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In this video, a mathematician reflects on their own motivations for pursuing mathematics and its importance in the modern world. They explore the transition from pre-Scientific Revolution to current times and consider the implications of Artificial Intelligence on the field. They suggest that appreciating mathematics as a live performance can be a way to celebrate the commitment of humans working together and maintain a highly functioning culture. Don't forget to watch this thought-provoking video about mathematics and its role in our lives.
The speaker reflects on their own motivations for pursuing mathematics and suggests that AI could potentially undermine the feeling of creating something new in the field. They discuss the transition from pre-Scientific Revolution to current times, and suggest that appreciating mathematics as a live performance can be a way to celebrate the commitment of humans working together. Ultimately, it is important to maintain a highly functioning culture that passes on its knowledge and doesn't forget everything every generation.
The speaker chose mathematics as a career, but it wasn't a well thought out process. He finds research meaningful and is willing to make sacrifices for it. People in mathematics have different motivations, such as competing, solving puzzles, and proving they're smarter than most people. The speaker's own motivation is not to compete, but to solve increasingly difficult puzzles. He finds this attractive and believes there's an endless source of levels.
Many people are motivated to pursue AI research for a variety of reasons, including wanting to contribute to something greater than themselves, a religious commitment, pride in achieving a difficult task, and the potential to do good for the world. Some may have fallen into the field due to a love of solving puzzles, while others may have the potential to go far due to their combination of wanting to help and having the necessary qualifications. These motivations are often intertwined, and the effects of AI progress on them will continue to be felt strongly.
The speaker discusses the value of mathematics to humanity. They question what their own personal contribution to mathematics would be and how it can be distinguished from the progress made in the field as a whole. They reflect on the three different reasons for their interest in mathematics, including the experiential and aesthetic aspects. They suggest that the beauty of mathematics is something that can be experienced, not just seen as an edifice.
The speaker discusses the difference between appreciating beauty and creating something new, which is what drives their passion for mathematics. They believe that advances in AI could undermine this feeling of creating something new. They suggest that when they reach the twilight of their career, they would likely transition to supervising students, teaching, or writing books, as elders have a role to play in any community in keeping knowledge alive and making sure the younger generation are doing okay.
Mathematics is an important task that should be done well and has been a part of intellectual life for hundreds of years. Progress in mathematics may not be as deep as in other fields, but there is still reinterpretation and new views on the mathematics as other ideas evolve. It is reductive to think of it as progress, but it is still important to maintain a highly functioning culture that passes on its knowledge and doesn't forget everything every generation.
The discussion reflects on the transition from the pre-Scientific Revolution period of mathematics to the current era. It is suggested that if AI is able to prove theorems and understand the underlying concepts as deeply as humans do, this could mark a difficult period for maintaining the same motivations for learning mathematics. It is suggested that appreciating mathematics in the same way as a live performance can be a way to celebrate the commitment of humans working together to achieve a beautiful thing.
The transcription discusses how AI may devalue the important element of mathematics that humans strive to achieve. It is referenced to a quote from Lisa Doll who retired from professional Go playing in 2019, expressing his feeling of having to work hard to reach the forefront of knowledge, but no matter what, he would always be behind the AI. It is suggested that stories of humans, such as Yitang Zhang, working hard and sacrificing other sources of well-being to achieve a narrow end, may not be seen as heroic anymore, as the AI could do it much easier. The transcription ends with a suggestion to continue the discussion in the tea break location.
uh one of the things I wanted to talk about and maybe we can chat about that a little uh is um how the progress in in AI has affected uh well I was going to talk about how it's affected my view on mathematics and what it means to me to do mathematics um and yeah I'd be interested in in your takes on this as well so um it's not so obviously I chose mathematics as a career and you know Maybe because I don't want to pretend it was some very well thought out process right where I wrote it down a list of 10 things and made lists of pros and cons and actually made some rational decision it wasn't really like that uh it was partly just one what else am I going to do and I kind of like doing this and I everything else seems uninteresting to me or just not that interesting right now so I'll keep going with this but if I reflect more on what what I found meaningful about the activity of doing mathematics um as a career well I like teaching that's part of it but if I was only teaching I wouldn't want to do this job I'd go do something else um so what really keeps me in it as a career is is the research that's true of a lot of people and why is why do I find research a kind of meaningful activity um and that's not a question that should be sort of has to be considered in the context of the costs right so as a uh anybody who's done a Masters or a PhD in an area like mathematics knows it's not that it's a hobby that takes one hour of your day or something right it's quite a consuming activity uh and it comes with opportunity costs you're not spending time on other things you may be sometimes not spending as much time with your loved ones as you'd wish when there are lots of things to do and difficult things to prove so why do all that why make those sacrifices for the research what is the what is the motivating factor there and it varies so when I ask my friends and colleagues about why they do it sometimes it's people like to compete and Mathematics is a very for some people a very competitive activity and you get to prove you're smarter than most people and if you climb up far enough maybe one of the smartest people that's attractive to some people it's not that's a very small part of my motivation if any but that is that is important to some people and I don't begrudge them that for others it's a sense of liking to solve puzzles and here's a kind of endless source of increasingly difficult puzzles it's like Bubba is you but you never run out of levels uh that's pretty attractive to some people
and then and then for others there's a sense of contributing to something greater than yourself that isn't sullied by corruption and is maybe true even uh and has been building for hundreds of years and has made a positive contribution to human well-being and Maybe for many of that approaches something like a religious commitment right there's platonic heaven and I get to see a little bit of it people are as to varying Degrees open about that as a feeling that they value uh many may like only say it in private but I think it's a it's a part of the motivation for many people and for most it's kind of a mix of of all of those and in various proportions and maybe other motivations you can think of uh and I think it's an un uh it's under thought of how much the progress in AI affects some of all of those motivations and we'll we'll come to be felt strongly by many people that affects those motivations can you think of other motivations besides the ones I listed that you personally feel strongly or that you could think of other people as feeling maybe just having like a doctor in front of your name yeah you just need a PhD for that and then you can just go do something else and you still get to keep the doctor but do you mean like reaching without some level of attainment um like doing a difficult thing that you can be proud of is that yeah yeah I think that's I think that's fair Ben uh I was thinking um like I guess something that I've always thought constantly what you're saying about how kind of helping people maybe maybe quite indirectly through Springfield Mass but you know you still contributing to society in a positive way um I think something I've wondered is like oh why do I actually used to do it in this kind of abstract indirect way than to go I don't know work somewhere else doing something probably more Hands-On helpful but I think because like you said I kind of just fell into enjoying solving puzzles and now I'm like in a PhD because I get to keep solving puzzles and it's like well I also have a strong desire to like I guess do something good for the world um but you know most people who have this feeling haven't already got a master's degree in mathematics and so maybe it makes sense to just like keep going in this field because the amount of people who I guess have this overlap or people who like want to help but also have the potential to go far go far and that's it's quite small hmm at least that's kind of my thought process on it are you going to say something going on
oh all right again I've never really thought of it as um something that's particularly helpful to humanity um I guess I I mean you know I can say why people would think that um I suppose maybe I mean more in terms of like my you know what I would be able to like personally contribute compute like um yeah I suppose one has to distinguish between good for Humanity in the sense that uh tomorrow or even in the indefinite future it will have applications that you know saying the health or yeah something tangible in the real world versus just well contributing a concerto to the benefit of the sum total of Beauty in the world or something along those lines yeah yeah and and I suppose the sort of like the mathematical culture as a whole you could by sort of I mean it's not just you know you do a PhD and it's like a little little brick get added to the last adipose um the mathematical knowledge um but probably the ways in which mathematical culture is valuable is not exactly doesn't exactly correspond to progress in the search do you say more about that well um like I don't know like say just like on a personal level like I don't think what I've you know um what I might have might have done with my PhD will ever kind of like see the light of day in terms of like an application um but just so you don't know yeah there's a brick no I I don't think so um but I mean it just seems kind of under it seems importable um what is the edifice there if the edifice is just human knowledge it's kind of um I'm sorry I don't quite think of it as really being an edifice because I mean mathematics have forgotten as well like right yeah um it's a it's a kind of culture that's alive um and you know of course it makes progress you know in in a very real sense but um yeah okay yeah I think I see the point about the analogy of an edifice yeah yeah um foreign yeah I mean I guess if I'm thinking about my own motivations it's very hard to um I find it very hard to know exactly what you know I I think there's sort of three there's kind of three different reasons that you outline um they I mean they all seem relevant in various degrees I mean I would probably you could sort of reflect them slightly differently um but yeah I mean I wonder like where do you think that in terms of the the experiential aspect of it they are um or the aesthetic aspect of it the the part which is kind of you know beautiful um because that's a beauty something you experience not a kind of yeah and there's a part of it yeah there's a
part on that list today suppose I didn't that needs expanding which is the difference between appreciating Beauty so I can listen to a performance or or hear someone present a proof or read a proof that is beautiful and I can admire it yeah that's a good feeling but a different although related good feeling is coming up with something new yourself that you think is beautiful um and that feeling of going beyond the the sum total of human knowledge and carving out a little thing uh that is the really attractive part of doing research if if uh in mathematics all I could foresee doing for the rest of my career was just I mean I like reading books and learning new things and yeah a big kick out of acquiring and understanding interesting proofs but if that was all I was going to get out of the rest of my career in mathematics like I wouldn't be sad about that to get paid to do that is pretty good right that's a lot that's a very privileged flight but I would get antsy and uh go do something else after some time I I it wouldn't wouldn't retain the vibrancy that is what attracts me to this career so for me it is important that I'm at least can manage to fool myself into thinking I'm doing something new and maybe uh In My Own by my own life significant uh that's that's the part of the motivational sort of system that really matters for me and I think it's it's the part that I I foresee being pretty rapidly undermined by advances in AI actually unfortunately um if in like the Twilight of your career Dan do you think if you realize say in 20 years that you aren't going to contribute anything new um but you're still like employed with that like motivates to retire or would you still want to like stick around to like I guess read and teach or something yeah I mean I suppose people usually transition at some point to I mean you can always keep doing new things right they may not be at the level of what you used to do so it's not once you've acquired enough knowledge and you know and in particular areas you can always keep making contributions so you usually don't have to quite face that question straight on but you know usually people will do more supervising of students or teach more or write books I mean the mathematical culture as Owen said is is a living thing and you know Elders have a role to play in any community and sort of keeping it sane and keeping alive the knowledge that should be kept alive and making sure the younger generation are doing okay and not going crazy in overly
High proportions and so and those are not easy things right it's it's not trivial to maintain a highly functioning culture that passes on its knowledge and doesn't forget everything every generation so those are worthy tasks to do they're not the same tasks as you know proving deep theorems but they are also important and you know deserve to be done well so yeah I think it's uh I wouldn't just retire I think I think that would be a bit selfish to kind of just retire the moment that the the kind of hedonistic Joy of proving cool new theorems starts to evaporate or something and then I mean you think like the mathematism will have the kind of irregular role in the sense that you know it's the AI that you know covering ethereum but um I mean I suppose you know it's just a matter of you know I mean I I don't really understand how the how the systems would work you know I mean the there's a process by which you know um you know like someone comes up with a new proof of something the the community tries to understand it um yeah and I guess that would work in a similar way um sorry people might think of it you know what what do you what do you actually happening that's what I expect to be what mathematics looks like within a generation or so yeah I mean you could say that mathematics and much of intellectual life was like that for hundreds of years right prior to the uh Scientific Revolution right if it was just kind of passing down knowledge and you know people were having ideas but the sort of uh there wasn't a lot of progress maybe for hundreds of years 15th 14th 16th centuries as far as I understand it right that's I didn't know I mean I'm not sure I would see it that way I don't really like if you I don't know just like a random example but like if you think about I don't know like Thomas the planet something like that like I mean I I agree that I wouldn't be as for medieval Christian philosopher like that in a kind of sort of like a kind of progression exactly like a way I mean I think that would be the wrong way to think about it but um I also think maybe thinking about it that way is it's a bit reductive yeah I would agree with that yeah maybe progress is the wrong framing to put on it but it's more like uh perhaps there's not deep progress uh originating from humans in say mathematics in that period but there's reinterpretation and there's like as other ideas evolve things not the outside of mathematics there may be new views on the mathematics and we sort of
think about it differently and it's not that's not a bad thing right but it's very different from the Flavor of mathematics as it has felt to be a part of it over the last few hundred years yeah yeah that's true and I think this period I mean uh I don't know when you'd exactly date the beginning of it but let's say from say Newton's time or 100 years before that until now or a few decades from now I think it probably will be looked back on as a rather exceptional period in the history of mathematics in terms of mathematical culture uh and we probably we find it a bit hard to imagine now but the that that transition from the the period before that time to the period that we're in now that is also hard for us to imagine I think the kind of mindset I found it very difficult to inhabit the mindset of of the world kind of before the Scientific Revolution right yeah that's uh yeah I can it's not like the people there weren't brilliant there were many brilliant people there but when you read what they write it's clearly a different relationship to the ideas than we're used to um so yeah I do I do think that well if if the trajectory that I expect turns out to be the case and AI is a proving theorems at human level and not only proving theorems but they kind of get it right not in some superficial mechanical way but they get it as deeply as we do and can grasp the ideas and present them as beautifully as we can then it will be a very difficult time to maintain the same kind of motivations that we currently have at least the ones that I value I mean I had this discussion with a colleague of mine Arun Ram who many of you know um and I I talked about this with him and he said oh that's fine you know I I'll be perfectly happy I'll I'll be happy to learn math in the same way that I go to a classical performance and appreciate how beautiful it is and and and I actually think that's like a part of me just viscerally rejects that that's like not at all cool with me but I I can see like it's also quite wise I think right it's if you think about attending a live performance it's you value that humans are doing it right and there's some there's some it's a it's a celebration of the commitment that it takes to train to do that and to work together and that human beings working together can achieve this this beautiful thing and you get to be a part of that uh just sitting in the audience and I can imagine people getting the same thrill out of doing that with mathematics and in the end that's kind of what meta uni
is to some degree right it's like we or a university we come together we watch each other present and learn mathematics and we feel good about that even if you know it's only a relatively small percentage of the time that we're doing new math or really pushing the boundaries on anything and that that can keep going um but I do think that there will be some important element that that gets uh quite devalued as the as the AIS progress and there's an interesting we've discussed this before in the seminar but it's it's good to be reminded about Lisa doll's quote when he retired from professional go playing in 2019 I think so he said with the debut of AI and go games I'm not at the top even if I become the number one through frantic efforts and uh I think that definitely captures a bit of my feeling looking forward to AIS in mathematics uh he's motivated by competition as you can see in that quote more than I am but the feeling of having to sacrifice a lot and work really hard to get to the the Forefront of knowledge in some Direction but then no matter what you do you're always going to be way behind the frontier because you can never match up to the AIS that'll be so nice anymore right which is I mean look at them important um but sorry say that again I didn't hear the beginning of that well identity it's harder to sort of it doesn't make as much sense you know that uh um this idea that yeah that you would go to these sort of immense efforts and um um yeah yeah I agree with you yeah we see stories about for example yitang Zhang recently you know he's working at Subway and sleeping in his car for years toiling away at proving some deep theoremen and right now we think of that as heroic right that's like go human like I don't want that life that sounds terrible but go human you know like doing it for the team Ah that's great but in a world where the AIS could do it in 30 seconds for five cents it would it would seem rather different right it would seem kind of actually a little bit insane uh right which is really sad somehow you know it's it's a losing something about the world to to not be able to feel that pride in your fellow human and to instead feel it's kind of a little bit pointless or like or like sacrificing other sources of well-being that a human can find in a fully realized life in order to pursue some narrow end that actually can be achieved in a much easier way uh all right um we can continue this discussion I propose we migrate over to the the tea break location so if you can