Amazing that when ai "solves" an erdos problem by finding the solution in an existing paper it gets hundreds of points and comments, but when ai fails a more rigorous test designed by practitioners (i.e. a much better test of the claim that ai will soon do research level mathematics) it gets zip.
C is the only way to make a field out of pairs of reals. Also (or rather just another facet of the same phenomenon) we might be interested in polynomials with integer coefficients, but some of those will have non integral roots. And we might be interested in polynomials with rational coeffs but some will not have rational roots. Same with the reals but the buck stops with the complex numbers. They are definitely not accidental they are the natural (so to speak) completion of our number system. That they exist physically in some sense is "unreasonable effectiveness" territory.
In my experience, the so-called 1% are mostly just thinkers and researchers who have dedicated a lot more time from an earlier age to thinking and/or researching. There are a few geniuses out there but it's 1 in millions not in hundreds.
People like to, ahem, parrot this view, that we are not much more than parrots ourselves. But it's nonsense. There is something it is like to be me. I might be doing some things "on autopilot" but while I'm doing that I'm having dreams, nostalgia, dealing with suffering, and so on.
It’s a weird product of this hype cycle that inevitably involves denying the crazy power of the human brain - every second you are awake or asleep the brain is processing enormous amounts of information available to it without you even realizing it, and even when you abuse the crap out of the brain, or damage it, it still will adapt and keep working as long as it has energy.
No current ai technology could come close to what even the dumbest human brain does already.
A lot of that behind-the-scenes processing is keeping our meatbags alive, though, and is shared with a lot of other animals. Language and higher-order reasoning (that AI seems better and better at) has only evolved quite recently.
All your thoughts are and experiences are real and pretty unique in some ways. However, the circumstances are usually well-defined and expected (our life is generally very standardized), so the responses can be generalized successfully.
You can see it here as well -- discussions under similar topics often touch the same topics again and again, so you can predict what will be discussed when the next similar idea comes to the front page.
So what if we are quite predictable. That doesn't mean we are "trying" to predict the next word, or "trying" to be predictable, which is what llms are doing.
Over a large population, trends emerge. An LLM is not a member of the population, it is a replicator of trends in a population, not a population of souls but of sentences, a corpus.
International law does not apply to the leaders of the western hegemony. It is merely a tool used to oppress poor nations even further.
This fact only further proves one thing: the CIA is a terrorist organization and the state behind it is responsible for some of the most disgusting things this planet has ever seen.
Given the period of 2010-2012, the president at the time was Barack Obama. It does not seem realistic that people would accept opening a criminal case.
It is approaches like that which gives some hope to the future. War crimes are indeed something which should never be allowed or overlooked. Being a political leader doesn't make people immune to criticism, but rather should be someone held to a higher expectation.
Why does it matter if it was Obama or Bush in power? Sure, their politics influence the nation's foreign policies. But domestic partisan politics is largely irrelevant to the international partners. To the foreign nationals affected by it, you're just USA either way.
I mentioned just the other day, the problem with anti-intellectualism in the US and how it's fed by these sorts of egregious meddling by the administration. There are much less educated and affluent countries that are nowhere near as anti-science as the US. Yet unfortunately, the US exports it abroad too. I explicitly referred the same Pakistani case as an example of that. I'm all for Osama's elimination, but they jeopardized the entire humanity's future by misusing the vaccination program for it.
Despite a century of this nonsense (remember the radium girls?), neither political party cares enough to not pervert science in the interests of humanity. Smallpox and Polio were horrible diseases that caused untold miseries. Even the remote tribes of Pakistan knew their dangers well enough to participate in their elimination, until the US pulled off this dirty stunt. This is a deeply ingrained toxic culture that was reinforced by both parties over the decade. This should be a war crime irrespective of party allegiances.
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Why does it matter if it was Obama or Bush in power?
If Bush was in Power, of course the accusation would have to made against Bush. So, of course, the accusation has to be made against the president that was in charge at the time. Dark skin color does not give him a "Get Out of Jail Free Card".
> Why does it matter if it was Obama or Bush in power?
How can you open a war crime case against a guy who already got a Peace Nobel Prize? And what war crime? Was there a war? Maybe some special military operation against Bin Laden.
Are you kidding? A way to smear Obama and portray him as disrespectful to non-whites? The only reason it’s not on Fox is that it reminds Americans that we’ve only had one victory in the War on Terror and the Republican Party contributed nothing positive.
The thing about norman doors is that it's not really a design flaw, not in every case. Like handles on push doors. It's tempting to think of that as a design flaw but more likely it's designed to be mass produced and reversible, the cost of making two (or more) configurations being much higher than the occasional confused user. You could argue this only enhances the metaphor as a lot of design issues occur when things are optimised for the company and not the user.
I still see this as a design flaw, even if it explains why it was done. They save a little in manufacturing, and then thousands of people per day end up using it wrong for decades, in the case of a high traffic door, like at a mall.
Related… this is one of my favorite Far Side comics.
Wouldn't the solution to make the door so different handles can fit on both sides and then the installer can simply put the correct handle on each side as needed? Surely that is just as much of a manufacturing efficiency improvement.
Can you give an analogous example for data science? I confess ignorance here, and always took the term at face value. Is the issue that "data science" tries to be agnostic about the source of the data? (I'm not claiming that that is true, just guessing)
Sure. There are many examples of data scientists attempting to use complex Machine Learning and Deep Learning models to predict machine (bearings, gears, etc.) failures from vibration data, where a simple Fourier Transform (FFT) provides a lot more insight and predictive powers about the same problem.
However, spectrum analysis is not something that data scientists learn at school, yet every mechanical/electronics engineer working in the field knows about it. So, without an expertise in a particular field, data scientists often reach for a big hammer, when more specialized tools exist and are known to the experts in the field.
Another classic example is data scientists trying to model biological processes (or answer questions about processes while ignorant of which components regulate others). Systems biology has a long history of largely clueless attempts to predict outcomes from complex processes that no one understands well enough to model usefully. The biologists know this but the data scientists do not.
huh. I'm a professional data scientist, and my masters was in signal processing. In one class the final exam required us to transcribe fourier transforms of speech into the actual words. In another the final exam required us to perform 2d FFTs in our head.
Please be careful about generalizing.
I agree that many 'data science' programs don't teach these skills, and you certainly have evidence behind your assertation.
I don’t think anyone is making the claim that data science has no merit, or data scientists are universally ignorant of anything.
Simply that some data scientists, formally trained or titled by themselves or others, have been known to apply their skills to data without having special knowledge regarding the data.
It is a bit of a cliche in some of our experiences. The consulting company that analyzes data for a decision paralyzed organization, that seeks outside guidance in lieu of getting better leadership, is something I see.
That is a real phenomenon, and despite good intentions, can have all the effectiveness of reading tea leaves.
Because there is always data to be scienced. Competently or not.
But, you are making my point for me here. Most data scientists don't get masters in signal processing. You are also acknowledging that gaining expertise in a particular field was worth pursuing.
It's much worse than that. If you dare to ask that a team speak with the problem owners - mechanics, managers, etc, you will get booted right quick.
Since the 2010's data science has gone from scientific based curiosity in solving problems to pure technicians work. There's a set of algorithms they follow, no exceptions allowed. Kaggle is a horrible anti-pattern.
i confess, i've read both of your comments on this - your analogy and a deeper explanation of the analogy - and i still have no idea what you are saying. i'm not stupid. so first, my feedback here is, it sounds like you are an educator or in an education-adjacent role, and you should focus on making more sense haha. like lay out your beefs clearly, it sounds like you have a beef with interdisciplinary work, specifically between some STEM departments and especially with humanities and STEM departments, which is subjective. you don't have to be objective about everything. you can just say, "i don't like this design thinking thing because i don't like the people involved" or whatever. but i don't know! i cannot figure out what you are saying.
it sounds like your point is: "some ways of solving problems are superior to others." i've heard this take a million times. one perspective i'll offer to you is, math is not the only way to solve problems. it's not even the best way in many cases. not everything can be solved by defining a narrow goal, and then having a dispute about the methods, and then picking some objective method and then applying it very optimally, or whatever. this is also on you, as an educator, to understand! i could give a bajillion specific examples.
but first, you have to concede: an analogy nobody understands is bad, and you have to own that, and two, it's not really clear, what exactly is your dispute with Design Thinking? it doesn't have anything to do with user interfaces... so why the hell are you talking about it? why "Design Thinking people"? What is your beef here?
Me too don't understand the analogy between design thinking and data science. Both are too different. But even if I am a designer and teach design, I don't think there superiority here. it is how to benefit from each approach to achieve in intended goal.
As many other people on HN, I am an advocate for software engineers and I think it is important that software engineers themselves develop expertise and become owners in their particular fields of application, their processes, etc.
Attempts to undermine their role and turn developers into simple cogs in the machine rub me the wrong way.
I perceive (you might disagree) that Design Thinking, Agile, Scrum, and similar things as attempt for designers, PMs, etc. to insert themselves into the process, not as equal partners, but as people with elevated privileges over software developers.
I don't necessarily disagree with the idea and ideals of Design Thinking. I disagree with the practitioners and their perception of themselves as something special over software developer.
I also think that my original analogy at the top is perfectly understood by a lot of people here as much as I understand the type of people on HN.
having a specific negative experience can be interesting, why don't you talk about that instead? generally, having been both the "design thinker" and the thinkee, in both the formal big corporate setting you are lamenting and in a less formal research environment, my and my colleagues experiences have been unequivocally positive. nobody is thinking about things in terms of, "perception of themselves as something special over software developer." that may be a problem unrelated to "design thinking," i can see how any creative thinking exercise can test people's interpersonal relationships differently than say, telling Claude what to do.
it is normal to see people advocate their favourite tool or process. However, I always tell my design students to be critical and strategic when choosing their tools.
I believe he is trying to articulate the failings of e.g., JFK's Whiz Kids who were experts of statistical analysis and tried to use that knowledge to domains they knew little about. In a nutshell, these experts tend to deep dive on parts of the problem where data was available and ignore the parts of the problem that is not quantified. Which is usually a huge mistake.
Are you an expert? Not gatekeeping here but I have no intuition for what is easy or hard to formalise. A lot of very simply stated graph theoretical results are apparently extremely hard to formalise.
I can't speak for ndriscoll, but I am a university math professor with extensive experience teaching these sorts of topics, and I agree with their comment in full.
You are right that some (other) statements are harder to formalize than they look. The Four Color Theorem from graph theory is an example. Generally speaking, discrete math, inequalities, for all/there exists, etc. are all easy to formalize. Anything involving geometry or topology is liable to be harder. For example, the Jordan curve theorem states that "any plane simple closed curve divides the plane into two regions, the interior and the exterior". As anyone who has slogged through an intro topology book knows, statements like this take more work to make precise (and still more to prove).
When someone takes the time to explain undergrad-level concepts in a comment, responding with "are you an expert?" is a level of skepticism that's bordering on hostile. The person you're responding to is correct, it's rare that the theorem statement itself is particularly hard to formalize. Whatever you read likely refers to the difficulty of formalizing a proof.
To be fair, the comment did not explain any concept that I can see, or why this statement is simple. It gave the statement and said it was simple to formalise. It does seem simple enough to me (basic arithmetic statement with a few variables and a bunch of quantifiers) but if somebody has no expertise/intuition, I think it is a fair question, without any hostile intent assumed.
> it's rare that the theorem statement itself is particularly hard to formalize
That's very dependent on the problem area. For example there's a gap between high school explanation of central limit theorem and actual formalization of it. And when dealing with turing machines sometimes you'll say that something grows e.g. Omega(n), but what happens is that there's some subsequence of inputs for which it does. Generally for complexity theory plain-language explanations can be very vague, because of how insensitive the theory is to small changes and you need to operate on a higher level of abstraction to have a chance to explain a proof in reasonable time.
Yes, if the theorem statement itself is "hard to formalize" even given our current tools, formal foundations etc. for this task, this suggests that the underlying math itself is still half-baked in some sense, and could be improved to better capture the concepts we're interested in. Much of analysis-heavy math is in that boat at present, compared to algebra.
Lol it’s weird seeing high school redditors saying gatekeeping and are you an expert in the same thread as university professors, all talking about the same topic. But I guess that’s HN for you.
As the sibling comment says, in my experience, the difficulty of formalizing the problem varies greatly between different areas. Probability theory is another notorious field in which modelling a problem correctly can be very subtle and difficult.
On the other hand, many problems in number theory and discrete structures tend to be rather simple to formalize. If you want to take your own look at that, I'd recommend to check out the lean games[1]. I'd say after the natural numbers game, you most likely know enough lean to write that problem down in lean with the "sufficiently small" being the trickiest part.
Voters: please reconsider your ups and downs. I think the “Are you an expert” question triggered a lot of downvotes when it was in fact asked in good faith to judge the person’s perspective of easy and hard.
And I would say there is no way to ask that question in good faith. (Tedious proof by cases left as an exercise for readers.)
The correct question would have been, does anyone else agree with the statement.
In this particular case, the amount knowledge needed (of e.g. Lean language, math and Erdos problems) means any credible statement about the difficulty requires an expert.
It doesn't require an expert though. That was kind of my point. If you've taken an intro proof class (so the intro class for math majors/the topic), and if you've fiddled with Lean a bit (e.g. played some of the Natural Numbers Game another commenter linked), you'll know it's easy (source: I did math in my undergrad, and have fiddled with Lean a bit). Honestly I expect intro proof classes will start to be centered around something like Lean soonish if some aren't already incorporating it, and we'll see math majors more explicitly making the connection between program and proof.
Like if someone were incredulous that we could reasonably analyze running time and memory usage of something like merge sort and I said that's a standard example in an intro algorithms course, presumably people would be like "yeah it is".
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