David Hilbert's 1930 Radio Address [video] | Hacker News Reader

David Hilbert's 1930 Radio Address [video]

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This is a nice summary of an earlier, more "optimistic" view of Mathematics and our understanding of Nature. The final words sum it up well: "We must know! We will know!"

Then things like Gödel's Impossibility theorem and the Halting problem came to light. Or quantum physics, with it's inescapable uncertainties, etc. In those earlier days, it must have seemed like humanity would in due time reveal all of the workings of the universe / uncover God's Plan.

Then we got a reality check (:

I feel like I've gone on a similar trajectory in my understanding of the world. Early on, I felt like "the answers" were known, and I just needed to apply myself to understand them. Perhaps it's a side-effect of the way school and academics are structured. And over time I've come to understand that all the elegant formulae and high-level concepts are just approximations (albeit useful ones) to reality: which is a wild, beautiful, never-fully-knowable mess.

Sometimes I think of it in terms of Plato's Cave[1]: the notion was that the Ideal is the "perfect thing", and our observed reality is just wavering shadows on the wall, derived from that ideal. But nowadays I think the shadows are the perfect reality, and the "ideal form" is just our derived, simplified, mental model, and we're more exploring our own limited ability to understand rather than some innate truths of nature itself.

[1] https://en.wikipedia.org/wiki/Allegory_of_the_cave

Well put. This notion of "ignorabimus"[1] which he opposes would seem to have gathered a great deal of evidence in the meantime. What I wish was more widely understood today was the cost of attempting to use models that are effective in the natural sciences in domains where they seem to be consistently ineffective. The replication crisis [2] , where in some cases less than 40% of key studies in psychology and the social sciences could be replicated, is often chalked up to improper statistical analysis or lack of integrity on the part of the authors. But it seems more likely to be the result of relentlessly applying linear mathematics and statistical methods to a domain where things simply do not work the way they works in physics or the natural sciences. To be sure - there is some baby in that bathwater, but the social "sciences" have thus far failed to articulate the domains that are baby and the domains that are bathwater. The amount of human effort and time that is wasted because "We must know" and "We will know" - trying to fit a square peg in a round hole - seems immense.

[1] https://en.wikipedia.org/wiki/Ignoramus_et_ignorabimus [2] https://en.wikipedia.org/wiki/Replication_crisis

Always amazes me to see that society as a whole has been and continues to be willing to use public (or private) funding to support natural sciences. In the short term, one often faces the argument about the meaningless of doing things just for the sake of knowing or understanding nature. But in the long run, attracting scientists and engineers to work on such problems must (insert my optimism) add a significant value to our society as a whole.

Just think about all the computer science stuff from last century that gets traction lately.

Theory is just much faster than practice.

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).

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.

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?

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.

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.

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.

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.

> 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.

What the heck is this accent of German?

Hilbert was from Konigsberg/Kaliningrad. Not very likely to be heard today.

Prussian presumably as that is where he was from. According to wikipedia he used to say he was born in Königsberg but there is a possibility he was born in another place near there. [1]

[1] https://en.wikipedia.org/wiki/David_Hilbert

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