After the i-th iteration of the for loop, ans will contain n!/((n-i)!i!) which is exactly \binom{n}{i}, an integer.
Technically "ans" can grow above the final result in my example, but even that could be fixed if one really wants (e.g. i must divide either ans or n-i, you play a bit with divmod to figure out which division you do first.)
"The government sucks therefore aliens built the pyramids" has to be the line of thinking I sympathize the least with in the entire span of human opinions.
I am open to the idea that we should handle immigration differently, but I want a plan and specifics, not slogans. What we want to achieve, and by what mechanisms you plan to get there. Open any newspaper: are you more likely to find careful and considerate opinions or racist screeds?
And that is the problem. Time and energy and money and political capital are routinely spent on inconsequential electoral poliTICS rather than substantial poliCY.
This is unfortunately the problem. The level of the public debate is abysmal, most politicians push unbelivably stupid shit about immigration and other identitarian nonsense, budget gets spent to ensure cheese and wine have the proper AOC certifications on them. Honestly up to a point I even understand it, many people don't see themselves as having a meaningful identity as EU citizens and you can't force it upon them.
Asking for sensible AI policy is like asking for a base on mars.
Agreed, I don't know if it's going to stay like this forever, but right now, if anything, the difference is amplified. You can make unbelivable stuff happen through the sheer power of knowing what you're doing.
Yeah, GPT 5.5 + Fable beating either individually is belivable, but 2x Opus > Fable is what makes me a bit dubious about the whole thing. They might be measuring skills that are too specific or benefit a lot from more tokens being thrown at them. Also Claude Code (the harness) is not the best at the moment, that might be part of it as well?
Not all translations are the same. Literary translations are often works of art in and of themselves, and automating them would be missing the point entirely, like automating homework or weightlifting at the gym. I don't really know what's the state of the art, but I do buy that, on the other hand, translating toaster manuals or generic copy could soon be automatic.
If you're a "React person", as the article puts it, friendly reminder that you can render components to HTML and serve that to the user.
I have done exactly that on a project that was under similar constraints. The UI models live in .tsx files and the browser gets pure HTML with zero JS by default.
I take the "2 unsolved" claim to mean "not solved by any model in any configuration in any stage with any number of attempts", the "benchmark results" are much lower. To be clear: it's extremely impressive, I still remember I was in utter disbelief when models started solving AIME problems, and this is obviously several levels above that.
It's also interesting that OpenAI models perform that much better on math and math-adjacent stuff. I assume this comes down to differences in post-training?
Look, I've never been someone who mindlessly hypes AI companies, as a matter of fact I think they have serious leadership problems across the board, but you people are straw-manning them so badly it actually makes me sympathize with them.
They aren't saying they have fully automated luxury AGI, they specifically list the ways models fall short of that bar and caution against people taking the 8x figure as the actual uplift number. At the same time they recognize that 80% of new code is now AI-authored, when two years ago those models were little more than toys. And frankly that checks out: if two years ago you told me we'd have something like Opus 4.8/GPT 5.5 I would have rolled to disbelieve.
I'm dumb as a rock and I don't have a PhD, but since ~1 year ago I started forcing myself to do small bits of coding and math manually.
I'm not noticing a "cognitive decline" per se, but I do see I'm a lot "lazier", even stuff that used to be routine when I started coding now feel heavy.
The object-level discussion is interesting, but I disagree with the premise to such an extent it feels like a moot point. It feels like the article doesn't play out the line to its logical conclusion.
Why would agents want GUIs made for humans? It's already the case that, like everyone who's good at computers, agents want a terminal and good APIs, not some ad-ridden crap.
If anything, AI is a reason why it will never be the year of the linux desktop but also it doesn't matter anymore, because if the higher-order bit of productivity is defined by AI, then my tmux+vim is as good as your Visual Studio.
I'm with you that people are insanely hyped about Claude Code in particular when e.g. Codex isn't far behind (and with recent models I actually prefer it).
But I'm going to need a citation for this:
> a lot of GenZ and young Millenials who were already bitter at their employers have used the tokenmaxxing push to sabotage the AI
The 3 people on reddit doing this don't even register on a company budget. What seems more plausible to me is that budgets were calibrated to spending before agents were actually useful, and late '25/early '26 changed the pattern significantly.
I don't know what this table is supposed to measure but it doesn't check out.
(C, C++) and (JS, TS) are almost source-compatible, chances are you can rename test.c to test.cpp and test.js to test.ts and you're done. Yet they're showing massive differences?
Also most of the compiled languages with no runtime should get results that are very close to each other: good compilers should produce similar object-code for this type of microbenchmark.
Not to mention this is really measuring the implementation, you can't measure a language. Mike Pall wouldn't be down there, and JS/TS wouldn't be up there without V8 and friends.
I'm sure the model is fine, but it's not Google Search, and when I want Search I want Search. If I wanted to ask an AI, why can't I ask the one from my subscription... that I'm already paying for... that's actually good... that can also search the web?
I assume it's a play to test the waters for how the ad market is going to work, because as a product I really can't see why I would ever use it. Dropbox comment moment incoming?
I'm not at liberty to talk more about the details, but last year I worked on a project to modernize a process that critically relied on a VBA macro to handle billions (yes, with a B).
> they run in such a sandbox
What makes them interesting is that they can talk with the outside world: API calls, databases, the terminal named after a former Democratic primary candidate...
I have almost never seen someone start a sentence with "Christian roots" or "Judeo-Christian values" and not end it with a tirade that uses religion as the fig leaf to justify and authorize their reactionary politics.
The minimalist claim that the West is massively influenced by the Church is true to the point of banality, the maximalist claims those ideas are usually deployed to champion simply do not follow.
If only there were a name for this rhetorical fallacy...
> Much of Western thought traces back to serious work by Church theologians.
The problem I have with this is that it's structurally a motte-and-bailey claim. If I have to take it literally, then it's obviously true and it's simply unserious to deny it: the Church does have a pervasive influence on Western civilization. The way it's often rhetorically used, however, is in opposition and to the exclusion of other strands of thought that are equally foundational: the renaissance, the enlightenment, the revolutions of the 17th and 18th centuries, the scientific enterprise, in a smaller but still real way classical antiquity. To the extent it can be said to exist, Western civilization is a patchwork. It is beautiful and I very much like it, but I don't think any one patch gets to have all the credit.
> In fact I think atheists should make more effort to learn about the vast diversity of other faiths
A better version of myself for sure would make that effort. The problem, of course, is that other faiths are just as deep and complicated as "our own", and it would take a lot of time and effort to do so with any level of seriousness.
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