Why llms are suprisingly good at math, and what it means to process language.
https://lemmy.world/post/24708084
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Are they good at math, though? I can get ChatGPT to add numbers. But every division and other operation seems to give a wrong result almost every time.
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They will never be as efficient or as certain as calculators, absolutely. Even with function calling its better to just use calculators for calculation. Just like they will never replace a definitive database for factual information calling like wolframalpha.
However it is surprising that despite not being purpose built for math computation, they seem to understand artihmatic, try to work with numbers, and are getting better in accuracy over time just through training. They are surprisingly good at math when considering how much worse they were at it a few years ago. Not sure if you tried the newest models but deepseek can really keep up with consistent notation across operations which is a big win in itself.
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I agree. Though I don't think I'm surprised how good they are. I've just tried ChatGPT and Llama3 for now. And they struggle with literally everything. Comparing numbers, dividing them, multiplicating them... Division so far had a 100% failure rate for me. I think that model just memorized the basic multiplication tables and a few common additions and subtractions. I don't see it getting the concepts. But I'll try DeepSeek as you suggested and see how good it does. I doubt it's far off but I'll have to check. And I'll try some middle school maths. Maybe it's better at reasoning and transforming equations.
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theyre not good at math. But its still impressive that they can mostly get addition right at all, considering theyre a glorified predictive keyboard. And thats what this post is getting at.
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So, a few weeks ago I was cooking and needed 3 liters of water. My largest measuring cup is 500ml and I couldn’t be bothered to fill it 6 times so I had the brilliant idea of asking chatgpt how high should I fill a pot that’s 22cm in diameter to get 3 liters because I thought it’d be faster than doing the math myself. It told me 7 meters.
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Lol. I hope you took that as an invitation to excercise your brain. I mean not everyone needs to know this... But it's fairly simple maths. A cylinder has a volume of πr²h. So it's 3000/(3.141111) or bit less than 8cm.
The smart method is to use your kitchen scale and just weigh stuff. That's usually easier and qucker with most ingredients. And you generalky get less measuring cups dirty. Kinda depends on who wrote your recipes, though. Mine usually come with measurings in weight. Whereas very old recipe books and American people often measure in volume. And the kitchen scale won't really help there, unless you memorize the density of flour and butter 😅
And I got pots with a liter scale engraved inside. That's also very nice to have.
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I did end up doing it myself. Only tried chatgpt because that’s where I got the recipe I was following and thought it’d save me some time. I didn’t expect it to screw up a simple division. Weighting the water seems awfully cumbersome, though.
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More importantly, what was the recipe and was it any good?
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It was good but unfortunately I didn’t save it because I had no intention of eating it again. Nothing to do with the quality of the recipe, I just had to get rid of 300g of fettuccine and half a kilo of ground pork and I don’t think I’ll be in that situation again. It basically told me to season the pork with Italian seasoning, chop onion, garlic and tomatoes, throw everything in a pan with the pasta and top with mozarella.
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Thanks for the answer! I hadn’t thought about asking for recipes based on the specific ingredients you have left.
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OpenAI and ChatGPT have been smoked by the competition for awhile now. I wouldnt know, I only run open models locally Here’s what my local deepseek distill of qwen2.5-14b running on an old nvidia 1070ti has to say about your question. Its been awhile since I had to do volume equations but its answer seems about right, 7.89 cm sounds closer to the right answer than 7 meters anyway lol
Question:
how high should I fill a pot that’s 22cm in diameter to get 3 liters?
Answer: "Alright, let’s tackle this problem. The user wants to know how high they should fill a pot that’s 22 cm in diameter to get 3 liters of water.
First, I need to understand what exactly is being asked here. It seems like they’re trying to determine the height of water when poured into a pot with a specific diameter, such that the volume of water is 3 liters.
Okay, so the pot can be assumed to be cylindrical since pots are typically round and symmetrical. That makes sense because the diameter is given, and we can model it as a cylinder.
Now, the formula for the volume of a cylinder is:
V = \pi r^2 h
Where:
( V ) is the volume,
( r ) is the radius,
( h ) is the height.
The user provided the diameter, which is 22 cm. Since the radius is half of the diameter, the radius ( r ) would be 11 cm.
The volume they want is 3 liters. I know that 1 liter is equal to 1000 cubic centimeters (cm³), so 3 liters would be 3000 cm³.
So, plugging in the values we have:
3000 = pi (11)^2 h
Calculating ( 11^2 ):
11^2 = 121
So now the equation becomes:
3000 = pi times 121 times h
To solve for ( h ), we’ll divide both sides by ( pi times 121 ):
h = 3000/( pi times 121 )
Calculating the denominator first:
pi approx 3.1416
3.1416 times 121 = approx 380.132
Now, dividing 3000 by 380.132:
h = 3000 divided by 380.132 = approx 7.89 cm
So, the height of the water should be approximately 7.89 cm to get 3 liters.
Since it’s not practical to measure 0.89 cm precisely, rounding up to 8 cm would ensure there’s enough water, but if precision is important, sticking with 7.89 cm is better.
Therefore, the pot should be filled to about 7.89 cm high to hold exactly 3 liters.
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There is a difference between arithmetic and MATH.
They all can’t do division (because of tokenization) but deepseek can’t pretty accurately explain how to change the basis for a linear vector system
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Yeah I know. I just didn't feel like proceeding to proper math if it can't even do arithmatic. But seems you're all right. It can do things like "Simplify (2+r)²-(2-r)² give a step by step solution."
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They are fine at programming numpy and sympy given an interface, and they are surprisingly good at explaining advanced symbolic math concepts. I wouldn’t expect them to be good at arithmetic, but a good reasoning model should be really good at mathematical reasoning.
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Any old calculator with a lookup table is better than an LLM at math
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There is a difference between arithmetic and Maths, LLMs cannot do arithmetic, but the thinking models are really quite good at mathematics these days.
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I wanted to divide my work out weighs by 4 so that I have 2 dumbbells with the same weight on both sides. Only after I said “hey, this is not possible” it said “you are correct! This is not possible”
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TIL, llm is just a big virtual cat
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I thought it was a tooth
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This looks like Africa on left south America on right
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