and then I became a member of the American Academy of Arts and Sciences that dates to 1760 and then I got an old barn in Woodstock New York which I converted into a house and it's 250 years old so that goes back a little further now I'm back to 1660 and it's wonderful the just a few things about Britannica that you might be very amused about in the 1768 edition it's three volumes the first is a to be the next is C to D and then it goes e to Z that's because they realized it would take them until now to finish it if they were doing that the pace that they've gone and it has wonderful entries you look up California and it says in island in the West Indies perhaps in the second edition that was done in 1777 you look up there's no mention anywhere in it of the American Revolution the closest it comes is under the entry in Philadelphia and it says the problem with the American States is the euphemism for it so it's a delightful it's a delightful book on a reflection of our times you look up the entry in the first edition for man and it runs quite long you look up the Edition the entry for woman and it says partner of man three words but as some of my colleagues pointed out at least it said partner could have said servant dearth or yeah so maybe maybe we have progressed in some respects I'm a writer by profession and the kind of people I write about are those that are passionate about whatever they do I've written about chess players who spend 20 hours a day behind a board I've written about biologists who spend all day in the lab trying to find what one gene does and those are the kind of people I like who do things to excess and a friend of mine Ron Graham who was the chief of mathematics at AT&T Bell Labs knew about my passion for passionate people and said to me Paul you've got to write the story of the mathematician Paul air dish if someone who's very passionate about what he does is getting on in years and if you don't tell his story he may pass away before someone has a chance to interview him this was back in the mid-1980s so I said fine I'd like to meet the guy so I went to run run and tell me much about him other than that it was an eminent mathematician so I went to Ron's house in New Jersey to met him and I met a man who was stooped over who had white hair jutting out from his sides who was dressed in a kind of pajama suit and I extended my hand to greet him and he didn't extend his hand back and he wouldn't shake hands with people you barely noticed that I was there and after about a minute he said when did you arrive so I looked at my watch and Ron tapped me on the shoulder and said no he's asking when you were born and this started my getting used to the fact that I had to pick up an entire language and tire it was a man he was the Bob Hope of mathematics spouting aphorisms all the time mathematicians are machines for turning coffee into theorems he'd say it was very obsessed with old age and he'd say there are three signs of senility the first sign is that a man forgets his theorems the second sign is that he forgets to zip up the third sign is that he forgets to zip down well pull air dish never achieved any of these signs of senility he went on doing mathematics to the age of 83 proving that mathematics is not just a young man's game so I got more and more fascinated I couldn't understand everything he was saying because he spoke in a special language that was all his own that I had to get used to he called women bosses he called men slaves if you were married he said you were captured if you were divorced he said you were liberated if you were giving a lecture like I'm giving now he would say you were preaching if someone stopped doing mathematics he said you died if someone really died he said you left but my favorite word that he had was the SF short for supreme fascist the number-one guy up there God and he was a very absent-minded man not the SF air dish was and air dish was very absent-minded he was obviously miss placing his Hungarian passport he was always losing his wallet he was always losing his glasses and he would blame this on the ESF it would curse the SF for taking these things from him but what he held against the supreme fascist the most was that he was concealing from Paul the most elegant solutions to the world's mathematical problems I mean he believed that the SF is sitting up there in the sky with what he called the book and each page of the book had the most elegant solution to a mathematical problem and he believed that it was his mission on earth and the mission of his fellow mathematical colleagues to reveal the pages in God's book and when I heard this it resonated with what I had an experience I had in college about mathematical elegance and this is what attracted me to math and ultimately to heritage after I met him I was taking a calculus course and was with a rather surly professor who was always always seemed to be in a foul mood and never had much time for us well one day he came charging in buoyantly carrying two bottles of champagne in his and cracked them open this was in 1976 it was because the four colormap theorem had been solved and he wanted to celebrate it for those of you who aren't mathematicians the four colormap theorem is very simple to describe the idea is that any map that you draw of countries no matter how convoluted you make their borders I mean you can make a country that's going also sorts of red then take out a set of crayons and color each country solidly one color what's the maximum number of crayons that you need to be able to cover color any conceivable map such that two countries that border on each other don't have the same colors well for 124 years before was proved in 1976 the answer had bought two before and many of the world's ablest mathematicians had tried to prove this weren't able to and many of the world's biggest cranks had tried to find a counterexample in other words a map that required five colors but no one could so finally it was proven and that's how we had our most enjoyable math class with champagne well the following week we came back and he was more surly and more depressed and more fidgety than ever when you asked why and it was because he had learned that the proof had been done by computers and it's not that a computer did the proof that bothered him it's that you mean he believed it you know he thought other people can run the software they can check it for bugs that wasn't the issue the issue was what the computer had done it had managed to reduce every conceivable set of maps to fifteen hundred and then it had hand colored them spending a thousand hours doing this and had demonstrated that so the problem was not that he didn't think the theorem was true he believed it was true but you didn't know why it was true the proof was too complicated to follow when mathematical elegance is about it you've got to understand why it's true me why isn't it seven colors instead of four you can't tell from this proof and this was the kind of elegance that that pole air dish stood for the other thing that he believed and again he was always concerned about growing old actually since the age of four he worried about it apparently and you know had all sorts of jokes about old age but and you know and as he got older he spent more and more hours doing math because he knew he had less time left and you had to reveal yet another page in in God's book but he believed that mathematics gave him and anyone who does it a certain kind of immortality I asked what do you mean by a and he said what gives you immortality because you were discovering truths that are immortal I mean when Euclid ancient Greek mathematician proved more than 2,000 years ago that there's an infinite number of prime numbers prime numbers are numbers like 3 5 7 11 13 17 that have no divisors unlike numbers like 4 that's 2 times 2 or 9 that's 3 times 3 so you could prove that there's an infinite number of prime numbers well this proof was true not just in his time it's true today it's true in any other world that exists it would be true long after people are gone from the planet so error said that by finding these immortal truths you're buying yourself a little bit of immortality yourself by brushing up against it so I was hooked by my first discussions with him and and I really wanted to follow him around but I quickly learned how much it was going to be taxing on on my stamina I was in my 30s then this was again in the mid 80s he was 73 and that first night I stayed at Ron's house by the way he's married to a very great mathematician and fan Chun and the two of them do a lot of math together and the reason why air dish likes to stay with them is because there are two mathematical playmates that he can pester instead of just one so I watched them do math it started at lunchtime and they did it all afternoon and they sort of worked through dinner on napkins and this went on and although they had the evening news on at 11:00 it went on and finally it was about one o'clock and Ron suggested that you know they should go to bed and editor said there'll be plenty of time to rest in the great so they went on for like another hour and finally Ron said you know just we've got to go we've got to go to bed so when they went to bed about two o'clock I went lay on the couch thought I'd get a good night's sleep what about 4:30 I'm waking up because in the kitchen next door ear dishes banging pots and pans together he's banging them and banging them in banging them because he wants to wake up one of his two mathematical playmates to come down finally Ron comes down they do some math and and for a few hours actually because they're making great headway on a problem that had been lurking them for a long time but 8:00 a.m. in the morning suddenly air dish says I know how to prove such-and-such theorem he says I've got to call this guy in California Ron points out that it's 5:00 a.m. in California since it's 8:00 in New Jersey and airier says good that means he'll be home so nothing would stand in the way of his search for mathematics so at that point I decided that I was going to follow him around this is a man who had no home he had no possessions all those possessions fit into one small suitcase and some plastic bag that he had from some shopping store in Budapest and part of this briefcase was taken up by a large old-fashioned dinosaur of a radio I think it still might event tubes in it shortwave radio this was so that he could monitor the world for the downfall of communism which he had been doing for many many years so this is all he had I mean he had no family he had no wife he had no kids he had no sexual relationships with anybody his entire mission was devoted to mathematics and he made a circuit of 25 countries and he would go and show up often unannounced on the doorstep of a fellow mathematician he declare my brain is open which meant hit me with your most challenging mathematical problem and then he would stay with you as long as you could entertain him with math problems as soon as you couldn't then he moved on and lucky you you had to pay his airfare or train fare plan to his next destination he didn't have much of an income but he would get exorbitant gay rates from places like IBM Tom Thomas Watson Research Center AT&T Bell Labs the and solve problems the money he didn't care about he had to hear the problem first if the problem interested he showed up then he collected his twenty five thousand bucks for the day and then he would pay back all his friends who had lent him money because he kept track of how much money people had given him he was also a sucker for any good clause I mean if National Public Radio was having a fun drive he'd take whatever money he had in his pockets out give it to you supposed to mail to them if you passed you know a billboard about you know a home for wayward girls he immediately wants you to write down the phone number and send off a contribution if he passed a beggar on the street because I was with him many times and saw this he'd give him whatever money he had if it was a quarter it was a quarter if you happen to have fifty bucks in his pocket he gave the guy fifty bucks I mean in some sense he was a great great humanitarian and didn't care anything about material goods so the question was now I'm going to follow him around but how are people going to respond when I show up on it now it's 2:00 with them it's the big question so I asked Ron decided that he was going to call a hundred of his closest collaborators who would be the people he'd be most likely to show up because I was going to fall him around four full months so I could absorb what he was doing there was a poll has a lot of collaborators I mean this is one of the things that distinguish in from other mathematicians this stereotype which of course isn't true but the stereotype of mathematicians is someone who squirreled away in their study working long hours scribbling and that it's not a social activity Paul turned it in to a communal social activity in a single-handedly probably responsible for the that way that mathematics has become he had 485 co-authors 485 papers ran with different people he wrote 1500 papers and all and just to give you a sense of that most I mean you can't really measure mathematics and numbers of papers because someone could write one paper that would change the world but all of these papers were important none of them were trivial some were very significant was far more papers than anybody else has written in the century even in the last years of his life he would publish 50 papers a year which is more than most good mathematical published in a lifetime so now that Paul now that Ron had called a lot of his collaborators I tagged along and we started in New Jersey and I watched him do mathematics it was absolutely fascinating he often did it like a way chess grandmaster plays simultaneous chess if you've ever seen that there's a whole bunch of boards set up and the Grandmaster runs from one board to know their you know pauses for just a few seconds and then moves this is how he did mathematics would be a circle of people and he'd go from one to the next working on each of them with a problem and it was really good for the mathematicians that weren't quite as Swift as their dish because it gave you the chance to think about what you were going to say while they went to rat it was also good because it exposed mathematicians to what other people were working on and I saw him do this in numerous occasions usually at conferences he might go to one or two talks at a math conference but then he would end up camping out in someone's hotel room or in the lobby and attracting a whole group of people that would sit around him but as I struggled to stay up because at this point he was doing math 20 hours a day and he had been on he took him feta means for years he had been doing this but he didn't seem wired at all I mean it wasn't a person who was hyper at all but that kept him up and and I was having trouble with my coffee cups keeping up with him at this point and and John and Alan was happening and I found that everywhere I went I mean he talked in as I said the Bob Hope of mathematics with these little aphorisms that he was constantly spouting and he didn't want to take time out to talk to me very much it wasn't because he objected to my being there he didn't want to take time out from doing mathematics that was the principal thing but every now and again he'd go for a walk and it was on these walks where I joined him where I started to learn his life story because I was absolutely taken by him and I learned that he was born in in 1913 in Budapest to two mathematicians there were high school math teachers which meant they both had PhDs in mathematics and when he was his mother was giving birth to him she had two daughters who were aged three and five and they contracted scarlet fevers while she was in the hospital and they died the day he was born her two daughters imagine that she comes home to an empty home without her two kids and the result of this was that she did not let him go to school and rarely out of the house until after the age of ten because she was afraid that he would contract a childhood fatal childhood disease and she wouldn't let him be around other infants for that reason so he's at home but then at the age of one and a half his father was captured by the Russians and a Russian offensive and thrown into a Siberian prisoner of war camp for six and a half years so now there's no father from the aged one and a half on his mother still has to make a living so she's off teaching high school math there was a German governess that was around there were a lot of math books that were round and he said he taught himself to read by reading math books and that he immediately fell in love with numbers at a young age at the age of three that was his first great discovery he told me he discovered negative numbers the idea that if you subtracted a hundred from 50 you got minus 50 and when his mom came home from work he proudly told her this he also said he told her that was the year he discovered death and that he knew he was going to die something that's when he was obsessed with as I said for the whole rest of his life so his father too passed the time in this prisoner of war camp decides to teach himself English from a book there's nobody in this camp that speaks English so he teaches himself English from the book and then when he finally returns home when Paul is seven he teaches Paul English so neither of them have ever heard a native speaker speak English which explains why air dishes accent was so impossible to follow I mean it took me three days before I could understand what he's say and whenever there been news footage of him on American TV they and even though he's speaking English they have subtitles so that you can understand what he's saying so after the age of 10 he starts to go to school but every other year his mother yanked amount of school because she could still couldn't decide whether it was safe for him to be in school they were extremely close she did everything for him and she made every meal she buttered his toast for in the morning he never buttered toast until he was the age of 17 he never tied his shoes until he was 12 I mean she literally did everything for him and at the age of 17 this is 1930 now he went to the University of Budapest and he graduated in four years both with an undergraduate degree in a PhD and that's when he did some of his first work on prime numbers prime numbers were his closest friends he told me and it was in his first year as a college freshman when he was 17 he came up with a very remarkable proof it had been proven before but in a very convoluted way it certainly wasn't the proof that was in the SF's book and air dish we placed this proof with one that went in the SF's book and it was the original proof was done by sort of the father of Russian mathematics named path nu V F nu D chebychev and it's called chebyshev's theorem and the idea is that between any number and it's double there has to be a prime number so if you take the number four and double it it's eight there has to be a prime number between at least one prime number between four and eight sure enough there's two prime numbers five and seven but he was able to prove this in a very elegant and simple way and he became you know very well known not just hungee in hungarian mathematical circles but around the world at that point and in fact it was spread by a little poem that when chebyshev said it and i say it again there is always a prime between N and 2n people sent out in postcards to to their colleagues so in its now he graduates it's 1934 stuff is getting rough in I should backtrack for one moment after World War one in 1919 when we had the Russian Revolution and there the communist regime was in power for decades obviously you also had a Bolshevik Revolution in Hungary but there it really failed the Bolshevik government was only in power for 133 days it was quickly overthrown by very right-wing folks that instituted the first fascist regime first fascist post-world War 1 regime in Europe because some of the leaders of the Bolshevik Revolution had been Jewish fascist thugs retaliated by attacking Jews left and right in Budapest this is responsible for the Exodus at that time of many eminent garyun mathematicians and scientists john von neumann edward teller eugene wigner people that went to the states and then went to Los Alamos and responsible for the atomic bomb all left at about that time there was a synagogue opposite arrow dishes apartment and if you look at the window he could often see and he's how old is he now this is 1919 so he's he's six six-and-a-half actually when this happened and he could see Jews being beat up after they came out his services from the window and his mother said to him we're going to baptize you and make you a Catholic so that you'll be protected so that you'll be safe so that you can pretend that you're not Jewish and he said to his mom no I was born a Jew I'm going to stay a Jew which is incredibly remarkable statement for six and a half year old to show that amount of will and he was not a religious person throughout his whole life but he was a very principled person I mean he believed in being who you were I mean one of the things that I was most impressed bias he got tons of honorary degrees from universities at least 32 my count and if he ever heard that at that university someone was having a ten-year struggle and the nature of the tenure struggle was that they had some kind of unpopular view he would immediately return the honorary degree he would never give a speech or talk at that university again and believed very much and sticking up for individual rights so in 1934 now when he has his PhD things are getting rough in Europe more and more anti-jewish legislation is being passed and hungry they're limiting the number of Jews that can go into certain professions they're limiting the number of Jews that can go into universities each year the law changes and the percentage is reduced so he knew that Hungary was not a great place for him so he got a postdoctoral fellowship at here at Manchester where he was for four years from 34 to 38 and he would go back and see his mother who of course he was very attached to three or four times a year in 38 starting in March it became unsafe to do that in March was when the Nazis invaded when Austria surrendered to to the Nazis which meant that the third right was now within a hundred miles of Budapest then came September of 38 with the Czech crisis and I just decided that Europe was not a place that he could stay so he went to the United States where he went to the Institute for Advanced Study for a year and a half in Princeton then for the next ten years this was before he get his circuit of 25 countries he did his circuit of universities all around the United States during those years in 1944 of all the atrocities in world war ii Churchill said that the greatest atrocity was when the Nazis moved into Budapest and that was in 1944 in the period of two and a half months five hundred thousand Jews were killed in Budapest Paul had no news I mean mail was cut off to the United States even though Hitler had invaded Hungary Hungary was thought to be sympathetic to the Nazis beforehand so there was no mail and he didn't know what had happened to his family it took a few years before he found out his mother made it through his father died when the Nazis forced his parents to move to the ghetto and four of his five aunts and uncles were killed by the Nazis after that he had a problem as the Cold War started the United States decided that he must be a Hungarian spy and Hungary decided because he had spent so much time in the United States that he must be an American spy so neither country would let him in so at that point he spent most of his time in Israel that did welcome him and he went to some other countries in Europe like Holland at the time he didn't get back into the United States believe it or not until about the time of Kennedy's assassination in the early 60s they finally lifted the embargo on him and then he came to the United States permanently I say permanently because he was a nomad and really didn't have a home except Ron Graham built the extra bedroom onto his house for him which is where copies of all his papers were stored he probably spent about two months a year they are between all all his travels at that time once he came to United States his mother started traveling with him they did everything together she sat there right next to him when he spoke even though she couldn't understand Stan a word of English and most of his lectures were in English he held her hand every night when they went to bed together they were inseparable when his mother died about seven years later that was when he started taking amphetamines very seriously and that's when he started churning up the number of hours that he was doing mathematics to 20 hours a day I mean that's what I observed during the month that that I was with him his eyesight started to fail him but he didn't want to take time out for like you needed a cataract operation and that would have slowed him down but his friends at the University of Memphis he had a lot of close collaborators insisted you have to have cataract operation or soon you won't be able to see finally they got a suitable donor it was all arranged and orders sat down with the doctor it'sh was holding a mathematical paper reading and most of the time he was talking to the doctor but he asked the doctor one point will I be able to see the doctor said of course that's the whole point of the operation and pull smile that was B me so now they lead him into the operating theatre and he's still carrying this mathematical paper reading it about up to here because that's that's only what his eyesight would allow and they get in and they start to dim the lights down and he has a tantrum he says to the doctor but you said I'd be able to see doctor said yes after the operation and they said but you're doing the cataract operation just on one eye so can I like read with a good eye while you're doing at that point the surgeon didn't know what to do so he phoned the mathematics department the University of Memphis and said can you send over anybody who can talk math with this guy while we put him under with the anesthesia and sure enough a few of his colleagues showed up and that's what they did in 1996 which was the last year of his life he by the way he had a heart attack earlier in Budapest that he was in a hospital for a while but he continued to do math the whole time people would visit him and again he would do math with six or seven people in the room the doctor came in to check his blood pressure one of his colleagues told me he threw the doctor out and said come back in an hour and a half because we're finishing this important result but in 1996 he was at a in March in Boca Raton Florida conference he went to semi a conference and he was giving a talk and when he just got to a point where he was going to end a proof he fell over completely passed out no one knew what had happened you can imagine everyone's rushing around security guards are then trying to evacuate the room and say you know get out get out get a wireless mic attached to him like I did and as people are leaving you hear him say no please don't leave I have two more points to make that was in March of 96 in June of 96 and Santa Cruz he was in the audience at a talk and mathematician was presenting his work and said here's a problem I'm stuck on Paul immediately leaped up maybe leapt up as a too strong a word for an old man he got up out of his chair and he started to complete the proof that this guy had been stuck on at that point he fell over and had a heart attack the conference and he had to be taken out in an ambulance two days later was when the closing banquet of this conference was and you can imagine it wasn't exactly a happy occasion I mean the conference was mostly a large part made up by many of his closest collaborators and there was a it wasn't a happy time at the banquet and when everybody's sitting there suddenly the door opens and in comes Paul air dish arm-in-arm with his two heart surgeons who had put in a pacemaker and he thanks the hearts of heart surgeons in front of everybody and then without losing a beat completes the proof that he was doing he wanted to die with his bootstraps on he wanted to die working and he told me that he most admired the 18th century mathematician Leonardo Euler because he did mathematics up until his deathbed if anybody did more math than air dish its oiler who wrote 19 volumes supposedly during the between the first and second calls to dinner and in the year I think it's 1787 when the planet Uranus was discovered Euler was sitting there he was old man at this point his grandson was on one knee yet a cigar in his mouth and there he was calculating the orbit of Uranus and as he finished calculating the orbit he said I died and fell over and he was dead so a dish told me I was once telling this story at a at a conference much like this one and somebody jumped up from the back when I got to that point and said yes another theorem of Euler's has now been proven and airier said that's how I want to die doing mathematics we almost had his death wish he was at a geometry conference in Warsaw he hadn't finished an important proof he didn't dive from the audience but he went back to his hotel room and he had a heart attack which left him on OA to speak in another heart attack several hours later and died and in a way it's very sad because he was a man that couldn't be alone who always surrounded himself by people and that his very last moments that he had to spend alone in the hotel room is kind of sad his legacies to mathematics I want to talk about just for a moment he did a lot of work in prime number theory as I said he was responsible for nurturing loads of child prodigies the only thing that he took time out from doing math achill math mathematical research to do was to go to elementary schools even kindergarten schools occasionally nursery schools believe it or not and talk about mathematics and if a child seemed to perk up and show some interest where the rest of them were just playing and ignoring him he would go and talk to that child and then he would meet the child's parents and then he would find a mathematician in that local community who he could pair the child up with to nurture that mathematical talent did this especially with girls and is responsible for quite a few female mathematicians despite his vocabulary about bosses and slaves he was very open-minded he would do math with anybody it was a saying that if he got on a train he'd end up proving a theorem with the conductor he worked with great mathematicians he would work with people that hardly knew any mathematics if they wanted to talk to him about it he was certainly game he has legacies in terms of whole fields of mathematics which he helped if not pioneer really launched one is called Ramsey theory this is a very appealing to me because it has a neat philosophical underpinning the idea is that complete disorder is impossible that there's order to everything if you look deep enough and I'll give you an example Carl Sagan and his show cosmos used to say sometimes people look up at the heavens and they see seven stars that are almost in a complete realm and they go that can't be my chance that must be because mmm aliens put them there is an extra terrestrials trade route to lead us to their civilization what when aired asserted that he would start calculating and say well how many stars you have to throw up there at random before you're guaranteed to find seven that are almost in a row these are the kind of problems you get or take a sheet of paper what mathematicians call plane and put points on it at random okay how many points do you have to put it random such as you're guaranteed to find somewhere three points that if you connect them to form a triangle then all sides are equal or how many points do you have to put there and two you're guaranteed to find five points so that if you connect them you form a Pentagon with all sides equal he was always trying to find order and though Ramsey theory is named for Ramsey who did the first theorem in this it was really ear - and his colleagues who put this on the map was interesting was back in Budapest in the 30s when he was in college and there was a law against meeting in public parks particularly there was a law against Jewish people meeting in public park meeting anywhere in public they used to go and meet in a park and prove these theorems and scatter before the police would come and the group that proved these is called the anonymous group because there was some statue in this park of a the first historian of Hungary who was called anonymous so they called themselves the anonymous group so Ramsey theory started back in the 30s that's very important he did a lot of work with what's called common a torx that has to do it's hard to describe but it's discrete mathematics it's about counting and classifying objects it forms the basis of many algorithms or recipes that computers use to solve problems the irony in this is that air dish would never use a computer ok he refused to use a computer not because he had anything against them but again he wanted to see all the steps in a proof so that he didn't want to miss something it's not that he thought the computer would do something wrong he was happy to have his friends use computers to you know check on his own calculations the other thing that I think he leaves in this world is a lot of great mathematical problems that are unsolved he put monetary contracts out and problems based on their difficulty something would be worth three bucks some are worth three thousand bucks I think there's $25,000 worth of problems out there and a foundation has a actually an oilman in Texas has offered to match the amount if people solve them so that they'll still be aired as papers published in the future even though he he's done around now and he was a Johnny Appleseed of mathematics he spread mathematical ideas wherever he went he knew what your strengths were so he'd come up with a problem that was just beyond your reach but one that you'd be able to do you often knew your abilities better than you did and in spreading mathematical news he was much like you know a medieval monk before there were newspapers who went from one town to another to spread the news that's what he did within his area of mathematics and I think the other thing that he certainly did for me is I mean he showed how important it is to follow your passion to do whatever you want to do passionately I mean how many of us are going to be able to go through life and end up doing what we want until the age of 83 and dying happily that we were able to do it and if you think about this guy's life and what happened to him I mean in a way you could look at him as I mean he wasn't oversized personality the way you could look at him as a complete weirdo in terms of how he lived his life and in a way you could look at him as somebody who had overcome so much that would have put somebody else in a mental home if you think of the fact that he was at home into the age of 10 basically with no parents that he wasn't allowed out had very little contact with children that he had a relationship with his mother where she completely smothered him I mean their stories I can't confirm but they but they fit in you know that they they shared the same bad until he went off to college he had no sexual relationships with anybody man a woman he told me and certainly this was confirmed by his closest closest friends he had no interest in that when he formed no you know real intimate friendships with people other than mathematical ones yeah he was enormous ly kind if he he would ask you about your children if they were sick he'd want to do something to help but I mean I think the fact that this guy took these difficulties that he had as a child and then all the deaths in his family with World War two and then being homeless because neither hungry nor the United States would have him and considered him to be a spy all these things that might have driven other people mad he took this and channeled this into an activity that made him enormous ly happy he was a happy man he radiated happiness he wasn't like John Nash the mathematical economist who was schizophrenic who was a depressed individual this is a guy who loved what he did and radiated that and I think that's what inspired me the most the fact that he was able to overcome these difficulties that might have done in the rest of us and channel that into something and then leave a lasting legacy with all these people that he had turned on to mathematics I mean his contributions were enormous thank well thank you very much Paul and we've now got some time for questions and because we're filming this we'd like if anybody wants to ask a question Imelda we'll do it or Joe they've got two microphones to give you two so that you can ask the question and for the record could you please also when you ask before you ask the question say your name and then we will have a nice record for that for the whole thing now anybody want to ask a question oh yes please here's the microphone John guy over and when Paul air dish asked people is your mind open I assumed that everyone would have said yes no one would have said no it's closed so did he ever find anyone else apart from himself that actually had an open mind because there are very very few around and no I don't think so so occasionally people turn him down and doing math again you know at xx hours some people were just falling asleep and you know he was the houseguest from hell you had to do everything for him or put it this way your non-mathematical spouse had to do everything for him since he couldn't boil water for tea he had one change of clothes which meant you had to do his laundry every day he couldn't drive so he would order you to drive him around so occasionally people got fed up with him but that was the minority I mean he had 485 collaborators because people loved him and they couldn't wait for him to come he would save you years of your research and he would think of all sorts of intriguing problems that would leave you a lifetime of of problems to work on so even if this was he had an idea that was quite remote from anything that they thought the they might find the solution they would listen well if he had he was very good about not telling you a problem unless he thought your abilities and your air if math were such that you'd respond to the problem what would he do if he suddenly had a brainstorm about something else which he had constantly he'd grabbed the phone and call you get huge phone bills after he left I mean he'd call everywhere ll hours you know whenever he had something to add to something Barry Lewis which achievement mathematical or otherwise was he less proud he was very proud of some work he did jointly on what what's called the prime number theorem and mathematicians in the room know what that is but for the rest of you as I said to you Euclid the Greek mathematician proved that there's an infinite number of primes as you get larger and larger the primes thin out it's harder to find them the prime number theory it tells you what the density of primes is in other words it tells you roughly how many there are in a certain gap you know whether it's between no a billion and two billion or a trillion and two trillion this too had been proved before in a rather complicated way and in joint work he did with a thing swedish in the region method issue named Selberg they were able to prove this in a much simpler way he was very proud of that it became marred in controversy though over which of them contributed the most to it and so Paul didn't like to talk about it he had no patience for I mean it's interesting in mathematics the number of priority fights that there are I mean unlike physics where you if you've discover a particle you could produce an image from an accelerator or biology where you might be able to show something you grew or cultured in a test tube mathematics it's very hard to prove when who does who did what to whom when and it just shows the passion of the subject that people have very lively disputes going back to man who wouldn't didn't stand in this room but in the Royal Society's headquarters back in the 1600s Isaac Newton and his dispute with Leibniz there's been a royal tradition of this Paul had no patience for this though he thought it didn't matter who got credit for it he left his name off all sorts of results he didn't care the idea was to knock off another page in God's book that's all that counted Jim Kennedy I presume that at in the early stages of his career he must have been often some sort of post with a university yes I mean the closest he came to a full-time job was Perdue offered him a sort of part-time teaching job which he did for just a few days and dropped because what would happen is he'd be lecturing and then he'd come up with a brainstorm and when a call you know a mathematician and hungry and it became incompatible with the idea of teaching so he never had a full-time job he had agreements like with the University of Memphis I think for over 15 years he came there in two weeks a year to do math with some of its faculty members and he delivered electro to that time so he had a few arrangements like that where he'd appear for we get in University but it wasn't conventional teaching it was working with people and delivering a talk you know I should add that in the mathematics world there's something called an air dish number that's a very coveted distinction if you did a if you wrote a paper with air dish you have an air dish number of one if you wrote a paper with someone who wrote a paper with the air dish you have a nearest number of two Einstein has an interest number of two if you wrote a paper with someone who wrote a paper with someone who wrote a paper with air that's driven out you have an air dish number of three the highest known air dish number is eight used to be thought to be seven but recently someone wrote a paper finding it was a of course if you consider the unwashed masses like myself or not mathematicians maybe we have their dish numbers of infinity water Haman a douche number two I would like just to modify a little bit what you said about his personality because I don't think people stayed with him merely because they did mathematical service with with them but I saw a lot of him and I'm not sure the ayodhya did much in the way of proving films with him he was a very lovable person in many ways all right he was really irritating yes a lot of wife fed that I mean what who said this by the light my own wife but he could also be very jealous and he did take another interested and he went on with you yes I mean he was a very very good person really good person he wasn't one of these into that so think of nobody bright sense he did think of all the people and so on he was very concerned about people's health the health their kids yes definitely and there was one other interest he had and that was politics he did like to talk politics he did read about politics he was very interested having been kicked out of so many countries politics meant a lot to him pull I'm Shawn you mentioned that you have a passion for passionate people what do you think drives passionate people and was Paul's passion in some way related to his adverse circumstances in growing up I think yeah I think Pat I think passion did that extreme I mean it was obviously driven by avoiding some things I mean clearly I know that more because I was a tournament chess player and gave it up at the age of 12 because that's all I did all day and in a way it was as much as I enjoyed it and also avoided my doing all sorts of having a normal adolescence and things like that so I mean I think it can be part of it but but not in all people by any means I think a lot of passion people who succeed in what they're doing and usually they have to succeed or they would have dropped their passion have childlike personalities in the sense that and I don't mean that in a pejorative way I mean it in the way that a child is completely open minded to things one of poles won't make him very successful is he could meet a mathematician and know nothing about the field in which the person in their work and he'd say what are you working on person would explain the problem Paul would then have to interrupt him and ask you know old definitions of terms and all these things because it was really unfamiliar to him once he understood it then he would often come up with a solution very quickly and it would be a simple solution and you would think why didn't people who have been spending their days working in this where the real experts find it well the reason they didn't find it is because he you know found something out of left field something that was so different I mean most of us who are successful you know fall into a rut we do the same kind of thing again and again he was someone who was always jumping around and I think that's very important to to passion particularly successful passion is to be able to have that kind of open mindedness that most of us don't have solutely did he prioritize the mathematical problems that he solved at home did he prioritize them in the sense that he knocked the ones off that he thought were the easiest to do because then you were done with another page in God's book and he prioritized them by the monetary values he assigned to the unsolved ones if it were three bucks meant he thought someone was going to solve it it was three thousand it meant he didn't think he was going to be soft in this lifetime so yes he did he wants someone once asked him because he had no money well Paul what if tomorrow all your problems are solved how are you going to be able to pay up and he said well what if tomorrow everybody goes to the Bank of England and demands their money he said it's more likely that everybody will go tomorrow to the Bank of England and demand their money than it is that all my problems will be solved tomorrow David Wallace you seem to imply that he was a mathematical nomad as it were from a very early stage in his mathematical career and was his reputation established very very early on so that in fact he could survive or was it quite difficult it was even when he went to in 1934 so he's 21 that's when he went for his postdoctoral fellowship in Manchester for four years he rarely slept in the same bed for more than one night in the row he went all around the UK to different universities people wrote about that the time that was impossible to track him down you never knew where he was he went to every University practic that existed here then in search of what people were doing so it was established very on early on then once the world opened up after the Cold War he could do his 20 and I literally mean 25 countries because I counted them all and I was going to do a graph in my book of life just charting back and forth between all these places but confining it to one page of the book you wouldn't be able to read it because there would everything would courts crossed too much how how did L douche get with the Goldbach conjecture it's a good question I don't know he certainly gave up on it early on because he thought it was too difficult so you know it's something he returned to a few times but he told me he didn't have any particular insights into it so that he stopped well thank you very much for most lively answers to the questions Paul and I think it's been a really interesting lecture could you then show your appreciation I usually always wear a t-shirt but I thought in a place that dates to 1660 I at least had to wear something over it but this is the the coveted paul air - t-shirt you can see him on the front and on the back you can see the way he signed his name it started with PG om which stood for poor great old man and that's what he put after his name just before in the early 60s then he started adding other initials like LD for living-dead ad for archaeological discovery than another LD for legally dead and then cd4 counts dead but you can find these at eBay and they go for a lot of money thank you very much you

Channel: Graduate Mathematics

Views: 45,955

Rating: 4.8941178 out of 5

Keywords: Paul Erdős, The Man Who Loved Only Numbers

Id: 9634A0iBw7w

Length: 53min 23sec (3203 seconds)

Published: Fri Jul 01 2016