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Can AI do maths yet? Thoughts from a mathematician

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Re: Can AI do maths yet? Thoughts from a mathematician

#351

Post by alphan0n »

skydhash wrote: post #343
alphan0n wrote: post #167

Earlier quoted context omitted.

You’ll have to show me what you mean. I’ve yet to encounter an equation that 4o couldn’t answer in 1-2 prompts unless it timed out. Even then it can provide the solution in a Jupyter notebook that can be run locally.

> I’ve yet to encounter an equation that 4o couldn’t answer in 1-2 prompts unless it timed out. I've yet to encounter one of such sessions where the person is not handholding the LLMs during the whole process, basically describing the solution (instead of the problem) in natural language.

You’ll have to show me what you mean, that’s not my experience at all.

Re: Can AI do maths yet? Thoughts from a mathematician

#352

Post by alphan0n »

cruffle_duffle wrote: post #196
alphan0n wrote: post #167

Earlier quoted context omitted.

You’ll have to show me what you mean. I’ve yet to encounter an equation that 4o couldn’t answer in 1-2 prompts unless it timed out. Even then it can provide the solution in a Jupyter notebook that can be run locally.

Never really pushed it. I have to reason to believe it wouldn’t get most of that stuff correctly. Math is very much like programming and I’m sure it can output really good python for its notebook to use execute.

> I have to reason to believe it wouldn’t get most of that stuff correctly.

Right, so that reasoning is based on what, exactly?

Re: Can AI do maths yet? Thoughts from a mathematician

#353

Post by blagie »

rafaelmn wrote: post #212
blagie wrote: post #208

Earlier quoted context omitted.

It's important to base life decisions on very real technological change. We don't know what the change will be, but it's coming. At the very least, that suggests more diverse skills. We're all usually (but not always) better off, with more productivity, eventually, but in the meantime, jobs do disappear. Robotics did not fully displace machinists and factory workers, but single-skilled people in Detroit did not do we…

If AI reaches this level socioeconomic impact is going to be so immense, that choosing what subject you study will have no impact on your outcome - no matter what it is - so it's a pointless consideration.

That's just about the silliest thing I've read in a long time.

We've had changes before, the most recent one being the rise of computers and then the internet, and before that, manufacturing automation. In all cases, some people were better prepared for change, and some less so.

The general consensus is that diverse skills and foundational skills (e.g. math, communication) best prepare people for transitions, relative to specialized skills (e.g. one technology). In addition, many careers are likely to be less impacted, such as plumbing.

Re: Can AI do maths yet? Thoughts from a mathematician

#354

Post by jvanderbot »

kens wrote: post #239
jvanderbot wrote: post #67

Earlier quoted context omitted.

When you give it a large math problem and the answer is "seven point one three five ... ", and it shows a plot of the result v some randomly selected domain, well there could be more I'd like to know. You can unlock a full derivation of the solution, for cases where you say "Solve" or "Simplify", but what I (and I suspect GP) might want, is to know why a few of the key steps might work. It's a fantastic tool that hel…

What book was it that you found helpful?

A survey on matrix theory and matrix inequalities - Marvin Marcus

https://www.amazon.com/gp/product/048667102X/ref=ppx_yo_dt_b...

Re: Can AI do maths yet? Thoughts from a mathematician

#355

Post by jvanderbot »

seattleeng wrote: post #260
jvanderbot wrote: post #67

Earlier quoted context omitted.

When you give it a large math problem and the answer is "seven point one three five ... ", and it shows a plot of the result v some randomly selected domain, well there could be more I'd like to know. You can unlock a full derivation of the solution, for cases where you say "Solve" or "Simplify", but what I (and I suspect GP) might want, is to know why a few of the key steps might work. It's a fantastic tool that hel…

Im reviewing linear algebra now and would also love to know that book!

It was this one (in case you miss sibling response): https://www.amazon.com/gp/product/048667102X/ref=ppx_yo_dt_b...

I make no claim about its usefulness for anyone else!

Re: Can AI do maths yet? Thoughts from a mathematician

#356

Post by fire_lake »

exprofmaddy wrote: post #309
fire_lake wrote: post #300

Earlier quoted context omitted.

> Agreed. If someone believes the world is purely mechanistic, then it follows that a sufficiently large computing machine can model the world---like Leibniz's Ratiocinator. I don’t think it does. Taking computers as an analogy… if you have a computer with 1GB memory, then you can’t simulate a computer with more than 1GB memory inside of it.

"sufficiently large machine" ... It's a thought experiment. Leibniz didn't have a computer, but he still imagined it.

But this machine (even a tremendously large one) will have to operate in our reality and therefore can’t be “bigger” than it.

Re: Can AI do maths yet? Thoughts from a mathematician

#357

Post by rafaelmn »

blagie wrote: post #353
rafaelmn wrote: post #212

Earlier quoted context omitted.

If AI reaches this level socioeconomic impact is going to be so immense, that choosing what subject you study will have no impact on your outcome - no matter what it is - so it's a pointless consideration.

That's just about the silliest thing I've read in a long time. We've had changes before, the most recent one being the rise of computers and then the internet, and before that, manufacturing automation. In all cases, some people were better prepared for change, and some less so. The general consensus is that diverse skills and foundational skills (e.g. math, communication) best prepare people for transitions, relativ…

If we reach superhuman AGI the best preparation you can make is weapons, combat training and maybe look to build/join a militia to do a quick takeover while it's still ramping up. Society is built on cooperation outperforming violence - there's 0 chance that holds past real AGI - game theory works very different when we aren't living in an iterated prisoners dilemma.

Re: Can AI do maths yet? Thoughts from a mathematician

#358

Post by Flenkno »

TeamDman wrote: post #129
Flenkno wrote: post #25

Earlier quoted context omitted.

AWS announced 2 or 3 weeks a way of formulating rules into a formal language. AI doesn't need to learn everything, our LLM Models already contain EVERYTHING. Including ways of how to find a solution step by step. Which means, you can tell an LLM to translate whatever you want, into a logical language and use an external logic verifier. The only thing a LLM or AI needs to 'understand' at this point is to make sure tha…

Is this the AWS thing you referenced? https://aws.amazon.com/what-is/automated-reasoning/

yes

Re: Can AI do maths yet? Thoughts from a mathematician

#359

Post by ikrenji »

voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

so the interpretation happens inside the soul? otherwise it matters very little if a specific computation happens in a silicone chip or a human neuron...

Re: Can AI do maths yet? Thoughts from a mathematician

#360

Post by busyant »

ykonstant wrote: post #281
busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

> I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". (｡•́︿•̀｡)

> (｡•́︿•̀｡)

Don't cry for me, (Argentina).

When "God" tells you that you're merely dotting "i"s and crossing "t"s ... he's kind of correct.

But I was arrogant enough to believe that I was still a good researcher. I just wasn't "God."

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