#math and ai

[anja-nuehm]

I know I originally only made this account to post what I draw/paint etc. but I feel like I need to vent. This post is about AI (specifically LLMs like ChatGPT and not image generation). Currently I study for a B.sc. in math (in the summer I‘ll start on my masters) and I assist one the professors by grading homework. The course is Calculus/Analysis for computer science majors. Its basically just an entry point with some insight into applications.

The students need 50% of all available homework points to get permission to write the exam. This is important. The homework exists to practice the material. Obviously if you don‘t do the homework by yourself you won‘t learn anything. Especially in math you need to actually engage with the problems and concepts. Just visiting the lecture and going to the practice sessions isn‘t going to cut it.

We have 90 people who hand in homework every week. Of those 90 about 20 visit the lecture and the practice sessions (I know for a fact that the quality of the lecture itself is not to blame). Therefore 70 students hand in homework and skate by with only my feedback and that of my collegues. A while back we made a survey to see how many students use LLMs. Result: The majority does use LLMs.

Personally I don‘t think there is anything inherently wrong with using LLMs to help with ideas/solutions, they are a different kind of search engine. IF you question the result - IF you take steps to verify it. This should be obvious. The thing that I have a problem with, is people copying the „solution“ of the LLMs and handing it in without any changes or further consideration. I have a problem with students relying ONLY on LLMs while ignoring better tools that don‘t do ✨complicated✨ guessing. For example in calculus specifically GeoGebra, WolframAlpha or just the literature.

How do I know that students pass off AI generated solutions as their own? Easy: they are awful. Awfully similar (but not the same) and awfully wrong. The form is abysmal. They refer to things outside of the lecture. The plain calculation is false because the results are randomly generated without context. I mean it couldn‘t be clearer that its wrong. Retorical question: Since when is (-1)^n a converging sequence?

These are mistakes a human who thinks for two seconds wouldn‘t make. Especially 40 students in a row. What is the theorem of Bolzano-Weierstraß? How strange … what you and 40 other students wrote is equivalent but not the one in the skript. How can people be too lazy to literally copy from the easiest source with a gurantee that its correct?

LMMs are dangerous because their output could be true, but it could also be garbage. Nobody knows where it‘s coming from. Nobody seems to care to check.

Some mistakes are obvious, some aren‘t. I don‘t trust my own ability to identify all of them. I don‘t think anybody should.

I write this specifically to whoever is a student in school or university. Sure it saves time to let the LLM do all the work. But you go to school and to university to learn and grow. When you get to working an actual job later in life. Shouldn‘t you know what you are doing? Wouldn‘t you like it if people in other work fields knew as well?

[lumsel]

chinese room 2

So there’s this guy, right? He sits in a room by himself, with a computer and a keyboard full of Chinese characters. He doesn’t know Chinese, though, in fact he doesn’t even realise that Chinese is a language. He just thinks it’s a bunch of odd symbols. Anyway, the computer prints out a paragraph of Chinese, and he thinks, whoa, cool shapes. And then a message is displayed on the computer monitor: which character comes next?

This guy has no idea how the hell he’s meant to know that, so he just presses a random character on the keyboard. And then the computer goes BZZZT, wrong! The correct character was THIS one, and it flashes a character on the screen. And the guy thinks, augh, dammit! I hope I get it right next time. And sure enough, computer prints out another paragraph of Chinese, and then it asks the guy, what comes next?

He guesses again, and he gets it wrong again, and he goes augh again, and this carries on for a while. But eventually, he presses the button and it goes DING! You got it right this time! And he is so happy, you have no idea. This is the best day of his life. He is going to do everything in his power to make that machine go DING again. So he starts paying attention. He looks at the paragraph of Chinese printed out by the machine, and cross-compares it against all the other paragraphs he’s gotten. And, recall, this guy doesn’t even know that this is a language, it’s just a sequence of weird symbols to him. But it’s a sequence that forms patterns. He notices that if a particular symbol is displayed, then the next symbol is more likely to be this one. He notices some symbols are more common in general. Bit by bit, he starts to draw statistical inferences about the symbols, he analyses the printouts every way he can, he writes extensive notes to himself on how to recognise the patterns.

Over time, his guesses begin to get more and more accurate. He hears those lovely DING sounds that indicate his prediction was correct more and more often, and he manages to use that to condition his instincts better and better, picking up on cues consciously and subconsciously to get better and better at pressing the right button on the keyboard. Eventually, his accuracy is like 70% or something -- pretty damn good for a guy who doesn’t even know Chinese is a language.

* * *

One day, something odd happens.

He gets a printout, the machine asks what character comes next, and he presses a button on the keyboard and-- silence. No sound at all. Instead, the machine prints out the exact same sequence again, but with one small change. The character he input on the keyboard has been added to the end of the sequence.

Which character comes next?

This weirds the guy out, but he thinks, well. This is clearly a test of my prediction abilities. So I’m not going to treat this printout any differently to any other printout made by the machine -- shit, I’ll pretend that last printout I got? Never even happened. I’m just going to keep acting like this is a normal day on the job, and I’m going to predict the next symbol in this sequence as if it was one of the thousands of printouts I’ve seen before. And that’s what he does! He presses what symbol comes next, and then another printout comes out with that symbol added to the end, and then he presses what he thinks will be the next symbol in that sequence. And then, eventually, he thinks, “hm. I don’t think there’s any symbol after this one. I think this is the end of the sequence.” And so he presses the “END” button on his keyboard, and sits back, satisfied.

Unbeknownst to him, the sequence of characters he input wasn’t just some meaningless string of symbols. See, the printouts he was getting, they were all always grammatically correct Chinese. And that first printout he’d gotten that day in particular? It was a question: “How do I open a door.” The string of characters he had just input, what he had determined to be the most likely string of symbols to come next, formed a comprehensible response that read, “You turn the handle and push”.

* * *

One day you decide to visit this guy’s office. You’ve heard he’s learning Chinese, and for whatever reason you decide to test his progress. So you ask him, “Hey, which character means dog?”

He looks at you like you’ve got two heads. You may as well have asked him which of his shoes means “dog”, or which of the hairs on the back of his arm. There’s no connection in his mind at all between language and his little symbol prediction game, indeed, he thinks of it as an advanced form of mathematics rather than anything to do with linguistics. He hadn’t even conceived of the idea that what he was doing could be considered a kind of communication any more than algebra is. He says to you, “Buddy, they’re just funny symbols. No need to get all philosophical about it.”

Suddenly, another printout comes out of the machine. He stares at it, puzzles over it, but you can tell he doesn’t know what it says. You do, though. You’re fluent in the language. You can see that it says the words, “Do you actually speak Chinese, or are you just a guy in a room doing statistics and shit?”

The guy leans over to you, and says confidently, “I know it looks like a jumble of completely random characters. But it’s actually a very sophisticated mathematical sequence,” and then he presses a button on the keyboard. And another, and another, and another, and slowly but surely he composes a sequence of characters that, unbeknownst to him, reads “Yes, I know Chinese fluently! If I didn’t I would not be able to speak with you.”

That is how ChatGPT works.

[chongoblog]

It's actually magic how quickly I'll lose interest in your Youtube video when you can tell its using AI voiceover

[endlessmazin]

DELAUNAY

[apotelesmaa]

I find it incredibly funny that emu and rui are made out to be the most academically talented out of the wxs unit given that they both also need to be babysat anytime the group goes out in public. Their boundless intelligence and unending whimsy is matched only by their need to get sillay.

[szimmetria-airtemmizs]

I got these accidentally from an ai.

[snetofed]

Matty i love!!!

his fingers traced patterns on your back, his other hand cupping your cheek. mattheo couldn't stop the smile from spreading on his face or the soft red blush that was on his cheeks. he was in heaven, surrounded by you and your warmth. he sighed softly, pressing his forehead against yours, his

mattheo felt like he was on cloud nine, his heart bursting with warmth and love as he sat there with you in his arms. he kissed the top of your head, his embrace becoming more snug and secure

You are my favorite girl, my confidant, my lover, my everything. There is no one else in this world that I care about as much as you. I love you with all my heart and soul, you are my heaven, my earth and my everything.

And the funny thing is that we love each other, we hate each other, we don't like each other, we hurt each other, we lie to each other, but at the end of the day you are, you are and you will always be my home.

And at the end of the day I can assure you with my life that I love you

[why-ai]

Computers are good at math