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Hilbert's optimism (we will know) was not a given in the 1930s. What can we make of this almost 100 years later? On the one hand, mathematics and science are i

Hilbert's optimism (we will know) was not a given in the 1930s. What can we make of this almost 100 years later? On the one hand, mathematics and science are incredibly successful. On the other hand, we have Gödel's and Tarski's theorems and still no convincing Theory of Everything (quantum gravity, string theory).

Frummy 2y ago
It's probably a cultural expression not just individual, Göttingen carried the development of mathematics for a while and then got butchered due to the political events. ToE or not, the same type of optimism will make itself known during periods of strong mathematical culture and high rates of progress. "Wir mussen wissen. Wir werden wissen" is a religious dream, mathematics will probably not be the primary arena for facing God for some time, the influences of Bourbaki took over and made math more like accounting than intuitional dreaming. I would have hoped to say that the AI age brings math back to intuitionism for wilder developments but it doesn't look to be remotely within current capabilities to handle the more bureaucratic formal processes within modern math.
- p1esk 2y ago
  the same type of optimism will make itself known during periods of strong mathematical culture and high rates of progress Would you characterize present time as one of such periods? I view current AI research as a branch of math, and the progress is rapid. Would you agree?
  - Frummy 2y ago
    AI research is making grand progress at a rapid pace as everyone is aware. As for the human experts of the field, I can't say, I'm not up to speed. I'm not looped in enough to tell if the developments border at theological inquiry at this point. The ethical concerns, such as military applications, and potential negative social effects, lends a manic, rabid tint to the trend, that existential risk can cause some people to pray. The field of research deals with its own existential questions as everyone knows. Douglas Hofstadter said he was depressed about it. It's fair to call the research a branch of math, but it's certainly applied, the developments are often explored via empiricism and not pure reason, in the sense that results are achieved partly through practice and then described with reason, rather than pure analytical reason causing results. I'm not intending to denigrate that, iterating on experience is the method of great painters and so on. Yeah, let's quote Leonardo Da Vinci: "Experience never errs; it is only your judgments that err by promising themselves effects such as are not caused by your experiments". It's undeniably giving life force to science and math, less in the Abel prize/Fields medal area and more in the Turing award area obviously. One or many Turing awards and the like are probably imminent to be given out. The optimism is more in the realm of business, isn't it. After all it is institutions of business, not academy, that are the driving force. AI is undeniably an optimistic space, I passed on buying NVIDIA in april 2023 and it has quadrupled since then as an example. So I suppose I'm not looped in with the hype, even though behaviourally I left work and returned to academia due to it arriving. The technology itself is unlikely to produce an extension of our limit to knowledge in the same way as the mathematicians of the former century, not because it's without utility but because it can't reason in such a structured way yet. Rather the technology itself will like a very broad irrigation system fill in the gaps and ease the flow downstream, rather than heightening the peak. We are starting to see this institutional efficiency become realised, but also the produced slop itself is starting to cause negative effects especially in the social sphere. Yes, the current period and the research branch has to be deemed optimistic in the sense that it extends the limits of what we know, not in the purely analytical way, but in a mix of reason and experience that is part of daily life itself. Wonder what the generation growing up with it will accomplish, and what difficulties they will face.
  - FabHK 2y ago
    I wouldn't call AI a branch of math. It uses fairly basic mathematical building blocks and applies them at huge scale. Not sure there is much cross fertilisation back into pure mathematics. Research in cryptography is much closer to the front of mathematics; mathematical finance (derivatives) used to be.
  - chriskanan 2y ago
    AI professor here. Most of AI is much closer to engineering or our knowledge of electricity before Maxwell, where we had been using it for 100+ years with big gaps in our understanding. Statistical learning theory is the branch of AI that is closely aligned with mathematics and is very proof heavy; however, my learning theory friends lament that what they can contribute in the current era is much more limited than 20+ years ago, where they gave us algorithms like boosting.
lisper 2y ago
IMHO the big win has been the reification of Turing machines as an essential commodity. Software is no longer a mathematical abstraction but a reality that permeates every aspect of day-to-day life for just about every human being on earth. This democratizes mathematics because you can explain it to ordinary people in terms of computer programs and they can easily understand what you are talking about. The fact that there are fundamental limits on what computers (and hence mathematics) can do it surprising and interesting, but not even remotely cause for despair. As for our failure to find a ToE, it has been barely 50 years since we got the Standard Model figured out, and since then we've been stymied by the lack of data in the relevant regimes. It's really, really hard to do experiments where both GR and QM have measurable impacts. Give it time.
- heresie-dabord 2y ago
  > This democratizes mathematics because you can explain it to ordinary people in terms of computer programs and they can easily understand what you are talking about. The fact that there are fundamental limits on what computers (and hence mathematics) can do it surprising and interesting I would take this further. The ubiquity of computing tools helps us humans face our greatest intellectual challenge: learning to think about the effects of scale.

Frummy 2y ago

It's probably a cultural expression not just individual, Göttingen carried the development of mathematics for a while and then got butchered due to the political events. ToE or not, the same type of optimism will make itself known during periods of strong mathematical culture and high rates of progress. "Wir mussen wissen. Wir werden wissen" is a religious dream, mathematics will probably not be the primary arena for facing God for some time, the influences of Bourbaki took over and made math more like accounting than intuitional dreaming. I would have hoped to say that the AI age brings math back to intuitionism for wilder developments but it doesn't look to be remotely within current capabilities to handle the more bureaucratic formal processes within modern math.

p1esk 2y ago
the same type of optimism will make itself known during periods of strong mathematical culture and high rates of progress Would you characterize present time as one of such periods? I view current AI research as a branch of math, and the progress is rapid. Would you agree?
- Frummy 2y ago
  AI research is making grand progress at a rapid pace as everyone is aware. As for the human experts of the field, I can't say, I'm not up to speed. I'm not looped in enough to tell if the developments border at theological inquiry at this point. The ethical concerns, such as military applications, and potential negative social effects, lends a manic, rabid tint to the trend, that existential risk can cause some people to pray. The field of research deals with its own existential questions as everyone knows. Douglas Hofstadter said he was depressed about it. It's fair to call the research a branch of math, but it's certainly applied, the developments are often explored via empiricism and not pure reason, in the sense that results are achieved partly through practice and then described with reason, rather than pure analytical reason causing results. I'm not intending to denigrate that, iterating on experience is the method of great painters and so on. Yeah, let's quote Leonardo Da Vinci: "Experience never errs; it is only your judgments that err by promising themselves effects such as are not caused by your experiments". It's undeniably giving life force to science and math, less in the Abel prize/Fields medal area and more in the Turing award area obviously. One or many Turing awards and the like are probably imminent to be given out. The optimism is more in the realm of business, isn't it. After all it is institutions of business, not academy, that are the driving force. AI is undeniably an optimistic space, I passed on buying NVIDIA in april 2023 and it has quadrupled since then as an example. So I suppose I'm not looped in with the hype, even though behaviourally I left work and returned to academia due to it arriving. The technology itself is unlikely to produce an extension of our limit to knowledge in the same way as the mathematicians of the former century, not because it's without utility but because it can't reason in such a structured way yet. Rather the technology itself will like a very broad irrigation system fill in the gaps and ease the flow downstream, rather than heightening the peak. We are starting to see this institutional efficiency become realised, but also the produced slop itself is starting to cause negative effects especially in the social sphere. Yes, the current period and the research branch has to be deemed optimistic in the sense that it extends the limits of what we know, not in the purely analytical way, but in a mix of reason and experience that is part of daily life itself. Wonder what the generation growing up with it will accomplish, and what difficulties they will face.
- FabHK 2y ago
  I wouldn't call AI a branch of math. It uses fairly basic mathematical building blocks and applies them at huge scale. Not sure there is much cross fertilisation back into pure mathematics. Research in cryptography is much closer to the front of mathematics; mathematical finance (derivatives) used to be.
- chriskanan 2y ago
  AI professor here. Most of AI is much closer to engineering or our knowledge of electricity before Maxwell, where we had been using it for 100+ years with big gaps in our understanding. Statistical learning theory is the branch of AI that is closely aligned with mathematics and is very proof heavy; however, my learning theory friends lament that what they can contribute in the current era is much more limited than 20+ years ago, where they gave us algorithms like boosting.

lisper 2y ago

IMHO the big win has been the reification of Turing machines as an essential commodity. Software is no longer a mathematical abstraction but a reality that permeates every aspect of day-to-day life for just about every human being on earth. This democratizes mathematics because you can explain it to ordinary people in terms of computer programs and they can easily understand what you are talking about. The fact that there are fundamental limits on what computers (and hence mathematics) can do it surprising and interesting, but not even remotely cause for despair. As for our failure to find a ToE, it has been barely 50 years since we got the Standard Model figured out, and since then we've been stymied by the lack of data in the relevant regimes. It's really, really hard to do experiments where both GR and QM have measurable impacts. Give it time.

heresie-dabord 2y ago
> This democratizes mathematics because you can explain it to ordinary people in terms of computer programs and they can easily understand what you are talking about. The fact that there are fundamental limits on what computers (and hence mathematics) can do it surprising and interesting I would take this further. The ubiquity of computing tools helps us humans face our greatest intellectual challenge: learning to think about the effects of scale.