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Realising that I may be smarter than others


Making a surprising mathematical discovery
W Daniel Hillis Scientist
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But then the deserved thing, the one that I'm more proud of, you know, was I had a professor named Jean Carlo Rhoda who was quite a character. And he taught the probability course. And... Or as he put it, probability was common rhetorics divided by EM. And so he taught this course and he was very interested in this new formulation of common rhetorics where instead of sets you consider something called multisets. And a multiset is something you can be a member of more than once...

And so, you know, there's a kind of formula. If I have ten things, the number of ways of choosing three of them. It's called 'n choose k'. Well there's a similar thing for multisets. It's sort of 'n multiset k'. And when we were studying these I realised there was a relationship between two of these that was really mathematically very surprising. And this was something he had studied. So I went up to Rhoda afterwards, after the class... Now Rhoda knew me very well because this was the semester that I was taking all the classes. And so I was always late to his class because I had another class before it on the other side of campus. And so he would always be writing on the blackboard when I would walk into the class. But he must have had eyes in the back of his head because I would slip into the classroom and he would be saying, and so we have 'n choose k, summed over – and we notice that Mr Hillis has arrived late again – summed over the...' And then he would continue. And he would do that every time.

So anyway, I discovered this amazing relationship between these two mathematical things that didn't necessarily seem to be related. And so I went up to him afterwards and I said, 'Look, I've... Look at this relationship.' And he said, 'Oh, that is incorrect. Go...' And I said, 'Well, I have a proof.' And he says, 'Go and try a few examples.' So I had access to a computer which was a rare thing in those days. Remember, this is a time when MIT students had slide rules, not calculators. But I had access to a computer. So I printed out 10,000 examples on a big sheet. And I came back to him, went to his office and knocked on the door and said, 'I tried some examples, you see?' And he said to his graduate student, Dr Baclawski, he said, 'Dr Baclawski, would you please talk to Mr Hillis and find out where he has made a mistake?' And then he goes back to work. So I go over to Baclawski and I say, 'Look, I have...' You know, I showed it to him. He said, 'That can't be true', I said, 'Well, let me show you the proof.' And I show him the proof and Dr Baclawski says, 'Wow, that's really amazing.' And Rhoda who's been in the office but pretending to pay no attention slams down his pencil and says, 'Dr Baclawski, don't tell me that you've been taken in by Mr Hillis.'

And he goes, and he walks up, and he looks at the board. And I start to try to explain and he says, 'Hush.' And he looks at the proof. And he puts down the chalk and he goes back. He sits down at his desk and he picks up his pencil and he says, 'Mr Hillis, you are correct. I take my hat off to you. You may go now.' So I was very proud of that one. And then I thought I'd been... That he'd be a little bit dismissive of me, but then shortly afterwards I get an invitation to be an editor on his mathematics journal with people, you know, great mathematicians like Erdős and so and so. I got my name up on the masthead right under Erdős'. And so he more than paid me back for having surprised him.

W Daniel Hillis (b. 1956) is an American inventor, scientist, author and engineer. While doing his doctoral work at MIT under artificial intelligence pioneer, Marvin Minsky, he invented the concept of parallel computers, that is now the basis for most supercomputers. He also co-founded the famous parallel computing company, Thinking Machines, in 1983 which marked a new era in computing. In 1996, Hillis left MIT for California, where he spent time leading Disney’s Imagineers. He developed new technologies and business strategies for Disney's theme parks, television, motion pictures, Internet and consumer product businesses. More recently, Hillis co-founded an engineering and design company, Applied Minds, and several start-ups, among them Applied Proteomics in San Diego, MetaWeb Technologies (acquired by Google) in San Francisco, and his current passion, Applied Invention in Cambridge, MA, which 'partners with clients to create innovative products and services'. He holds over 100 US patents, covering parallel computers, disk arrays, forgery prevention methods, and various electronic and mechanical devices (including a 10,000-year mechanical clock), and has recently moved into working on problems in medicine. In recognition of his work Hillis has won many awards, including the Dan David Prize.

Listeners: Christopher Sykes George Dyson

Christopher Sykes is an independent documentary producer who has made a number of films about science and scientists for BBC TV, Channel Four, and PBS.

Tags: Massachussets Intitute of Technology, Jean Carlo Rhoda, Kenneth Baclwaski

Duration: 4 minutes, 50 seconds

Date story recorded: October 2016

Date story went live: 08 August 2017