Great. Progress. Now here's the important thing: If you understood Shor's algorithm you would know that 28 couldn't possibly have been the number. So this should cause you to conclude that you are in general overconfident about how much you know or understand about how quantum computers would function. This doesn't mean you are necessarily wrong, but it should indicate that you are overconfident here or could you use a more detailed introduction or refresher on the topic. My preferred recommendation is Aaronson's "Quantum Computing Since Democritus." The book assumes no technical prereqs beyond basic calculus and a tiny amount of linear algebra.

If you think there's some specific indication that I'm in general ignorant about algorithmic complexity, please feel free to point it out. If there's a specific statement I've made that indicates that, by all means show it.

This is not really accurate. The way qubits work, they don't expand in that simple a way because you cannot just test all arrangements of 1s and 0s in superposition. You can only solve problems with a quantum computer where all the non-solution superpositions carefully cancel out. That's part why for example it is strongly suspected that quantum computers cannot efficiently solve NP-complete problems, or more formally that NP is not contained in BQP. This is also why Shor's algorithm https://en.wikipedia.org/wiki/Shor's_algorithm for using a quantum computer requires a number of qubits slightly more than the square of the number of digits a number to factor a number. If qubits corresponded directly in the exponential way you are describing, that would be linear in the number of ditis.

> The numbers I saw suggested a 1% change in humanity's emissions, half the CO2 budget for the world, would solve the problem.

Where did you see that? Even the Paris Accords - which are kinda the minium effort - calls for 50% CO2 reduction by 2030.

=Smidge=

> However we don't have data on the deep ocean.

Of course we do. What a silly thing to even suggest.

https://agupubs.onlinelibrary....
https://sos.noaa.gov/catalog/d...
https://www.nature.com/article...

=Smidge=

> The measures taken did - nothing.

"The doctor said I needed surgery to treat this cancer. I took some aspirin instead. The measures I took did nothing, so clearly the doctor lied to me."

> Perhaps it is time to exercise our collective masses of grey matter (and our AIs) to figure out some feasible coping measures and implement them.

We know what to do. We've known what to do for decades. He simply have not done them, mostly because there's too much money and power to be had in maintaining the status quot. We don't need "AI" to solve this already solved problem and, in fact, "AI" is sucking up the resources we need to solve it while also making the problem worse, faster.
=Smidge=

Normally during bubbles, things like this keep working fine until the bubble bursts because when the stocks and other assets keep going up in value it is hard to see if someone is making reasonable investments or not. That Situational Awareness fell apart even in the middle of this may mean they were overly risky even for ventures like this, or it may be evidence that we're in less of a bubble than many (including myself) think. One curious detail is that at least some people (such as many of the people who seem to be fans of Ed Zitron) see he collapse of SA as a sign that the bubble is in the process of bursting. The collapse of SA occurred about a month ago, so it is still recent enough to see if they are correct. But Zitron and his fans have been predicting an imminent collapse for years now, so I'm not sure I'd read too much into it.

I'm in complete agreement that none of these sorts of issues are at all likely with Xinuous (thankfully). My comment was to add some detail to how the system functions in general.

I'm not expecting quantum computers to happen tomorrow. Are you at least capable of understanding that your claim about "28" being the largest number factored was wrong for the basic reason that Shor's algorithm only factors odd numbers?

There are some complications. Sometimes SCOTUS will rule against a specific motion or part of a ruling, or refuse to hear something, even as another piece of an appeal can occur. One can also file in some circumstances a petition for the Supreme Court to reconsider its own ruling. But this is basically never successful. You also can in some circumstances ask an appeals court to change a prior ruling based on a recent Supreme Court ruling, and this has some success. The circumstances where you can do this sort of thing are complicated. Jean Carroll's lawsuit against Trump is an example of this https://en.wikipedia.org/wiki/E._Jean_Carroll_v._Donald_J._Trump where Trump tried basically everything to try and prevent having to pay out even some ver low percentage strategies. Frankly, if someone other than Trump had done this, I suspect the court response would have been more negative.

Most of this is wrong or missing important context.

Scaling in terms of what? The other user was talking about energy usage. This is pretty obviously not the case. Most forms of quantum computers have to be kept incredibly cold, often in miliKelvin. If there were exponential energy use, then adding even in a few more quantum gates would make that energy total massive. But we don't see that. So by what metric are you claiming exponential scaling effort?

I don't know what "QC effort" is, but the obvious metric for this is just false. For example, Shor's algorithm, which is the algorithm for factoring using a quantum computer, has a number of qubits which scales slightly worse than the square of the number of digits https://en.wikipedia.org/wiki/Shor's_algorithm.

This is highly garbled. First, of all the record for factoring cannot be 28, and it cannot be 28 for a pretty obvious reason. Shor's algorithm only works for *odd numbers*. This is a very basic part of how the algorithm functions. The number you are thinking of is 21, not 28. https://arxiv.org/abs/1111.4147. Your point about that these have been "no-decision algorithm" is not completely accurate, but is approximately so. They did use a compiled circuit which used prior knowledge of the solution to optimize the arrangement of the qubits.

But there are also good reasons that factorization records have not expanded. First, Shor's algorithm has high overhead if you trace out the number of gates, and requires very high coherence to even start getting used. It isn't a useful metric of where things are going. This is like looking at the number of people going to space in the 1950s when no one has gone to space and ignoring that rockets had been steadily improving since the 1930s. The coherence time for quantum computers continues to improve. For a while it was improving at a rate of a factor of 10 roughly every 3 years https://en.wikipedia.org/wiki/Quantum_computing_scaling_laws#Schoelkopf's_law . That has slowed down in the last decade or so, so it is now improving by about a factor of 3 to 5 every 3 years. Similar remarks apply to other metrics like number of gates. And we know that if you can get error levels down and coherence times long then quantum error correcting codes https://en.wikipedia.org/wiki/Quantum_error_correction works. In particular, the threshold theorem https://en.wikipedia.org/wiki/Threshold_theorem says that once your physical error rate is low enough, the logical error rate can be as low as you want, regardless of the size of the computation.

It isn't unreasonable to have this gut reaction to how quantum computers are described frequently to the general public. But one important thing to realize is that they don't let you do magic parallel information processing. There's this way of describing them as "trying all solutions at once," or things like that. But a quantum computer cannot in general do that, since if one has all potential "solutions" one needs some way of making sure that the non-solutions cancel out. In that context. there are some problems where we can do that, such as factoring numbers via Shor's algorithm https://en.wikipedia.org/wiki/Shor's_algorithm. Even there, what is going on is more subtle than just trying all factorizations, as noted by the number of quantum gates needed scaling at slightly worse than the number of binary digits of the number. If it were just trying everything in parallel this would scale close to linear with the total number of gates.

A different related situation to look at which may also be useful is how we strongly suspect that NP problems cannot be efficiently solved on a quantum computer. In particular, that NP is not contained in BQP https://en.wikipedia.org/wiki/BQP, the set of problems which can be done efficiently on a quantum computer. If a quantum computer could do "magic parallel information processing" then we'd expect NP to be contained in BQP.

I have not had time to look at the Helion claims in detail, but I'm not sure why you think Aaronson should do so. His position a few years ago was that many current claims about practical quantum computing were being exaggerated (including very much the claims by D-Wave with their quantum annealing systems) but that in the near future practical quantum computers were likely. Aaronson has been careful to say that even as he's also been one of the people most vocal in arguing that the burden of proof is on skeptics of quantum computers who would claim it would never be possible. It may help to look at Aaronson's recent post, for example what he says here https://scottaaronson.blog/?p=9979.

I'm reasonably confident I have a pretty good understanding of what doing math is like given that I'm a published mathematician. Heck, I'll be a little egotistical and just to my own recent paper directly https://cs.uwaterloo.ca/journals/JIS/VOL29/Zelinsky/zel14.html. But this also isn't terribly relevant.

LLMs have been very good at doing searches. But they've done a lot of things that are pretty obviously not mere searches. For example, in the case of Erdos 1196, the LLM solution constructed a Markov chain using a weighing via the von Mangoldt function https://en.wikipedia.org/wiki/Von_Mangoldt_function. That wasn't in the literature at all. In the case of the Jacobian Conjecture for n=3, the AI constructed a complicated polynomial which was certainly not in the literature, since the entire reason the polynomial is of interest is as a counterexample to the Jacobian conjecture.

It is true that a Fields Medalist does not imply expertise in other areas. But these are people who have also spent time working with these systems. And understanding *how* an LLM functions in this way isn't as important as them being able to see what the system can do. One can evaluate that a black box is useful for specific purposes without knowing anything about how the black box functions. And this is not just the Fields Medalists, this is almost the entire community of mathematicians, including people like the one I linked to who is explicitly very anti-AI. This doesn't mean that they are necessarily correct by itself. But it should be a pretty serious warning that these are not mere "morons" here and that you possibly are just mistaken about what capabilities these systems have.

No one needs to believe in magic to see that these systems are highly useful to do mathematics, At this point even the mathematicians who are unhappy about AI use and are advocating mathematicians not use AI are more than willing to acknowledge that in practice these systems are able to do a lot of math, but think that other ethical concerns mean they should not be used. See e.g. https://proofsandprompts.com/2026/08/09/the-ai-dissenter-viewpoint/ . At a certain point, it should occur to you that if nearly the entire mathematical community thinks these systems are powerful and useful, and that includes Fields Medalists like Terence Tao, James Maynard, and Tim Gowers, that maybe the people you disagree with are not "morons."

Not what is going on. While we initially thought that having these systems try to generate Lean proofs or proofs in another formal language would be a good approach (Deepseek tried that for example), almost all the success has been with models reasoning in natural language and only after they've constructed a natural language proof has there then been attempts to solve the problem in Lean. As you can see here https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925de8b/unit-distance-cot.pdf there's no use of Lean. And in that case, there could not have been Lean usage, because while the proof was later verified by mathematicians, it uses a whole bunch of algebraic number theory ideas which were not yet defined in Lean when it ran. You can look at other traces as well. The brute force here is not randomly generated constructions but rather trying a whole bunch of different methods and then seeing what works. The Unit Distance conjecture reasoning chain looks pretty close to what I'd expect to see if a mathematician kept a very careful diary of all their attempts on the problem over a multiyear period.