clever tricks has value for sure. But the main way progress is done in mathematics is by building new theory, the proof of Fermat's Last Theorem is much more important because of the math it created to solve the problem, rather than actually solving the problem.
Unlike the unit distance problem, the impressive thing here is that it is a proof rather than a counter-example.
However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed.
So not to dunk on this amazing result (or move the goal post), but it seems now the only achievement that AI hasn't managed in mathematics is presenting an autonomous "theory-building" proof of an open conjecture. That is a proof that requires creating a substantial new theory (developed say in at least 30+ pages) to crack an open problem.
Open any technical textbook in an area slightly outside your domain and you will quickly disabuse yourself of the notion that majority of words are obscure. Most complex words are just technical/jargon not archaic or forgotten.
Just top of my head (and I don't even follow his takes that closely), just check his takes on Magic Leap which he consistently promoted using quite dramatic langauge (along with the entire AR space) and check how it panned out.
I am also not sure about Finney, but Hal saw his death coming so it is plausible he handed the reins to one more person he deeply trusted, and asked him to tie some knots but not to keep the show going.
Anyone tried to run some stylometry to identify if satoshi-like comments appeared in any of the early post on hacker news discussing BTC? I would say there is a very significant chance he might have added to the discussion in say the first couple of posts before BTC went mainstream (or even mainstream within hacker circles).
It is getting to the point where all the top (living) credibly accused Satoshis are incurring all the cost of being outed as Satoshi without getting any of the upside.
In other words it is almost irrational to deny it is you (if it is really you) if you are outted after a major investigation by the paper of record, so it is rational to take Back’s denial as honest.
His security is already screwed anyone who is incentivised to harm him for billions will already do it for tens of millions (or if they think there is more than 50% chance Back is a multi billionaire), so he might as well take the credit for it and live with the consequenes if it is really him.
Wait it seems like doing unscalable things - like face-to-face teaching/examination - is exactly the sort of things that humanity can afford to do as it benefits from the surplus free time generated by AI efficiently doing the scalable things.
What are they top 3 languages that you have used that can be used as Go alternatives ranked by fun in your opinion (I am guessing Clojure and Rust are two of them)?
It’s a combination of the problem appearing to be low-hanging fruit in hindsight and the fact that almost nobody actually seemed to have checked whether it was low-hanging in the first place. We know it’s the latter because the problem was essentially uncited for the last three decades, and it didn't seem to have spread by word of mouth (spreading by word of mouth is how many interesting problems get spread in math).
This is different from the situation you are talking about, where a problem genuinely appears difficult, attracts sustained attention, and is cited repeatedly as many people attempt partial results or variations. Then eventually someone discovers a surprisingly simple solution to the original problem which basically make all the previous paper look ridiculous in hindsight.
In those cases, the problem only looks “easy” in hindsight, and the solution is rightly celebrated because there is clear evidence that many competent mathematicians tried and failed before.
Are there any evidence that this problem was ever attempted by a serious mathematician?
You can do a lot of money in swindles and bubbles if you time your exit well. There is a fair bit of opportunistic investors who did well in the NFT craze, who speculated knowing fully well that NFT is a craze that will go to zero.
Yes I should point out that I am a noob in this area, so you might be right in calling me out. My understanding is that CT was invented in part to provide a robust foundation for algebraic geometry, so it is quite ironic that people are now involved in trying to rework the foundation of the foundation.
This title is a bit ironic when you consider the fact that one of the motivations of inventing category theory is to provide a foundation for many branches of mathematics
It works perfectly on Gnome (ubuntu) though. There is simple toggle you have to do in one of the standard control panels as well.
I am surprised this issue is not gaining traction with the KDE crowd, as I imagine a substantial part of the userbase are emacs users and used to emacs keybindings.
I am used to having "Emacs key-bindings" on both gnome and Mac (so that for example ctrl-a will always go to the beginning of a textbox no matter the application, such as chrome).
For some strange reason this seems to be very hard thing to set up on KDE or am I missing something?
Actually things did happen in 2001 (9-11), 2008 (GFC), 2012-2015 (Eurozone crisis), 2020 (Covid) and 2022 (Russio-Nato war).
Each of these came very close for a major market depression (except 911).
The fact that none did only instilled in lots of people's brain to take an incremental bit more insurance in the form of gold (if you were to replay Covid or GFC today, what odds do you put that it won't lead to a great depression?)
Also you can argue that the gradual rise is tracking almost exactly the gradual geopolitical paradigm shift from unipolarity to multipolrity.
I know, my point is that it is not directly backed by gold, but indirectly you can make the point there astronomical gold reserve comes into play if gold prices go insanely high.