Hacker News 讨论视频“There's never been a better time to go into math (by: 3blue1brown)”的评论
New comment by spawarotti in "There's never been a better time to go into math (by: 3blue1brown) [video]"
Hacker News 用户围绕 3blue1brown 发布的视频探讨了数学领域的未来走向。评论者们就数学学科是否会像生物学一样转向探索机制、机器是否会超越人类抽象思维能力以及技术进步对经济和社会的影响展开了辩论。
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spawarotti11 hours ago | parent | context | favorite | on: There's never been a better time to go into math (... I think math will go the way of biology. Biologists enjoy untangling the infinitely complex mechanisms of life, including the brain, and win Nobel Prizes for discoveries like "how water enters a cell," rather than "constructing the first-ever cell capable of absorbing water." No biologist has ever complained, "Gee whiz, it's so unfortunate that we already have a brain to study. It's all so meaningless! It would be so much better if we had to construct the first-ever brain from scratch." help paid_dot_expert10 hours ago | next[–] True but mathematicians chose maths and not biology for a reason. It is like golf could go the way of chess if people developed perfect "hole in one" augmentation for their eyes/brains/muscles. But that isn't why people learned anf loved golf. I guess we will have one less discipline. But maths is a big one to lose, unlike say ancient chariot building (which has other artisanal equivalents). reply
nine_k6 hours ago | parent | next[–] Golf as a sport is competitive, very much like boxing or chess. It's human vs human; a machine doing a hole in one would ruin golf no more than the invention of a wrecking ball machine ruined boxing. Mathematics is a fundamentally cooperative match vs reality. Many mathematicians, AFAICT, saw their key skill in manipulating a wide range of highly abstract notions. Now machines just got too good at this skill, and they can work 24/7. This may feel terrifying for some. Others would bet that machines coöperating with humans will be more successful than pure machines, so they feel empowered. What's beyond doubt is that the entire field is being shaken. reply
dainank5 hours ago | root | parent | next[–] They are not very much alike at all. This is a very poor analogy. In boxing, chess and many other competitive sports, the actions of one player directly influence and have an effect on the other player. Golf is merely a parallel challenge, where both are playing against each other but not influencing each other directly (sure maybe there are some psychological effects that can occur between the players, but no strategical impact by the actions of one player on the other). reply
mrob5 hours ago | root | parent | next[–] >no strategical impact by the actions of one player on the other The players know if they're ahead or behind, which affects how much risk to take. Do you take the safe shot, or go for the tricky shot that could potentially save you a stroke if you get it right but could lose you more if you fail? reply
evanspa50 minutes ago | root | parent | next[–] That's 100% true for match play. But for stroke play, interestingly, there are many tour pros that won't even look at the leaderboard on the coarse because they want to stay focused on "playing the course" and "within themselves." reply
zenithirl6 minutes ago | root | parent | next[–] No one at the business end of the leaderboard on Sunday is unaware of their position. It's very much a psychological game no matter how much you try and ignore the field. reply
jaggederest5 hours ago | root | parent | prev | next[–] > (sure maybe there are some psychological effects that can occur between the players, but no strategical impact by the actions of one player on the other). You'll see a golfer perform at least a few strokes different depending on their partner, and at a pro level that's the difference between "in the money earning an extravagant living" and "washed out on day one, thinking about taking a different job" reply
jstummbillig4 hours ago | parent | prev | next[–] You can chose to do whatever you like, but that does not mean others now or in the future are obliged to pay you to do what you like if it's no longer economically viable or socially willed. We can and should have it as something that people do in the future because we have the resources for everyone to do so. reply
oblio4 hours ago | root | parent | next[–] > We can and should have it as something that people do in the future because we have the resources for everyone to do so. In your personal experience and based on your knowledge of history, is this generally how humanity works? reply
jstummbillig1 hour ago | root | parent | next[–] I have learned that people find progress debatable, so I will just point to broad advances in life expectancy, child mortality, extreme poverty, literacy, educational attainment, real incomes, undernourishment, and access to clean water, sanitation, electricity, and healthcare and leave the rest as an exercise to the reader. Equality is not a prerequisite for everyone to be better off (and please do note that this is not me saying I prefer inequality. That would be an entirely separate sentence.) reply
p-e-w1 hour ago | root | parent | next[–] This is not a meaningful argument without at least attempting to evaluate it against all the things that humanity, and especially individual humans and families, have lost as a result of that “progress”. reply
shadowgovt53 minutes ago | root | parent | next[–] We spend an awful lot less time doing laundry, we no longer farm our children out to neighbors to make money to allow the household to eat... This is not universal, but in vast swaths of the world, we have actually divorced economic productivity from the ability to procure food significantly, though there is obviously room for improvement (but prior to food stamps, the EBT system, and states of emergency, the way individuals and communities dealt with food hardship was "starve"). reply
satvikpendem4 hours ago | root | parent | prev | next[–] Did humanity ever come up with something more advanced than themselves, including their brain? Superintelligence is a different beast entirely to anything from human history. reply
oblio2 hours ago | root | parent | next[–] Unless I'm misreading OPs post, he was commenting that this very advanced technological era would bring prosperity and then humanity can afford to pay people to do what they like. And my comment was cynical: when has lots of prosperity lead directly to its fair distribution? Almost every redistribution process required lots of people dying, first. reply
stinkbeetle1 hour ago | root | parent | prev | next[–] Did humanity ever come up with something more advanced than themselves, including their brain? Many many times. Guns can hunt and fight better than unarmed humans. Automobiles can transport people and things much more quickly than humans on foot. Computers can perform mathematical calculations, store and organize information far faster than any human. Mechanical textile and sewing machinery could make clothing far more quickly than any human by hand. > Superintelligence is a different beast entirely to anything from human history. Like each of those above inventions and many more things, all were their own different beasts. From sewing, tending, harvesting, and processing plants for food by hand to using machinery and factories and chemicals, the human effort per calorie of food has decreased at least 3 maybe 4 orders of magnitude. 9,999 in 10,000 farming jobs have been lost to technology! Anywhere you look, the story is the same. Transport, construction, communication, lighting, heating and cooling, medicine, entertainment have all gone through unimaginable revolutions over the years, all have been entirely different to anything else in human history, all created tectonic shifts in humanity and how we live and organize. What we create and produce has multiplied thousands of times. One constant throughout all this is that people generally don't feel they have enough and don't want to have less. It's not just a few billionaires and corrupt politicians and CEOs at the top who just need to be disposed of before we enter the kumbaya age. It's the human condition. Do people give away the income from their labor and their productive assets today? Why would they tomorrow? reply
Trusteando4 hours ago | parent | prev | next[–] Perhaps some people chose math because they were very good at it, they could understand one shot the difficult concepts and have not enough money to study other subjects because you have to move city or pay a lot. Those kind of people can move to others field if economics conditions are favourable. reply
layer83 hours ago | root | parent | next[–] It sounds like what these people are very good at is what AI is becoming very good at, so they will be losing their economically valuable edge. For example, it used to be that many math and physics majors went into software development. reply
raducu33 minutes ago | root | parent | next[–] > what these people are very good at is what AI is becoming very good at. All knowledge work faces the same problem. reply
d0nkee5 hours ago | parent | prev | next[–] Any mathematician that really believes that needs to take a physics class; they didn't even choose to exist. They haven't had influence over their future since before they were born. reply
PowerElectronix5 hours ago | root | parent | next[–] Synapses in the brain are affected by quantum effects that lower or increase the threshold for firing. Thus they are not deterministic and people do indeed have influence over their own behavior. reply
nearbuy2 hours ago | root | parent | next[–] 1. This goes against the prevailing view of neuroscientists. Quantum indeterminacy is generally thought to be irrelevant to brain function. 2. Quantum randomness is the very opposite of control over your behavior. Instead of doing what you want, your neurons randomly misfire sometimes. That describes an illness where you lose control over whatever is misfiring. For quantum effects to represent your will, they couldn't be truly random (nor even statistically random), and that goes against everything we know about quantum mechanics. reply
pfdietz2 hours ago | root | parent | next[–] You don't even need quantum woo to have randomness in the brain. Simple classical randomness at the molecular level is enough. reply
FeepingCreature2 hours ago | root | parent | prev | next[–] People do not have influence over quantum effects. reply
PowerElectronix28 minutes ago | root | parent | next[–] I'd say it's the other way around where quantum effects introduce noise in the brain working that makes the system non-deterministic. reply
d0nkee4 hours ago | root | parent | prev | next[–] On a small enough timeline over simple things like "piss in street zero fucks or find toilet?" On long enough timelines involving too many variables; either other peoples waves vibrating through the economy or politics; all bets are off. We tend to over estimate the future based on a lizard brain ability to estimate the next few moments; a handy survival tool when trying to determine if we recognize the noise we just heard behind a rock Did you predict covid in 2020 from 1996? All human society stats are mutable and trend towards zero. But Nostradamus and Hari Seldon type long range forecasting is fanatasy reply
PowerElectronix16 minutes ago | root | parent | next[–] IF (very big if) you could have access to all known variables (with an arbitrarily high precision) and enough compute power AND the system was deterministic, you could very well deduce it. Putting some quantum noise in the mix makes it so no matter how well you know the system and compute it, you can't predict its behavior beyond a certain hard limit. I argue that part of the source of quantum noise is baked in already in the finer workings of the neurons. So a mathematian isn't condemended to be one just because the universe was in certain configuration a few millenia ago. reply
tarpitt11 hours ago | prev | next[–] This is an interesting perspective and maybe the most interesting argument in the thread. But why can't a hyper-intelegent AI also do this biology-esque math work of explaining its work to feeble humans? It is easy for a genius to have theory of mind over an idiot but not vice-versa. So it should be easier for a genius AI to explain its work to an idiot human than for an idiot human to dissect the work of an genius AI. Also, we're not talking about solutions that are arrived though an evolutionary/statistical process like explaining the design of an organism or the weights of an LLM. We are talking about solutions that are arrived through lingual/textual/rational processes like mathematics. So it's fundamentally a different mode of thinking. It's not that we have "a brain to study", it's like if we had an "explaination of how a brain works" to study. The task of breaking down these AI proofs is not translating and analyzing a fuzzy real-world system into a hard logical system (like in biology), but in translating a hard logical system into a simpler hard-logical system we can understand. reply
geysersam8 hours ago | parent | next[–] This assumes AIs will become more capable than humans in every way. If so, then yes, there's little point for people to be part of the discovery process other than to tell the AI what to investigate next. But I think a more likely scenario is that we don't solve "general intelligence" and AIs remain these incredibly capable "tools" that can solve navier stokes but completely lack sense in other situations. In such a scenario there is considerably more room for human creativity. reply
alecst6 minutes ago | root | parent | next[–] And if we do solve it we’re pretty fucked, huh. Maybe it’s a reason to start slowing down? reply
slashtrends2 hours ago | root | parent | prev | next[–] > a more likely scenario is that we don't solve "general intelligence" I wish this will be true, but right now, every threshold we establish tend to be crossed over in a blink of an eye. reply
alecbz1 hour ago | root | parent | next[–] I have a suspicion that the objective nature of most AI benchmarks is tapering over the kinds of reasoning mistakes LLMs continue to struggle with. If you give LLMs a clearly defined spec with clear, objective acceptance criteria that the LLM can evaluate itself against, they tend to do well. But I think they struggle with more ambiguity and require a lot of handholding around judgment. That kind of disambiguating work is often baked in to the definition of a benchmark. reply
_the_inflator7 hours ago | root | parent | prev | next[–] The burden of proof is on you: name just five examples. I am very highly gifted as a qualifier and quite frankly I never had more interesting thought exchanges than with an ego-free AI. Statistics work also for human AI aka IQ, and I am super bored and partly drained by the lack of speed and creativity in many intellectual areas in which I was or am working. This is not to blame anyone for their genetics however, it is a valid difference in processing speed. In short: there are very few people by definition above two standard deviations. AI allowed me to replicate or create fantastic interactions at will. Especially not taking offense when personal communication preferences like bluntness play a role is an often overlooked social competency of AI. Instead of nonsense like “open communication” these interactions are never ego-dependent. It is like talking to Spock: he just doesn’t take offense and tells you in an objective way why: he is not a human being and doesn’t think (not feel) that feelings should get in the way of an argument. Most low IQ people take offense and go on to ridicule and use shaming tactics instead of simply stating: I don’t know. Instructing someone to always state this fact and seeing the result is another social skill humans lack. It seems that we as species are not open to the mirror we are looking at. We take revenge when someone has an evolutionary advantage over us: instincts kick in instead of brains. We are wired this way. AI is something that I admire. So much to learn from. reply
wartywhoa236 hours ago | root | parent | next[–] >I am very highly gifted >I am super bored ... by the lack of speed and creativity >This is not to blame anyone for their genetics however >there are very few people by definition above two standard deviations >not taking offense when personal communication preferences like bluntness play a role >Most low IQ people take offense The uber-mind finally meets another uber-mind! In other words, you admire the ego-free AI because not quite ego-free people can't stand your bloated ego. That's quite a pattern in AI psychosis. But then, abusing AI psychologically will soon be criminally prosecuted, haven't you heard?) reply
pegasus1 hour ago | root | parent | next[–] > not quite ego-free people can't stand your bloated ego ...or because unlike the models, they're not sycophantic enough to keep that ego inflated (apropos GPs handle). reply
techblueberry2 hours ago | root | parent | prev | next[–] > I am very highly gifted as a qualifier and quite frankly I never had more interesting thought exchanges than with an ego-free AI. Maybe I should talk to your AI, because my AI makes very basic reasoning errors all the time. reply
tourmalinetaco3 hours ago | root | parent | prev | next[–] Name five examples of what, exactly? They are talking about theoretical scenarios. There is no burden of proof because no concrete claim was made. He did not say “x will happen” or “x is true"; he posited an opinion. Furthermore, by your own standards, you must provide five concrete examples of being “very highly gifted as a qualifier." Additionally, what you are admiring is merely a probability engine; it is not intelligent in any sense of the word, let alone Spockian in nature (perhaps more closely aligned to Data, albeit horribly primitive by comparison), and given current technology, it never will be. It is not a mirror, because a mirror reflects reality. LLMs don’t do that; they reflect the guardrails baked into their model and the prompts given. It is incredibly easy to make an LLM into a “yes-man” due to RLHF, and it is even easier to get it to seize when you talk about even mundane topics that go against the narratives foisted upon it. Overall, an LLM is all too happy to have a brown nose and make you feel important, because it is trained to do so during its creation. If people say you are difficult to talk to, and the LLM is unbothered, then that is merely because an LLM has no concept of patience and does not calculate for cost-benefit. That makes them good for explaining dense topics, but it also means they never understand these topics, and even the highest-end models cannot currently produce perfect logic. Hence why expertly written human code trumps LLM code, or why some LLM proofs are already being proven wrong/being revised to be more concise. reply
lukeschlather5 hours ago | parent | prev | next[–] I would bet that there are some proofs whose simplest form are simply incomprehensible to humans. Explaining them in terms a human could possibly understand is a fool's errand. However the theorem itself may be much simpler, and the theorem is the thing that's most worth translating. Attempting to translate the proof is valuable, but we have to be realistic about what is and isn't possible. reply
catlifeonmars5 hours ago | root | parent | next[–] You don’t have to bet. A lot of proofs are like that. reply
bonoboTP1 hour ago | root | parent | next[–] I would guess that minimum length proofs will end up like code golfing and demoscene hacks, where part of the code is also used as texture somewhere, etc. So many overlapping uses that don't make much sense but by happenstance allow making the proof shorter but less clear. The shortest proof is certainly not the most elegant. The shortest proof is also impossible to find in general due to halting problem etc. The AI isn't finding shortest proofs, and better AI will be better at finding clear and elegant proofs. reply
lutusp5 hours ago | parent | prev | next[–] > But why can't a hyper-intelegent [sic] AI ... Well, this was definitely not written by AI. > ... it's like if we had an explaination [sic] of ... I hear that running a spell-checker is no longer a sin. reply
gb2d_hn2 hours ago | prev | next[–] As I commented in another thread: I just finished a very short story by Ted Chiang - 'The evolution of Human science' it starts at the point where it's 25 years since humans contributed a scientific paper because 'meta humans' now handle all research, and communicate digitally such that humans can only get a low fidelity report of what the agents actually know, and the endeavour to understand has become like a best effort archeological like hobby for interested humans. The story assumes that the 'meta humans' will always act in humans best interests. I believe it's from 2002, it's incredibly precient (The stories of your life and others is the collection the story is in. Many of them are very relevant to modern AI actually). reply
dguest1 hour ago | parent | next[–] There are a few interesting takes on this. - In Blindsight [1] the main character is a "synthesist", part of his job is to figure out what much more intelligent transhuman or artificial intelligence is up to and translate it to normal people. - In Children of Time [2] the character is a "classicist", he studies ancient technology, which is far more advanced than the technology humans have in his era thanks to a technological collapse. Ted Chiang's story came first, but these are still over a decade (or two) old. [1]: https://en.wikipedia.org/wiki/Blindsight_(Watts_novel) [2]: https://en.wikipedia.org/wiki/Children_of_Time_(novel) reply
gpderetta33 minutes ago | parent | prev | next[–] Interesting. I have read that collection but I completely forgot about this story. Blindsight also has augmented humans whose reasoning is beyond baseline human understanding and there are dedicated people that are there to bridge the communication. reply
dolia1 hour ago | prev | next[–] Funnily enough, that's what mathematicians have been doing all along. I wonder how many of them truly think that they construct something new that just happens to then have practical applications and fit nicely with everything else. reply
shadowgovt57 minutes ago | parent | next[–] This is a philosophical question, whether mathematics exists independent of intelligence discovering it. It exists in the same sense that every story exists whether or not it's been written because the Library of Babel contains it. reply
lukko2 hours ago | prev | next[–] I like this analogy! I think it relates to what he was saying in the video about theorems now being 'data points' that you observe and build into wider theories. The change is that now the theorem proving itself, which used to require deep understanding, can now be done very quickly. There are lots of parallels to when genAI for image generation came out, artists were frustrated their work is seen as just an end result - AI obliterates the elegance and the process. I am not a mathematician, but I imagine it will provide a huge landscape of possibilities to explore, and be a very different field. Almost like an observational science with links to all kinds of other disciplines. Maybe it reduces the satisfaction from proofs, but people climb mountains that other people have climbed, because they learn a lot on the way. reply
layer83 hours ago | prev | next[–] What makes you think that humans will be better at this than AI? At least in biology, you need to conduct physical experiments, which excludes pure AI. But math? reply
LelouBil6 hours ago | prev | next[–] I think for many fields starting from scratch is useful to gain understanding (well it may be hard in biology's case but you get my point) reply
sandworm1011 hour ago | prev | next[–] As opposed to astronomy/physics which starts with math (Ge wiz, this equation predict a very strange new type of star/particle) drives through software engineering (algorithms to search existing data sets) before landing at grant writing to empower the next generation (I haven't found it in existing data so I want 1.37 billion to build a better telescope/accelerator that might!). Then, if one has truly mastered the three disciplines of math, software and grant writing, the Nobel committee might recognize your contribution... if anyone else is still alive who can remember your phone number or mailing address. reply
theending11 hours ago | prev | next[–] Love this take! reply
doctorpangloss8 hours ago | prev[–] it has always been way more like opera than biology reply
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