Well, it does make the solutions less impressive, right? Because it's much easier to compute the inverse of an integral than an integral. What's impressive here is more in composing problems that have nice answers and can't be solved by computer algebra systems, then the sock puppet trick to conceal that you ha the answer all along.
Reshetnikov didn't confess to them being reverse engineered, though. He confessed to them being conjecture arrived at after working on the problem for a bit by tweaking similar integrals in symbolic math software / numerical approximations. Every post was a gamble because it could have been wrong.
Of course, that could be a lie, but he came clean about other things that make sense retrospectively.
> Every post was a gamble because it could have been wrong
Symbolic differentiation is a deterministic algorithm. There is no reason for his posts to be a gamble. I'm sure there was a lots of interesting trial and error in developing good question and answer pairs, but once he posted the question he knew what the answer was already.
As I understand, he was specifically targeting problems that symbolic math software had given up on. He was only using symbolic software to solve the similarly shaped problems first, which allowed him to be fairly confident in his conjecture, as he became quite keen on how to slip his way from the output of symbolic math software from one solvable formula to a closely related formula that broke the software.
The symbolic math software couldn't perform the integration problems he posted. Integration lacks a deterministic algorithm and therefore permits constructing challenges for stack overflow and computer algebra systems. However, there is a deterministic algorithm to go the other way.
In other words, he was posting challenges to go from X -> Y (hard). However, going from Y -> X is easy. Therefore, since he had both X and Y before posting, he could verify the solutions perfectly well. The reason why constructing (X, Y) together is easier than going from Y->X is because you can always tweak Y a bit and then work backwards to see what X falls out.
There was certainly creativity in finding (X, Y) pairs where the symbolic software couldn't go from X -> Y. However, again this is more about trial and error iteration than producing brilliant insights from scratch, which is what it appeared Cleo was doing on Stack Overflow. Again, this is just a consequence of X -> Y being hard but Y -> X being easy. It was a wonderful parlor trick that took a good deal of effort to set up.
(It looks like OP's most recent post was deleted, but I spent some time writing this up so I'll post it anyway. The deleted post contended that Cleo never confessed to "cheating" by differentiating and then reversing the direction.)
I think you are misunderstanding something that is just implicit in the story. IE he doesn't need to "confess" this, it's a fundamental part of how the trick works.
I'll take one more stab at explaining what's going on. (Out of curiosity, are you familiar with calculus? I don't want to assume that you're not, but your comment reads as if you're not very familiar with it, so I'm going to explain things a bit better this time.)
Let's start with how the beautiful parlor trick looked to everyone else.
Random user: Asks how to integrate ABC expression.
(This is difficult, because integrate(ABC) has no general algorithm. It often requires many subtle tricks to perform a given integration, and there is no guarantee that there even is an elementary answer for integrate(ABC)).
Cleo: Answers integrate(ABC) = XYZ, with no notes.
(Wow! This obviously must have required many subtle tricks, but they are not provided!)
Importantly, anyone can verify that Cleo is right, because it turns out that UndoIntegration(XYZ) => ABC is easy, and there is a deterministic algorithm to do it. So, we all can tell that Cleo's answer is correct. But how could she have done this, since the integration direction is difficult???
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How the parlor trick really works.
First, as you can see, if Cleo takes any random XYZ, she can easily run UndoIntegration(XYZ) => ABC, and now she knows for free that Integrate(ABC) => XYZ. The neat thing is that doing this doesn't require figuring out any of the subtle steps required to run the Integrate operation either, which is convenient since Cleo doesn't plan to post them anyway.
So then, how does Cleo find a good ABC and XYZ without being a genius who is smarter than a computer? The most important thing is to find a pair such that ComputerAlgebraSystem_Integrate(ABC) doesn't work. Since integration is generally done by a bag of tricks, there are always holes you can find. So, you can basically just do this:
1. Start with a candidate XYZ_1.
2. Run UndoIntegration(XYZ_1) => ABC_1. (Remember, this is easy.)
3. Check if ComputerAlgebraSystem_Integrate(ABC_1) works. (Also easy to check, although the computer program has to work hard.)
4. If the computer is stumped, good. We can make a StackOverflow post.
5. Otherwise, try a different XYZ_2 and go back to step 1.
This is still an interesting game, but at no point does Cleo need to come up with a crazy bag of integration tricks here, the way that everyone assumes she did when she runs the parlor trick in the forum. This is the whole point of the trick, and the reason she hid her identity.
Apologies, I had figured out what distinction you were getting at right after writing my reply, so didn't feel the need to keep my misunderstanding up. But thanks for the detailed explanation!
Edit: Actually, I'm confused again. To be clear, it sounded to me from the discussion in the Joe McCann video that there was no tweaking the answer to get the question, i.e. that doing anything other than verification in reverse would have been against their ethic, that the answer must truly follow the question for it not to be cheating. The integral is fixed in place, and then legitimately solved by a highly competent Reshetnikov who is good at this, afforded plenty of time by scheming in advanced (as opposed to the illusion of only taking 3 hours), but is too lazy to formalize their work or is interested to see a 'clean' solution unbiased by their own approach to the problem or by the software that aided their work. And then it's verified trivially using differentiation (something symbolic math software almost never fails at), as opposed to my original misunderstanding that there still would have been uncertainty. Right?
No, although he was certainly an integral enthusiast, the video does not claim that he was solving them from scratch. Rather, it says he was starting from integrals with known answers and tweaking them slightly to see if he could break the CAS. At that point, although he did apparently try to solve the resulting problems himself, he already knew roughly what the answer would look like (by comparing to the previous answer, and also to the previous solution path.)
Specifically step 5 in my previous post is more work than it sounds, he was doing some calculations by hand, but it's like he's starting 90% of the way there and trying to do the last 10% by hand to fool the CAS. And remember, he can try as many variants of the tweak+10% as he wants until he finds something that works.
I guess I'm over-selling by implying it's a solution from scratch. Thanks to the nearby integrals that the software is able to serve up results for instantly, the tool is what lets you quickly explore until you run into something that will support a slight modification, as well as still be beautiful even after the modification. And of course, selection of the interesting questions is perfectly permissible in the ethic they were going for. Thinking about it like this, I could probably do the trick myself... time to refresh on my rusty calculus.
Yeah! It sounds like a pretty interesting and rewarding design process, but very much searching for a variant of a known problem that works, as opposed to somehow finding a crazy expression from nowhere that also happens to have a beautiful, simple integral, and then solving it without help although even the computers can't.
That is frankly, obvious horseshit. It couldn’t possibly be a gamble because you can just trivially differentiate the answer and see if it came out to be the expression in the question.
This is a definite integral. The specific endpoints might allow substantial simplifications that obscure the anti-derivative in question.
This is similar to the way that $\int_{-\infty}^\infty exp(-x^2) dx = \sqrt \pi$. The answer is a constant that doesn't give you any information about the function erf(x).
Remember he was producing the anti derivative/integral and already had the original expression. So all he needed to do is show that when you differentiate the integral answer you get the original question. That’s a lot easier than you’re making out.
You’re right, it just sucks. I don’t care how much AI anyone uses. It’s not that it’s “AI” slop, it’s slop. In this day and age we are almost certain AI was involved, but it has little to do with the criticism. It’s just a few short years ago we assume this kind of crap wouldn’t make it to the front page on the regular.
And the criticism isn’t even that it is off… things that are off can have artistic or entertainment value. This doesn’t. It’s just screams laziness.
"Some day, your immune system may decide to attack your pancreas."
Immune attack of the pancreas is usually a disease of youth. Type 2 diabetes which is overwhelmingly the diabetes associated with aging is not an autoimmune disease.
I don’t know how adult 22 is considered but yeah. A younger sibling got it when they were ~13.
When we noticed the signs and went into the ER a few of the (younger) doctors thought it was Type 2, while the attending knew it was just late onset Type 1.
You might want to check out the low vitamin a crowd. Some weirdos in there, but we all do very well. Seems to help with many autoimmune disorders (for me: allergies and nightly urination almost gone).
Jfc, no. I'll stick with my rheumatologist. Getting health advice from people online, much less X, is one of the core problems of modern society. People need to get a grip.
MODY is something else entirely (a genetic mutation driven disease with distinct pathophysiology from Type 1). What’s being discussed here is LADA (late autoimmune diabetes in adults).
LADA itself isn’t that rare but it is a small minority of all cases of diabetes in older adults.
Same. At first he was happy as he lost a load of weight, then it kept happening and he nearly died in the office. Just collapsed one day. Insulin is an amazing invention. My dog, a little pug, gets porcine insulin after prednisone saved her life but gave her type 1.
> so maybe I lower the temperature setting to try and extend the life of the contents.
Bullshit. The ideal refrigerator temperature is already close enough to freezing that any small adjustment you could make is unlikely to do any good. If this was actually a good idea then by your logic (similar to odd love for printer manufacturers) the all wise manufacturers would have already incorporated this into their “smart” fridges.
Because it has a different ink formulation that’s designed for mono-colored printing.
Let’s make another analogy: two wheels fall off my car. You tell me “hey, motorcycles exist, you can still use that car!!”
But my car isn’t a motorcycle, it’s a car.
If you buy a printer that requires two cartridges to function then you keep both cartridges filled to keep it functioning.
I’ve always felt like this whole discussion has mostly surrounded people who are penny pinching to an extreme level that doesn’t make sense. You didn’t run out of color ink because you never printed in color. And if you never printed in color you wouldn’t have bought a color printer. You’ve gotta refill your color ink eventually.
This is the same thing as people who add water to their liquid hand soap to try and make it last longer. It just makes the soap gross and saves 10 cents at best.
The reason to buy a colour inkjet printer is that it's the cheapest thing you can get your hands on. Usually because the various education systems throughout the world somehow fail to centrally handle printing of course material. Either that, or you're one of the couple of dozen people who prints photos, and additionally in the subset that hasn't also decided to pay for someone else to deal with the cursed product category.
After a quick check I found the "HP Deskjet Plus 4130" new for 350 NOK (so about 37 USD, which includes 25% VAT and a 2 or 5 (probably 5) year warranty mandated of the vendor). Seems similar to the others that come up when sorting by price on one of the local price comparison sites. So 70 USD would for most people appear to be about twice as much money up front for something that needs to produce the bare minimum and otherwise be easy to dust.
Is there some kind of information asymmetry at play where in 2026 customers can’t comprehend a more expensive printer being a lower cost in the long run?
And here we are talking about a difference in cost of roughly $35 or the price of a meal for 2 at Chipotle.
Would you say that it’s unfair that the Toyota Prius costs more to purchase than a Nissan Sentra but the Prius costs less to operate due to having much better fuel efficiency?
Are consumers somehow unable to understand why they might choose invest more up front?
There’s no value to this post honestly.
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