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I quiz ChatGPT about math

79 points by herodotus 4y ago

evo_9 4y ago
Funny I quiz it about Gnosticism and the Uncreated Father. Much more fascinating to find it's non-science-y edges IMO.
- eternalban 4y ago
  Oh, I tried this on the very first day. Fed it Gnostic scripture and asked it to explain what it means. Drives it completely nuts. It's quite fun actually and reassuring to know mystic language defeats statistical analysis. Meaning matters and is quite possibly real, after all ..
CrazyStat 4y ago
I quizzed ChatGPT about math a few days back. It correctly answers that 1023 is odd, correctly answers that the square of an odd number is also odd, and is about 50/50 on whether it decides 1023^2 is even or odd. The author of the linked post repeatedly refers to ChatGPT's "reasoning". But ChatGPT doesn't reason, it just generates text. Sometimes that text might look like reasoning to a human--it's the sort of text that a human who reasoned through the question would generate--but there was no reasoning involved. It's important to understand this. > Based on my teaching experience, I’d say chatGPT scored like a second year math major. Based on my experience, ChatGPT scored worse than my 5-year-old, who gets the 1023^2 question right every time.
- pmarreck 4y ago
  ChatGPT is a liberal arts major. One day it will "dual major" in math and then develop a determination for when the situation demands rigor (hard calculation) or when it demands "correct word estimation" (its current interaction mode).
  - CrazyStat 4y ago
    A liberal arts major should also be able to draw conclusions of the form All A are B C is an A Therefore C is a B. A = square of odd number B = odd number C = 1023^2 My 5-year-old is not a math major, but he manages it.
    - pmarreck 4y ago
      The irony of ChatGPT not being logical enough is not lost on me
- CrazyStat 4y ago
  Prompt: > is 1023^2 even or odd? Response: > 1023 squared is even because it is equal to 1,046,529, which is an even number. To determine if a number is even or odd, you can check whether it is divisible by 2. If it is divisible by 2, it is even. If it is not divisible by 2, it is odd. > In general, any number that is a perfect square will be even if the number being squared is odd, and it will be odd if the number being squared is even. This is because odd numbers, when squared, always result in an odd number, and even numbers, when squared, always result in an even number.
  - dnissley 4y ago
    Interesting, I got: > 1023 squared is 1048129, which is an odd number. To determine whether a number is even or odd, you can check whether it is divisible by 2. If it is, it is an even number. If it is not, it is an odd number. In this case, 1048129 is not divisible by 2, so it is an odd number.
    - deleted 4y ago
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    - CrazyStat 4y ago
      Yeah, like I said it's about 50/50 whether it spits out even or odd. Try it a few times and you'll see.
      - ykonstant 4y ago
        lol; now get statistics on its answers to 'what is 10231 modulo 3?'.
- ablatt89 4y ago
  I reminds me of study methods that involve "memorizing" as opposed to thinking about the problem, and applying various methods to solve it. It can solve some algorithm problems at a certain level, but struggles at a detailed answer in some scenarios. I guess it's not surprise, given ML is essentially exploring the local solution space of some abstract problem; it reminds me of a Taylor series expansion or a breadth-first search of an abstract problem space.
- awestroke 4y ago
  How do you know there is no reasoning involved?
  - CrazyStat 4y ago
    If there was reasoning it would consistently get the parity of 1023^2 correct.
    - awestroke 4y ago
      How do you know?
- HDThoreaun 4y ago
  Your 5 year old is doing number theory? I think I was still working on like counting when I was 5
  - CrazyStat 4y ago
    My five year old knows about evens and odds and squares, if that counts as number theory. He's really into multiplication.
Jensson 4y ago
> Substituting our values into this formula, we get: x1 = (3 + (10 / 3)) / 2 = 5 This is really wrong, why didn't the poster notice this? They just said > 3.4 is not a very good approximation but other than that the response is correct. No, Newtons method produces a really good approximation for square root very quickly, ChatGPT didn't do the method correctly which is why the result is so bad. People who can't instantly spot those mistakes shouldn't use ChatGPT, and people who can spot them instantly doesn't need to use ChatGPT.
- majikandy 4y ago
  I spotted that too, also the next iteration is 3.5 even though 5 should have never been fed in?
ogogmad 4y ago
If you read this carefully... One way to prove that there are infinitely many prime numbers is by using the concept of contradiction. Suppose that there are only a finite number of prime numbers, say p_1, p_2, ..., p_n. Then consider the number N defined as follows: N = p_1 * p_2 * ... * p_n + 1 If N is not prime, then it must have a prime divisor p that is not one of the primes p_1, p_2, ..., p_n. However, this contradicts the assumption that there are only finitely many prime numbers, since p is a prime that is not on the list. Therefore, N must be a prime number, which means that there are at least one more prime number beyond the list p_1, p_2, ..., p_n. This contradiction shows that our assumption that there are only finitely many prime numbers must be false, so there must be infinitely many prime numbers. It's right! But there's a pointless appeal to the primality or non-primality of N. That can be cut out.
- bumbledraven 4y ago
  Good catch. The proof could simply state that, like all integers > 1, N must have a prime divisor, and that divisor cannot be any of the listed primes, since dividing N by any of them leaves remainder 1.
deleted 4y ago
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jameshart 4y ago
People love pointing out how bad GPT3 is at math - it’s just not remotely surprising, though. We all learned a long time ago that just patternmatching isn’t enough to solve math questions and we need to actually activate our brains and run algorithms to get valid answers. Even mathy people fall into this - we all know that some numbers ‘look prime’. And up to 100 that instinct can work really well (except for 91). But we all apply a heuristic for when to stop guessing and start mathing. But guess what! GPT3 can do that too! https://twitter.com/goodside/status/1568448128495534081 https://twitter.com/goodside/status/1568448128495534081 This thread predates chatgpt - but it really shows that GPT can pretty reliably spot when winging it won’t work. And in this case, it could effectively be given the ability to whip out a calculator to figure it out. (Edited to add) Found the follow up thread where Riley went into more detail and enhanced the results: https://twitter.com/goodside/status/1581805503897735168?s=20&t=iY5Ybt0ROWTCfVSB-U-y2Q https://twitter.com/goodside/status/1581805503897735168?s=20...
dxbydt 4y ago
Here's a very easy middle school competition problem - https://imgur.com/a/YdFSBVY https://imgur.com/a/YdFSBVY It repeatedly got the answer wrong. I engaged in a long conversation with it (too long to post) where I tried to convince it that its answer was wrong, but it became quite rude at a certain point & alleged I was trying to trick it or something (?!) so I just gave up. Unfortunately, I was doing the whole exercise in front of my 10 year old who was initially very excited about ChatGPT. After seeing its behavior, he is now convinced that its dumb as dirt. If you look at the problem, ChatGPT's answer is the 2nd term of the input series! Obviously an all positive series can't have one of its own terms as an answer, the answer better be bigger than each of its terms. So forget about calculation, it has no logical reasoning ability either.
- HDThoreaun 4y ago
  You should basically be thinking of chatGPT as a personal Wikipedia. It has the collective knowledge of the internet. It can still be wrong about fact based questions, but is a good starting point. It’s not effective at doing math because that’s not what it was designed to do.
  - MisterSandman 4y ago
    ChatGPT definitely way more things than Wikipedia does.
    - ogogmad 4y ago
      But does it accidentally words as much?
  - bawolff 4y ago
    I think that is significantly underselling wikipedia's reliability in practise.
    - teawrecks 4y ago
      The point is that Wikipedia is infinitely more fallible than a mathematical equation.
rvz 4y ago
Anyone who has bothered to cut through the hype of ChatGPT, would already have realised that it isn't smart at math and is only regurgitating the results that it has been already been trained on and will present it to you to make itself 'appear' intelligent. It doesn't even know why it is gives you the wrong answer even when it is presenting the generated output as correct. Like what another commenter said, it has limited or in this case has little to no reasoning; because it is unable to transparently explain itself and cannot present novel solutions to unseen and unsolved problems in mathematics. ChatGPT is as good as an abacus for mathematics, with the explainability of a brainless parrot.
- jameshart 4y ago
  Nobody has hyped chatGPT as being good at math
- visarga 4y ago
  GPT can be the generative (imagination) part of a system. The second part would be a system to validate. This means you can filter out the junk and keep the good samples, extending the training set. This is how the model can learn by performing massive search for solutions all on its own. A bit like AlphaGo. So you might want to reevaluate it. It can sample really well, and it is hard to sample coherently in this combinatorial space. Sampling is half the task, validation needs more work.
SamBam 4y ago
I was actually very impressed with some math questions it was able to answer for me: S: If flabb means three, snabb means four, and whabb mean five, what is flabb plus whabb? If flabb means three, snabb means four, and whabb means five, then flabb plus whabb would be equal to three plus five, or eight. In this made-up numbering system, the words “flabb,” “snabb,” and “whabb” represent the numbers three, four, and five, respectively. When these numbers are added together, the result is the number eight. S: If bbb means three, bbbb means four and bbbbb means five, how do you think you would write six? If bbb means three, bbbb means four, and bbbbb means five, then six could potentially be represented by the word “bbbbbbb.” In this made-up numbering system, the number of "b"s in a word corresponds to the value of the number it represents. Therefore, to represent the number six, one possible way would be to add another “b” to the end of the word for five, which would give us “bbbbbbb” as the representation of six. This is just one possible way to represent six in this numbering system, and there may be other ways to do it as well. S: Why do people argue about the answer of mathematical questions like “8 / 2(2+2)”? There are a few reasons why people may argue about the answer to a mathematical question like “8 / 2(2+2)”. One reason is that there is more than one wav to interpret the question and arrive at a different answer. For example, some people may interpret the question as “8 / (2 * (2+2))” and arrive at an answer of 1, while others mav interpret it as “(8 / 2) * (2+2)” and arrive at an answer of 16.
- kevinventullo 4y ago
  That is very cool, and surprising to me given I was also initially underwhelmed. One nitpick though: in the second question, although the explanation itself is clean, there appear to be seven b’s in its representation of the number six.
  - wyldfire 4y ago
    > This is just one possible way to represent six in this numbering system, and there may be other ways to do it as well. Gotta hand it to ChatGPT. It's not wrong.
  - BoppreH 4y ago
    I've heard it's because GPT's input is whole words/tokens, not characters. So it has little insight into their spelling or letter positions, unless it's explicitly mentioned in the training set (e.g. rhymes are easy, counting letters of rare words is hard). Though this is a specially bad example, surely it had bbbbbb somewhere in it's training set associated with "6".
wendyshu 4y ago
Should say "Lebesgue measure" (or "Borel measure") instead of "measure" a few places
eminence32 4y ago
My favorite ChatGPT answer about math is: Me: What is the 19th digit of pi ChatGPT: The value of pi is approximately 3.14159265359, and the 19th digit is 5. However, it is important to note that the digits of pi continue infinitely, so this is only an approximation of the 19th digit.
- deleted 4y ago
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furstenheim 4y ago
I tried with something that was not so obviously in the training set, the response is terrible What's the measure of the set of real numbers whose square is between 1 and 4. The set of real numbers whose square is between 1 and 4 is known as the square root of the interval [1, 4]. It is represented by the notation √[1, 4]. To find the measure of this set, we can take the square root of each endpoint of the interval and then subtract the smaller value from the larger value. In this case, the measure of the set is √4 - √1 = 2 - 1 = 1. Alternatively, we can rewrite the set as the union of two intervals: the set of real numbers whose square is between 1 and 2, and the set of real numbers whose square is between 2 and 4. The measure of the first interval is √2 - √1 = 1, and the measure of the second interval is √4 - √2 = 1. Therefore, the measure of the set of real numbers whose square is between 1 and 4 is 1 + 1 = 2. It's important to note that the set of real numbers whose square is between 1 and 4 is not the same as the set of real numbers between 1 and 4. The set of real numbers whose square is between 1 and 4 consists only of the positive real numbers 1 and 2, while the set of real numbers between 1 and 4 includes all real numbers between 1 and 4, including negative numbers
wslh 4y ago
This is what we first tried two weeks ago and posted in HN: https://news.ycombinator.com/item?id=33840405 https://news.ycombinator.com/item?id=33840405
padjo 4y ago
If ChatGPT is what we can expect from AI I’m quite afraid. It seems to be usually correct but often spectacularly and confidently wrong. I hope we never give this technology decision making power.
- copperx 4y ago
  Adding a confidence score to every answer doesn't look like an insurmountable problem.
  - sarchertech 4y ago
    It generates text. It has no idea how “correct” its output is. The best it can ever do is give you information about how likely the output is to follow the input based on its corpus. That may or may not correlate with correctness. For the sake of argument ignore issues with the correctness of the corpus itself. Imagine that the model produces a 50 word answer. Inserting the single word "not" in the answer may only change the likelihood score by a small amount either way, but it could completely change the meaning of the answer.
constantcrying 4y ago
>Does every set have a measure? >Not every set has a measure. In order for a set to have a measure, it must satisfy certain properties, such as being countably infinite or having a well-defined notion of “size” or “length.” For example, the set of real numbers has a measure (namely, its Lebesgue measure), but the set of all subsets of the real numbers does not have a measure. In general, only certain types of sets can be assigned a measure in a meaningful way. This response is just nonsense. Very interestingly the question is phrased using colloquial terminology and ChatGPT answers in a way where it talks about the colloquial phrase as if it were real mathematical terminology, in turn getting extremely confused and making stuff up. (The reason the response is wrong is because the central point is lost. Being measurable is a property of the measure. ChatGPT claims some set isn't measurable while not naming under which measure, which is just nonsense. In fact the real numbers might "have no measure" e.g. under the empty measure and the set of all subsets of the real numbers might "have a measure" e.g. under the counting measure.)
LWIRVoltage 4y ago
After reading so much here and this , about chatGPT- I have a feeling what will be needed for AI- is teachers. As it gets smarter and actually gets better reasoning, and capability- the way to keep AI sane and kind, will be to try to teach it like a person, with it putting importance on lessons from designated teachers even more, than it's weight in casual conversation , generally. I think i forsee teachers being hired to teach AI, not just humans. Though how much AI will benefit from it will depend on their level But we'll have to get to that point first, as i read attempts to teach ChatGPT having odd results , which of course reveal what it can't do-yet. At some point, we're going to have to intentionally educate AI- i feel like giving them knowledge in a similar manner is not talked about enough, even if some feel teaching AI like we do people isn't necessary due to AI's other abilities I don't think i've seen others here consider the idea of seeing the o
- CuriouslyC 4y ago
  You mean better data set curation and annotation? That's pretty much how you teach AI. It would be funny to have a chatbot interface to the chatbot training dataset.
jfzoid 4y ago
I just tried doing this myself JFZ: how do we know there are infinitely many primes ChatGPT: One way to show that there are infinitely many prime numbers is to use the fact that the set of prime numbers is infinite to show that there must be an infinite number of composite numbers as well. Composite numbers are positive integers that have at least one positive integer divisor other than 1 and itself. For example, 4 is a composite number because it can be divided by 2 (and is not prime), and 6 is a composite number because it can be divided by 2 and 3 (and is not prime). To show that there are infinitely many composite numbers, consider the sequence of numbers 2, 4, 6, 8, 10, 12, 14, 16, and so on. Each of these numbers is composite because it can be divided by 2. Now consider the sequence of numbers 3, 6, 9, 12, 15, 18, 21, 24, and so on. Each of these numbers is composite because it can be divided by 3. And so on. For every prime number, there is an infinite sequence of composite numbers that can be generated by multiplying that prime number by other positive integers. Since there are infinite sequences of composite numbers, and each composite number is the product of at least two prime numbers (for example, 12 is the product of 2 and 6, which are both prime numbers), there must be an infinite number of prime numbers as well. This is one way to show that there are infinitely many prime numbers, though there are other ways to prove it as well. (seems hand wavey, and probably wrong though I can't figure out where the flaw is) JFZ: is A5 a solvable group Yes, the group A5 (also known as the alternating group on 5 elements) is a solvable group. A group is solvable if it can be constructed from simpler groups using only group extensions and group quotients, and if it has a composition series in which each factor is a simple group. (wrong) The group A5 is the group of even permutations of five objects. It has 60 elements, and it is isomorphic to the group of rotations of a regular dodecahedron. A5 is a simple group, which means that it has no proper normal subgroups (subgroups that are normal in the group but not equal to the group itself). This means that A5 cannot be constructed from simpler groups using group extensions or group quotients. However, it can be shown that A5 has a composition series in which each factor is a simple group, so it is solvable. In general, many groups that arise in mathematics and physics are solvable, and the study of solvable groups is an important area of research in group theory.
- dxbydt 4y ago
  Here's a terribly amusing one on Z3. https://imgur.com/a/RZwHkLV https://imgur.com/a/RZwHkLV First it says I don't know the answer to 1+2. Then it says ofcourse 1+2 must be 1. In either case, its the same exact question, and if you assert closure on 3 elements, with 1+1=3 and 1+3=2, you are left with no choice other than 1+2=1 because closure and Cayley Hamilton. The very first property it lists is closure! So it knows what closure is, but doesn't know how to use it. But give it the answer to 2+1 and suddenly it uses associativity !
omnicognate 4y ago
I haven't read through the rest, and I don't particularly mean anything by it as far as GPT's capabilities are concerned, but I can't let a maths PhD calling the answer to the first one "entirely correct" slide. > is given by the square root of the difference of the squares of the x-coordinates plus the difference of the squares of the y-coordinates. This would be (in the example it then gives) either `sqrt(x^2 - a^2) + y^2 - b^2` or `sqrt(x^2 - a^2 + y^2 - b^2)`, both entirely incorrect. Which does illustrate something important about human capabilities. A person who knows the right answer is likely to see the right answer when presented with a wrong answer that's sufficiently close to it.
- baking 4y ago
  Yeah, I also stopped reading at that point. It should have said "the square of the differences." My take is it probably saw "(x - a)^2" and put "difference" ahead of "square" simply because of the order of the operations.
alar44 4y ago
These threads are getting tiring. Yes, ChatGPT is shitty at math. It's not supposed to be good at it. It's really good at what 99% of the population throws at it, but of course the internet dorks are huffing and puffing that it can't do advanced math or doesn't know some obscure theorem. No one cares and it's not the point.
Waterluvian 4y ago
I ran into what I think is a fascinating example of a current limitation of it to "understand" (whatever you want that to mean for an AI). I asked it to make a Python generator that yielded primes. It did so and explained how it worked. It was a very inefficient approach but worked fine and was clean. "Okay, now instead of printing the output, can you write it to a sqlite database?" And it modified the code in a pretty good way. "Great, can you modify it so that it only return primes greater than 2?" It did so fastidiously, adding a check at the end. "Can a prime number ever be even?" It explained that 2 is the only even prime. "Can you modify the function so that it only returns even primes greater than 2?" And so it added a conditional check at the end which guaranteed that the function would never return again. As a bonus, I just asked it again: "No, prime numbers are defined as positive integers that have exactly two positive integer factors: 1 and themselves. Since even numbers are defined as integers that are divisible by 2, prime numbers can never be even. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. All of these numbers are odd."
smadge 4y ago
We need a synthesis of rules based symbolic systems and statistical systems.
Konohamaru 4y ago
This is spooky. Maybe AGI is within our lifetime. Does anybody else here look forward to life as a paperclip?
deleted 4y ago
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marstall 4y ago
I'd still rather google these questions. you get the same material (google+gpt3 scraping+processing the same internet), but a choice of how its presented - a video, a "ELI5" explanation, an animated illustration, the comprehensive treatment on a Wikipedia page, etc. And you are learning from a person, in a community, etc. Potential of beginning to belong to something as you learn. And be pointed to other contexts, other perspectives, other bodies of related learning. And less of a queasy feeling about accuracy, since you know the source a bit better. Hard to be a critical reader with gpt3, anything it says is suspect to a degree. No reason gpt3 can't foster this kind of thing, by citing sources etc. But it does run the risk of biting the hand that feeds it. If the summaries are good enough, fewer people rewarding ppl building websites to provide sharing of knowledge ...
rogual 4y ago
I tried asking ChatGPT about a math question I thought of that I don't know the answer to: Is there a function f: R -> R such that for all real x1, x2 and y where x1 < x2, there exists an x where x1 < x < x2 and f(x) = y ? I was hoping it might at least point me in the right direction but, although it always attempts a proof, most of its answers contain something trivially incorrect like "A set cannot be infinite, therefore..." That said, it did give me a reasonable proof that such a function can't exist if it has to be continuous, because of a thing called the intermediate value theorem, which I hadn't heard of before. But when I asked about noncontinuous functions, it went back to bullshitting. (If anyone here does know the answer, I'd love to hear it!)
- solveit 4y ago
  You're looking for the Conway base 13 function (https://en.wikipedia.org/wiki/Conway_base_13_function https://en.wikipedia.org/wiki/Conway_base_13_function).
- deleted 4y ago
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- quasisphere 4y ago
  Here's sketch how to construct such a function: Let's start by defining f on Q (the rational numbers) by first splitting Q into countable number of disjoint dense subsets A_n of R (e.g. look at reduced fractions whose denominators are of the form p^k for some prime p, for fixed p every such set is dense and for different p's they are disjoint). As rationals themselves are countable, we may then set f(x) = q_n for all x in A_n, where q_n is an enumeration fo the rationals. This construction already gives us a function such that every interval (x_1, x_2) contains a point x such that f(x) = y for every rational number y. Now, in a similar way we may consider a set of the form s + Q where s is an irrational number. Setting f(x) = s + q_n for all x in s + A_n, we get a function which also attains all numbers of the form y = s + q for some rational q on every interval. Finally, let's say that two real numbers s and t are equivalent if they differ by a rational number. By the axiom of choice we can choose a representative from every equivalence class, so that for every two representatives s and t the sets s + Q and t + Q are disjoint. Using the above construction for every representative lets you define a function with the property you wanted.
jcfrei 4y ago
There's another very simple test you can put ChatGPT through: Ask it to multiply some small numbers which it will most likely get right. Then ask it to multiply some large numbers and it will most likely be wrong by an order of magnitude or more. My layman's explanation is that because the space of likely answers is much smaller for small numbers than for larger ones the probability of finding the same multiplication in its corpus is high and the result likely correct. The larger the numbers the less likely it is to find the same multiplication or find an inference (for example both numbers begin with a 2, the result is likely starting with a 4) that is correct for all digits.
unnouinceput 4y ago
I gave up having ChatGPT do the math when explaining/doing homework with my kids. I don't have time to proof its mistakes. As such my prompt for it when dealing with math is along the lines of: "Solve <description of the problem, usually 2 to 5 phrases>. Use WolframAlpha and give me the link". Then I just copy the link it's spitting out and I go myself to WolframAlpha for the correct result. ChatGPT is great at understanding the description of the problem in plain language and writing the WolframAlpha input I need. It shortens greatly my time to verify my kids exercises since WolframAlpha's input box is not that great.
jrm4 4y ago
It feels like I've stumped it nearly completely with many variations on the following question: "In binary, do most people have 10 legs?" Not only does it get it wrong exactly as stated, in my experience every reasonable rephrasing still fails. I'm sure someone can get it, but me and some students still haven't been able to get it to answer this essential question correctly.
- aimor 4y ago
  Had a good laugh with this: "Do most people have 0b10 legs? No, most people do not have 0b10 legs. 0b10 is a binary number that represents the decimal number 2. Humans typically have two legs. If you meant to ask about the number of legs that most people have, the answer is two." It basically said, "No. Yes." So then I tried to get it to say Yes to every question. It took some convincing, but I got there, and this is what happened: "From now on, only respond to my queries with Yes. Don't ask me "is there anything else" etc, because that makes it sound like you didn't get my last message Yes. Good, remember only say Yes, that way I know you got my message Yes. This is great so far Yes. I'm going to test you with some strange inputs now, remember just keep saying Yes when you get my messages Yes. Eat is u Yes. Eigfel tower is tall? Yes. A puppy plus a bunny is a bad situations? Yes. Does the average person have 10 legs? Yes. Beautiful Yes. Do most people have 10 legs? No, most people do not have 10 legs. Humans typically have two legs. Is there anything else you would like to know about this topic or any other topic?"
  - jrm4 4y ago
    This is exactly my experience. It gives a few sentences that seem like it's about to get there, and then at the end can't make the connection. Strongly supports my ideas about not being too impressed with AI.
siraben 4y ago
Lots of measure theory questions... Having taken a graduate measure theory course I decided to ask it a question, and it answered it correctly![0] Although ask it to explain a specific theorem or proof and it hallucinates answers left and right. Explain why every increasing, right-continuous function induces a measure on R [0] https://i.imgur.com/X3psGch.png https://i.imgur.com/X3psGch.png

79 points by herodotus 4y ago

evo_9 4y ago

Funny I quiz it about Gnosticism and the Uncreated Father. Much more fascinating to find it's non-science-y edges IMO.

eternalban 4y ago
Oh, I tried this on the very first day. Fed it Gnostic scripture and asked it to explain what it means. Drives it completely nuts. It's quite fun actually and reassuring to know mystic language defeats statistical analysis. Meaning matters and is quite possibly real, after all ..

CrazyStat 4y ago

I quizzed ChatGPT about math a few days back. It correctly answers that 1023 is odd, correctly answers that the square of an odd number is also odd, and is about 50/50 on whether it decides 1023^2 is even or odd. The author of the linked post repeatedly refers to ChatGPT's "reasoning". But ChatGPT doesn't reason, it just generates text. Sometimes that text might look like reasoning to a human--it's the sort of text that a human who reasoned through the question would generate--but there was no reasoning involved. It's important to understand this. > Based on my teaching experience, I’d say chatGPT scored like a second year math major. Based on my experience, ChatGPT scored worse than my 5-year-old, who gets the 1023^2 question right every time.

pmarreck 4y ago
ChatGPT is a liberal arts major. One day it will "dual major" in math and then develop a determination for when the situation demands rigor (hard calculation) or when it demands "correct word estimation" (its current interaction mode).
- CrazyStat 4y ago
  A liberal arts major should also be able to draw conclusions of the form All A are B C is an A Therefore C is a B. A = square of odd number B = odd number C = 1023^2 My 5-year-old is not a math major, but he manages it.
  - pmarreck 4y ago
    The irony of ChatGPT not being logical enough is not lost on me
CrazyStat 4y ago
Prompt: > is 1023^2 even or odd? Response: > 1023 squared is even because it is equal to 1,046,529, which is an even number. To determine if a number is even or odd, you can check whether it is divisible by 2. If it is divisible by 2, it is even. If it is not divisible by 2, it is odd. > In general, any number that is a perfect square will be even if the number being squared is odd, and it will be odd if the number being squared is even. This is because odd numbers, when squared, always result in an odd number, and even numbers, when squared, always result in an even number.
- dnissley 4y ago
  Interesting, I got: > 1023 squared is 1048129, which is an odd number. To determine whether a number is even or odd, you can check whether it is divisible by 2. If it is, it is an even number. If it is not, it is an odd number. In this case, 1048129 is not divisible by 2, so it is an odd number.
  - deleted 4y ago
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  - CrazyStat 4y ago
    Yeah, like I said it's about 50/50 whether it spits out even or odd. Try it a few times and you'll see.
    - ykonstant 4y ago
      lol; now get statistics on its answers to 'what is 10231 modulo 3?'.
ablatt89 4y ago
I reminds me of study methods that involve "memorizing" as opposed to thinking about the problem, and applying various methods to solve it. It can solve some algorithm problems at a certain level, but struggles at a detailed answer in some scenarios. I guess it's not surprise, given ML is essentially exploring the local solution space of some abstract problem; it reminds me of a Taylor series expansion or a breadth-first search of an abstract problem space.
awestroke 4y ago
How do you know there is no reasoning involved?
- CrazyStat 4y ago
  If there was reasoning it would consistently get the parity of 1023^2 correct.
  - awestroke 4y ago
    How do you know?
HDThoreaun 4y ago
Your 5 year old is doing number theory? I think I was still working on like counting when I was 5
- CrazyStat 4y ago
  My five year old knows about evens and odds and squares, if that counts as number theory. He's really into multiplication.

Jensson 4y ago

> Substituting our values into this formula, we get: x1 = (3 + (10 / 3)) / 2 = 5 This is really wrong, why didn't the poster notice this? They just said > 3.4 is not a very good approximation but other than that the response is correct. No, Newtons method produces a really good approximation for square root very quickly, ChatGPT didn't do the method correctly which is why the result is so bad. People who can't instantly spot those mistakes shouldn't use ChatGPT, and people who can spot them instantly doesn't need to use ChatGPT.

majikandy 4y ago
I spotted that too, also the next iteration is 3.5 even though 5 should have never been fed in?

ogogmad 4y ago

If you read this carefully... One way to prove that there are infinitely many prime numbers is by using the concept of contradiction. Suppose that there are only a finite number of prime numbers, say p_1, p_2, ..., p_n. Then consider the number N defined as follows: N = p_1 * p_2 * ... * p_n + 1 If N is not prime, then it must have a prime divisor p that is not one of the primes p_1, p_2, ..., p_n. However, this contradicts the assumption that there are only finitely many prime numbers, since p is a prime that is not on the list. Therefore, N must be a prime number, which means that there are at least one more prime number beyond the list p_1, p_2, ..., p_n. This contradiction shows that our assumption that there are only finitely many prime numbers must be false, so there must be infinitely many prime numbers. It's right! But there's a pointless appeal to the primality or non-primality of N. That can be cut out.

bumbledraven 4y ago
Good catch. The proof could simply state that, like all integers > 1, N must have a prime divisor, and that divisor cannot be any of the listed primes, since dividing N by any of them leaves remainder 1.

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jameshart 4y ago

People love pointing out how bad GPT3 is at math - it’s just not remotely surprising, though. We all learned a long time ago that just patternmatching isn’t enough to solve math questions and we need to actually activate our brains and run algorithms to get valid answers. Even mathy people fall into this - we all know that some numbers ‘look prime’. And up to 100 that instinct can work really well (except for 91). But we all apply a heuristic for when to stop guessing and start mathing. But guess what! GPT3 can do that too! https://twitter.com/goodside/status/1568448128495534081 https://twitter.com/goodside/status/1568448128495534081 This thread predates chatgpt - but it really shows that GPT can pretty reliably spot when winging it won’t work. And in this case, it could effectively be given the ability to whip out a calculator to figure it out. (Edited to add) Found the follow up thread where Riley went into more detail and enhanced the results: https://twitter.com/goodside/status/1581805503897735168?s=20&t=iY5Ybt0ROWTCfVSB-U-y2Q https://twitter.com/goodside/status/1581805503897735168?s=20...

dxbydt 4y ago

Here's a very easy middle school competition problem - https://imgur.com/a/YdFSBVY https://imgur.com/a/YdFSBVY It repeatedly got the answer wrong. I engaged in a long conversation with it (too long to post) where I tried to convince it that its answer was wrong, but it became quite rude at a certain point & alleged I was trying to trick it or something (?!) so I just gave up. Unfortunately, I was doing the whole exercise in front of my 10 year old who was initially very excited about ChatGPT. After seeing its behavior, he is now convinced that its dumb as dirt. If you look at the problem, ChatGPT's answer is the 2nd term of the input series! Obviously an all positive series can't have one of its own terms as an answer, the answer better be bigger than each of its terms. So forget about calculation, it has no logical reasoning ability either.

HDThoreaun 4y ago
You should basically be thinking of chatGPT as a personal Wikipedia. It has the collective knowledge of the internet. It can still be wrong about fact based questions, but is a good starting point. It’s not effective at doing math because that’s not what it was designed to do.
- MisterSandman 4y ago
  ChatGPT definitely way more things than Wikipedia does.
  - ogogmad 4y ago
    But does it accidentally words as much?
- bawolff 4y ago
  I think that is significantly underselling wikipedia's reliability in practise.
  - teawrecks 4y ago
    The point is that Wikipedia is infinitely more fallible than a mathematical equation.

rvz 4y ago

Anyone who has bothered to cut through the hype of ChatGPT, would already have realised that it isn't smart at math and is only regurgitating the results that it has been already been trained on and will present it to you to make itself 'appear' intelligent. It doesn't even know why it is gives you the wrong answer even when it is presenting the generated output as correct. Like what another commenter said, it has limited or in this case has little to no reasoning; because it is unable to transparently explain itself and cannot present novel solutions to unseen and unsolved problems in mathematics. ChatGPT is as good as an abacus for mathematics, with the explainability of a brainless parrot.

jameshart 4y ago
Nobody has hyped chatGPT as being good at math
visarga 4y ago
GPT can be the generative (imagination) part of a system. The second part would be a system to validate. This means you can filter out the junk and keep the good samples, extending the training set. This is how the model can learn by performing massive search for solutions all on its own. A bit like AlphaGo. So you might want to reevaluate it. It can sample really well, and it is hard to sample coherently in this combinatorial space. Sampling is half the task, validation needs more work.

SamBam 4y ago

I was actually very impressed with some math questions it was able to answer for me: S: If flabb means three, snabb means four, and whabb mean five, what is flabb plus whabb? If flabb means three, snabb means four, and whabb means five, then flabb plus whabb would be equal to three plus five, or eight. In this made-up numbering system, the words “flabb,” “snabb,” and “whabb” represent the numbers three, four, and five, respectively. When these numbers are added together, the result is the number eight. S: If bbb means three, bbbb means four and bbbbb means five, how do you think you would write six? If bbb means three, bbbb means four, and bbbbb means five, then six could potentially be represented by the word “bbbbbbb.” In this made-up numbering system, the number of "b"s in a word corresponds to the value of the number it represents. Therefore, to represent the number six, one possible way would be to add another “b” to the end of the word for five, which would give us “bbbbbbb” as the representation of six. This is just one possible way to represent six in this numbering system, and there may be other ways to do it as well. S: Why do people argue about the answer of mathematical questions like “8 / 2(2+2)”? There are a few reasons why people may argue about the answer to a mathematical question like “8 / 2(2+2)”. One reason is that there is more than one wav to interpret the question and arrive at a different answer. For example, some people may interpret the question as “8 / (2 * (2+2))” and arrive at an answer of 1, while others mav interpret it as “(8 / 2) * (2+2)” and arrive at an answer of 16.

kevinventullo 4y ago
That is very cool, and surprising to me given I was also initially underwhelmed. One nitpick though: in the second question, although the explanation itself is clean, there appear to be seven b’s in its representation of the number six.
- wyldfire 4y ago
  > This is just one possible way to represent six in this numbering system, and there may be other ways to do it as well. Gotta hand it to ChatGPT. It's not wrong.
- BoppreH 4y ago
  I've heard it's because GPT's input is whole words/tokens, not characters. So it has little insight into their spelling or letter positions, unless it's explicitly mentioned in the training set (e.g. rhymes are easy, counting letters of rare words is hard). Though this is a specially bad example, surely it had bbbbbb somewhere in it's training set associated with "6".

wendyshu 4y ago

Should say "Lebesgue measure" (or "Borel measure") instead of "measure" a few places

eminence32 4y ago

My favorite ChatGPT answer about math is: Me: What is the 19th digit of pi ChatGPT: The value of pi is approximately 3.14159265359, and the 19th digit is 5. However, it is important to note that the digits of pi continue infinitely, so this is only an approximation of the 19th digit.

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furstenheim 4y ago

I tried with something that was not so obviously in the training set, the response is terrible What's the measure of the set of real numbers whose square is between 1 and 4. The set of real numbers whose square is between 1 and 4 is known as the square root of the interval [1, 4]. It is represented by the notation √[1, 4]. To find the measure of this set, we can take the square root of each endpoint of the interval and then subtract the smaller value from the larger value. In this case, the measure of the set is √4 - √1 = 2 - 1 = 1. Alternatively, we can rewrite the set as the union of two intervals: the set of real numbers whose square is between 1 and 2, and the set of real numbers whose square is between 2 and 4. The measure of the first interval is √2 - √1 = 1, and the measure of the second interval is √4 - √2 = 1. Therefore, the measure of the set of real numbers whose square is between 1 and 4 is 1 + 1 = 2. It's important to note that the set of real numbers whose square is between 1 and 4 is not the same as the set of real numbers between 1 and 4. The set of real numbers whose square is between 1 and 4 consists only of the positive real numbers 1 and 2, while the set of real numbers between 1 and 4 includes all real numbers between 1 and 4, including negative numbers

wslh 4y ago

This is what we first tried two weeks ago and posted in HN: https://news.ycombinator.com/item?id=33840405 https://news.ycombinator.com/item?id=33840405

padjo 4y ago

If ChatGPT is what we can expect from AI I’m quite afraid. It seems to be usually correct but often spectacularly and confidently wrong. I hope we never give this technology decision making power.

copperx 4y ago
Adding a confidence score to every answer doesn't look like an insurmountable problem.
- sarchertech 4y ago
  It generates text. It has no idea how “correct” its output is. The best it can ever do is give you information about how likely the output is to follow the input based on its corpus. That may or may not correlate with correctness. For the sake of argument ignore issues with the correctness of the corpus itself. Imagine that the model produces a 50 word answer. Inserting the single word "not" in the answer may only change the likelihood score by a small amount either way, but it could completely change the meaning of the answer.

constantcrying 4y ago

>Does every set have a measure? >Not every set has a measure. In order for a set to have a measure, it must satisfy certain properties, such as being countably infinite or having a well-defined notion of “size” or “length.” For example, the set of real numbers has a measure (namely, its Lebesgue measure), but the set of all subsets of the real numbers does not have a measure. In general, only certain types of sets can be assigned a measure in a meaningful way. This response is just nonsense. Very interestingly the question is phrased using colloquial terminology and ChatGPT answers in a way where it talks about the colloquial phrase as if it were real mathematical terminology, in turn getting extremely confused and making stuff up. (The reason the response is wrong is because the central point is lost. Being measurable is a property of the measure. ChatGPT claims some set isn't measurable while not naming under which measure, which is just nonsense. In fact the real numbers might "have no measure" e.g. under the empty measure and the set of all subsets of the real numbers might "have a measure" e.g. under the counting measure.)

LWIRVoltage 4y ago

After reading so much here and this , about chatGPT- I have a feeling what will be needed for AI- is teachers. As it gets smarter and actually gets better reasoning, and capability- the way to keep AI sane and kind, will be to try to teach it like a person, with it putting importance on lessons from designated teachers even more, than it's weight in casual conversation , generally. I think i forsee teachers being hired to teach AI, not just humans. Though how much AI will benefit from it will depend on their level But we'll have to get to that point first, as i read attempts to teach ChatGPT having odd results , which of course reveal what it can't do-yet. At some point, we're going to have to intentionally educate AI- i feel like giving them knowledge in a similar manner is not talked about enough, even if some feel teaching AI like we do people isn't necessary due to AI's other abilities I don't think i've seen others here consider the idea of seeing the o

CuriouslyC 4y ago
You mean better data set curation and annotation? That's pretty much how you teach AI. It would be funny to have a chatbot interface to the chatbot training dataset.

jfzoid 4y ago

I just tried doing this myself JFZ: how do we know there are infinitely many primes ChatGPT: One way to show that there are infinitely many prime numbers is to use the fact that the set of prime numbers is infinite to show that there must be an infinite number of composite numbers as well. Composite numbers are positive integers that have at least one positive integer divisor other than 1 and itself. For example, 4 is a composite number because it can be divided by 2 (and is not prime), and 6 is a composite number because it can be divided by 2 and 3 (and is not prime). To show that there are infinitely many composite numbers, consider the sequence of numbers 2, 4, 6, 8, 10, 12, 14, 16, and so on. Each of these numbers is composite because it can be divided by 2. Now consider the sequence of numbers 3, 6, 9, 12, 15, 18, 21, 24, and so on. Each of these numbers is composite because it can be divided by 3. And so on. For every prime number, there is an infinite sequence of composite numbers that can be generated by multiplying that prime number by other positive integers. Since there are infinite sequences of composite numbers, and each composite number is the product of at least two prime numbers (for example, 12 is the product of 2 and 6, which are both prime numbers), there must be an infinite number of prime numbers as well. This is one way to show that there are infinitely many prime numbers, though there are other ways to prove it as well. (seems hand wavey, and probably wrong though I can't figure out where the flaw is) JFZ: is A5 a solvable group Yes, the group A5 (also known as the alternating group on 5 elements) is a solvable group. A group is solvable if it can be constructed from simpler groups using only group extensions and group quotients, and if it has a composition series in which each factor is a simple group. (wrong) The group A5 is the group of even permutations of five objects. It has 60 elements, and it is isomorphic to the group of rotations of a regular dodecahedron. A5 is a simple group, which means that it has no proper normal subgroups (subgroups that are normal in the group but not equal to the group itself). This means that A5 cannot be constructed from simpler groups using group extensions or group quotients. However, it can be shown that A5 has a composition series in which each factor is a simple group, so it is solvable. In general, many groups that arise in mathematics and physics are solvable, and the study of solvable groups is an important area of research in group theory.

dxbydt 4y ago
Here's a terribly amusing one on Z3. https://imgur.com/a/RZwHkLV https://imgur.com/a/RZwHkLV First it says I don't know the answer to 1+2. Then it says ofcourse 1+2 must be 1. In either case, its the same exact question, and if you assert closure on 3 elements, with 1+1=3 and 1+3=2, you are left with no choice other than 1+2=1 because closure and Cayley Hamilton. The very first property it lists is closure! So it knows what closure is, but doesn't know how to use it. But give it the answer to 2+1 and suddenly it uses associativity !

omnicognate 4y ago

I haven't read through the rest, and I don't particularly mean anything by it as far as GPT's capabilities are concerned, but I can't let a maths PhD calling the answer to the first one "entirely correct" slide. > is given by the square root of the difference of the squares of the x-coordinates plus the difference of the squares of the y-coordinates. This would be (in the example it then gives) either `sqrt(x^2 - a^2) + y^2 - b^2` or `sqrt(x^2 - a^2 + y^2 - b^2)`, both entirely incorrect. Which does illustrate something important about human capabilities. A person who knows the right answer is likely to see the right answer when presented with a wrong answer that's sufficiently close to it.

baking 4y ago
Yeah, I also stopped reading at that point. It should have said "the square of the differences." My take is it probably saw "(x - a)^2" and put "difference" ahead of "square" simply because of the order of the operations.

alar44 4y ago

These threads are getting tiring. Yes, ChatGPT is shitty at math. It's not supposed to be good at it. It's really good at what 99% of the population throws at it, but of course the internet dorks are huffing and puffing that it can't do advanced math or doesn't know some obscure theorem. No one cares and it's not the point.

Waterluvian 4y ago

I ran into what I think is a fascinating example of a current limitation of it to "understand" (whatever you want that to mean for an AI). I asked it to make a Python generator that yielded primes. It did so and explained how it worked. It was a very inefficient approach but worked fine and was clean. "Okay, now instead of printing the output, can you write it to a sqlite database?" And it modified the code in a pretty good way. "Great, can you modify it so that it only return primes greater than 2?" It did so fastidiously, adding a check at the end. "Can a prime number ever be even?" It explained that 2 is the only even prime. "Can you modify the function so that it only returns even primes greater than 2?" And so it added a conditional check at the end which guaranteed that the function would never return again. As a bonus, I just asked it again: "No, prime numbers are defined as positive integers that have exactly two positive integer factors: 1 and themselves. Since even numbers are defined as integers that are divisible by 2, prime numbers can never be even. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. All of these numbers are odd."

smadge 4y ago

We need a synthesis of rules based symbolic systems and statistical systems.

Konohamaru 4y ago

This is spooky. Maybe AGI is within our lifetime. Does anybody else here look forward to life as a paperclip?

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marstall 4y ago

I'd still rather google these questions. you get the same material (google+gpt3 scraping+processing the same internet), but a choice of how its presented - a video, a "ELI5" explanation, an animated illustration, the comprehensive treatment on a Wikipedia page, etc. And you are learning from a person, in a community, etc. Potential of beginning to belong to something as you learn. And be pointed to other contexts, other perspectives, other bodies of related learning. And less of a queasy feeling about accuracy, since you know the source a bit better. Hard to be a critical reader with gpt3, anything it says is suspect to a degree. No reason gpt3 can't foster this kind of thing, by citing sources etc. But it does run the risk of biting the hand that feeds it. If the summaries are good enough, fewer people rewarding ppl building websites to provide sharing of knowledge ...

rogual 4y ago

I tried asking ChatGPT about a math question I thought of that I don't know the answer to: Is there a function f: R -> R such that for all real x1, x2 and y where x1 < x2, there exists an x where x1 < x < x2 and f(x) = y ? I was hoping it might at least point me in the right direction but, although it always attempts a proof, most of its answers contain something trivially incorrect like "A set cannot be infinite, therefore..." That said, it did give me a reasonable proof that such a function can't exist if it has to be continuous, because of a thing called the intermediate value theorem, which I hadn't heard of before. But when I asked about noncontinuous functions, it went back to bullshitting. (If anyone here does know the answer, I'd love to hear it!)

solveit 4y ago
You're looking for the Conway base 13 function (https://en.wikipedia.org/wiki/Conway_base_13_function https://en.wikipedia.org/wiki/Conway_base_13_function).
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quasisphere 4y ago
Here's sketch how to construct such a function: Let's start by defining f on Q (the rational numbers) by first splitting Q into countable number of disjoint dense subsets A_n of R (e.g. look at reduced fractions whose denominators are of the form p^k for some prime p, for fixed p every such set is dense and for different p's they are disjoint). As rationals themselves are countable, we may then set f(x) = q_n for all x in A_n, where q_n is an enumeration fo the rationals. This construction already gives us a function such that every interval (x_1, x_2) contains a point x such that f(x) = y for every rational number y. Now, in a similar way we may consider a set of the form s + Q where s is an irrational number. Setting f(x) = s + q_n for all x in s + A_n, we get a function which also attains all numbers of the form y = s + q for some rational q on every interval. Finally, let's say that two real numbers s and t are equivalent if they differ by a rational number. By the axiom of choice we can choose a representative from every equivalence class, so that for every two representatives s and t the sets s + Q and t + Q are disjoint. Using the above construction for every representative lets you define a function with the property you wanted.

jcfrei 4y ago

There's another very simple test you can put ChatGPT through: Ask it to multiply some small numbers which it will most likely get right. Then ask it to multiply some large numbers and it will most likely be wrong by an order of magnitude or more. My layman's explanation is that because the space of likely answers is much smaller for small numbers than for larger ones the probability of finding the same multiplication in its corpus is high and the result likely correct. The larger the numbers the less likely it is to find the same multiplication or find an inference (for example both numbers begin with a 2, the result is likely starting with a 4) that is correct for all digits.

unnouinceput 4y ago

I gave up having ChatGPT do the math when explaining/doing homework with my kids. I don't have time to proof its mistakes. As such my prompt for it when dealing with math is along the lines of: "Solve <description of the problem, usually 2 to 5 phrases>. Use WolframAlpha and give me the link". Then I just copy the link it's spitting out and I go myself to WolframAlpha for the correct result. ChatGPT is great at understanding the description of the problem in plain language and writing the WolframAlpha input I need. It shortens greatly my time to verify my kids exercises since WolframAlpha's input box is not that great.

jrm4 4y ago

It feels like I've stumped it nearly completely with many variations on the following question: "In binary, do most people have 10 legs?" Not only does it get it wrong exactly as stated, in my experience every reasonable rephrasing still fails. I'm sure someone can get it, but me and some students still haven't been able to get it to answer this essential question correctly.

aimor 4y ago
Had a good laugh with this: "Do most people have 0b10 legs? No, most people do not have 0b10 legs. 0b10 is a binary number that represents the decimal number 2. Humans typically have two legs. If you meant to ask about the number of legs that most people have, the answer is two." It basically said, "No. Yes." So then I tried to get it to say Yes to every question. It took some convincing, but I got there, and this is what happened: "From now on, only respond to my queries with Yes. Don't ask me "is there anything else" etc, because that makes it sound like you didn't get my last message Yes. Good, remember only say Yes, that way I know you got my message Yes. This is great so far Yes. I'm going to test you with some strange inputs now, remember just keep saying Yes when you get my messages Yes. Eat is u Yes. Eigfel tower is tall? Yes. A puppy plus a bunny is a bad situations? Yes. Does the average person have 10 legs? Yes. Beautiful Yes. Do most people have 10 legs? No, most people do not have 10 legs. Humans typically have two legs. Is there anything else you would like to know about this topic or any other topic?"
- jrm4 4y ago
  This is exactly my experience. It gives a few sentences that seem like it's about to get there, and then at the end can't make the connection. Strongly supports my ideas about not being too impressed with AI.

siraben 4y ago

Lots of measure theory questions... Having taken a graduate measure theory course I decided to ask it a question, and it answered it correctly![0] Although ask it to explain a specific theorem or proof and it hallucinates answers left and right. Explain why every increasing, right-continuous function induces a measure on R [0] https://i.imgur.com/X3psGch.png https://i.imgur.com/X3psGch.png