cs 70 is an immensely eye opening class and i am so grateful that i'm taking it. even as i sit here at 3 in the morning the day of my quiz forcing graph induction and planar graphs down my throat anxiously awaiting if i pass this week's topics, there exists an excitement as well. discrete mathematics is an interesting subject. i like to apply the same perspective to discrete math as to competition math and math really on any higher level. you are given a sort of small set of elementary methods (computation wise), but have to use them to derive novel and quite nontrivial insights. it's actually fascinating how much can be constructed from so little, and the entire solve process of a cs 70 problem is immensely more fulfilling than any bashing done in typical math classes (in my case, math 54. taking both at the same time i realize such a stark differnce lol). this i think is a huge fault with the way standard curriculums approach and teach mathematics (just like how babies are conditioned to hate vegetables from a young age), though that can be an article for another time. the main thing i'm trying to get at is that there is a lot of intrinsic pleasure within high level mathematics with perhaps less extrinsic immediate value. it really is sort of like art; a painting on its own provides little utility, but for the painter who spent arduous hours composing it and for the people who spend arduous hours understanding they derive a unique joy. i could extend this to classical music also (since that is something i can relate to a lot more), but at that point the analogy should probably become clear. for example, set theory and cardinal arithmetic generally have very little real world use cases and may never (though i should be careful because a lot of higher level abstractions from the path like noneuclidean geometry and knot theory ended proving to be super useful later), and yet ask any professor or scholar who studies the subject intimately and they will brim with excitement. who are we to judge, then, the necessity and value of the subject? and now to the main topic i want to discuss. there was a huge explosion on twitter after terrance tao and other mathematicians made comments on the progression of ai in mathematics, specifically with openai proposing a solution to the navier stokes problem and subsequently dropping a bank of ~400 papers containing proofs to existing problems (e.g. quasi riemann hypothesis). the consensus response from mathematicians was "mathematicians never asked these problems to be solved", to which many tweets were made DUNKING on this. one of the most common rebuttals was drawing a parallel to cancer research, and arguing that if a cancer scientist made the statement "cancer scientists never asked these problems to be solved" it would be ludicrous. which it would be! and i don't think anyone is saying otherwise. but per my previous spiel on the personal enjoyment that myself and other researchers in the field find within mathematics without necessary extrinsic value, this comparison becomes, completely, apples to oranges. undeniably would ai solving the field of cancer research immediately save millions and perhaps billions of lives. this effect would be direct, and the issue at hand begs a solution as soon as possible. but the same simply cannot be said about abstract mathematics subjects. solving navier stokes, while a tremendous and admittedly very cool feat, does not provide this real world utility, nor did it beg for a solution. with the uproar from people against push-backs to ai in mathematics, i'm very surprised to not see a similar reaction to the creation of DALL-E, Seedance, or equivalent. most people are generally averse to ai in art / video creation; why not illicit the same reaction for mathematics? perhaps the connection is not as linear, or it is because ai has not really "perfected" art or video creation, but i don't imagine that when it does people will be supporting it. and that is quite alarming. the more that ai intrudes on these much more personal, intrinsically human pursuits, the more the line between human and machine is blurred. the same goes for blogging! i would never have ai write blogs for me, as i want to own my self-expression, and choose the words i string together. and mathematics is simply a different form factor of this underlying idea. (perhaps this is why emotionally intelligent machines generally isn't a great idea... sorry avalon! i still think it would be immensely useful, though must be HYPER tailored for the right use cases). we must keep these realms absolutely separate. and if we are to create a defined line between artificial and human intelligence, then i think it is absolutely necessary we abstain ai from areas without immediacy and that are necessarily creative in nature, pursuits that belong to "us". this boundary itself is a bit abstract, and i would like the time to formalize it into more concrete words, but examples off the top of my head are writing (nuanced cases), music in any form, physical art (all mediums), poetry, satire, mathematics, hell even instagram reels! (because at least it retains its authenticity). my belief is that frontier labs such as openai and anthropic should be dedicating all their resources to finding novel solutions in medicine, economics, and any other fields with a very quantifiable, direct value. and i'm sure that these frontier labs are already doing a bunch of it. though what if they dedicated the totality of their resources towards it? how fast could we come to that solution if these frontier labs focus solely on it, and ignore other realms of diffusion or image creation? this take might be quite mainstream and/or naive, and i would love comments disputing it. but for what it is worth, seeing the opinions of my small sample size of twitter, i thought that it was important to get these thoughts down. i am absolutely for ai; it goes without saying that this technology has implications greater than anything humanity has ever seen. but we must be absolutely careful with the direction that we apply it to. there is so much at stake regarding the actual nature and innate value of humanity. as our capabilities are replicated by ai (and at a magnitude & speed greater than we can ever fathom), we must preserve at least a few.
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