prof-dr-ir
For example, the statement of e.g. Fermat's last theorem in Lean should be understandable to anyone who played The Natural Number Game [0] and knows a bit of mathematics and programming. For the proof, you trust the compiler.
The statement of other theorems can be much more delicate, and the Lean formalization may require an extensive introductory section which will need to be carefully checked.
Then there are the cases where no Lean formalization is currently available, and all we have right now is an often impenetrable pdf in the OpenAI repo. I would not at all be surprised if some of those contained logical gaps.
Time will surely tell, but there are certainly doubts and lots people are very busy checking these results.
People proclaim this with such confidence, especially in the UK before the Brexit years I must say, and yet there are so many arguments against it.
First, accepting this goes against a core tenet of the single market, since the single market for vacuum cleaners is now split into 27 little markets. We thus need 27 regulatory bodies to each investigate, and then make a political decision, on the maximum power setting of domestic vacuum cleaners. Then, producers in China will have to make (up to) 27 different models of vacuum cleaners. This is certainly not going to be cheaper, completely destroys the famous Brussels effect [0], all for some token amount of "sovereignty".
Nations states can sovereignly decide to delegate this process of rule making to Brussels, and domestic vacuum cleaners are a perfectly mundane "case in point" to showcase the benefits of this process. The EU is far from a perfect union, but throwing these frankly naive arguments around will not help it much.
It is a lot of fun to start from an empty file, add maybe an import LinearAlgebra, and develop things like a convolutional neural network or a Markov-chain Monte Carlo algorithm completely from scratch. And then it is very rewarding to have such a program be fast enough (looking at Python here) to train on the MNIST dataset or find reasonable estimates for critical exponents.
I am not sure there are languages better suited than Julia for these kind of things.
Do however note that it is possible to install another keyboard on iOS, which may alleviate your suffering before you switch to Android in about 120 days.
Personally I rely on Gboard [0] every day for the simple reason that it auto-detects several (more than two) languages, and of course it has the added benefit of not having this crazy bug. Gboard is google software however, so it does come with huge privacy issues, and others will hopefully point out better alternatives.
I guess what I want to convey is how sad your comment makes me. What went wrong that makes you, and anyone really, trust that man's opinion on physics?
Here is a cynical but overall rather accurate takedown of Mr. Weinstein:
https://www.youtube.com/watch?v=sAbP0magTVY
I think it is a great watch for anyone with an interest in the field.
I very much agree. Also really miss the ability to quickly group related emails.
(And no, that was not the same as adding a label; for one, the whole group simply appeared as one "bigger" email in the Inbox. It was a bit like a thread that you can manually add emails to.)
When everybody got kicked out of Inbox I happened to have a group of about ten emails related to an upcoming trip. Those ten emails got de-grouped and scattered all around in the ordinary gmail interface. I would have appreciated a smoother transition...
> .. my recent trip from Abu Dhabi to LA. 24 hours door-to-door. We have the technology to reduce that to under 10.
The direct flight (by Emirates) takes 16h15 mins, so that leaves 7h45 mins not in flight. If we want to bring that down to 10 hours just by making the flight supersonic then that would require a flight time of 2h15, corresponding to a (ridiculous) speed well over Mach 4.
Either this relation is not that strong, or factoring should "imminently" become a reasonable benchmark, or useful quantum computing cannot be "imminent". So which one is it?
I think you are the author of the blogpost I linked to? Did I maybe interpret it too negatively, and was it not meant to suggest that the second option is still quite some time away?
So the "useful quantum computing" that is "imminent" is not the kind of quantum computing that involves the factorization of nearly prime numbers?
Congratulation, you are now able to recognize an AI-generated text.
(As of December 2025 at least, who knows what they will look like next month.)
Here is my viewpoint, which somehow some people find controversial: quantum theory is first and foremost a description of individual particles. To describe their time evolution, we use the Schrodinger equation:
i d_t Psi = H Psi
What is that "i" there? Oh right, the imaginary unit. So... quantum theory uses complex numbers.
Now you are free to search for another theory without the "i", and perhaps even find something that is somehow mathematically consistent. But that theory either describes experiments just as well as ordinary quantum theory, in which case it is physically equivalent and of no advantage (except to those with strong allergies to complex numbers), or it does not, and then it is wrong.
Of course the last logical possibility is that your theory might do better than quantum theory... but that is the dream only of those who do not known quantum field theory.
/rant, with apologies
"Worst of all, the air was full of fumes; breathing was painful and difficult, and a dizziness came on them, so that they staggered and often fell. And yet their wills did not yield, and they struggled on."
Fortunately, good old Wikipedia has what we are both looking for:
https://en.wikipedia.org/wiki/List_of_countries_by_traffic-r...
For me the upshot is that UK still comes out quite good amongst its European peers, but the difference appears to be smaller.
This is preposterous. You are completely forgetting that there are actual groups of humans, people who know and respect each other, coming together and discussing the proposals.
Being involved in ranking grant applications is already a thankless job, and many scientists still do it, for the greater good if you want. They will therefore also critically look at any AI reviews, and eliminate them as soon as they are not convincing.
(I am, of course, not saying that the grant review process is without flaws - that is a different discussion.)
So I would recommend moving your civilization to a Dyson sphere around the black hole before aiming your cluster of LHCs at it.
Do you simply trust hetzner to not lose the data on your 1TB storage box?
(I am aware that I am currently trusting google and dropbox to do just that.)
The website explains it clearly enough I would say.
Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at:
https://en.wikipedia.org/wiki/Entropic_force
and in particular the example that is always used in a first class on this topic:
https://en.wikipedia.org/wiki/Ideal_chain
So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon".
Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy.
The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law.
[0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.
That is a very good idea for everyone. Putting together an emergency supplies kit is what various European governments, and now also the European Commission, are beginning to officially recommend:
https://www.euronews.com/my-europe/2025/03/26/brussels-ask-e...
> What’s going on? How bad is it? How long is it going to last?
I think some governments suggest that people buy a battery-powered or hand crank radio to address exactly this issue.
It is high time we got used to companies being fined a reasonable fraction of their revenue. And TikTok's global revenue last year alone was estimated at $20 billion to $26 billion [1].
[1] https://www.nytimes.com/2025/01/17/technology/tiktok-ban-byt...