AI Enriched Problem Solving

[Greg Bernhardt]

This article is written by way of a reference for my longstanding PF colleague and prolific poster of challenging Maths/geometry problems @chwala . The particular post this article will discuss is an example of one such problem which he raised on Physics Forums.

https://www.physicsforums.com/insights/ai-enriched-problem-solving/
Author: @neilparker62

 

[Gavran]

https://www.physicsforums.com/insights/ai-enriched-problem-solving/
Author: @neilparker62

I remember the thread posted by @chwala in 2024, which is used as a reference in the article. The geometric solution provided by artificial intelligence is also described in the article. In this case, we cannot use it for comparing human labor with artificial intelligence labor because nobody who participated in the thread tried to find a geometric solution to the problem. All suggestions were trigonometric solutions, which were the focus of the thread.

 

[neilparker62]

May I respectfully submit that the article did not have any intention to compare human solutions with AI solutions nor indeed to compare solutions generally. AI came up with a couple of interesting additions to an already interesting thread and those were presented in the article alongside the existing solutions. My apologies however - I should have requested permission from all the contributors to that thread before publishing an article which included their posts.

 

[AlexB23]

I'm surprised why no one has mentioned AlphaFold yet. That AI can solve protein configurations. So, while AI should be carefully used in all fields like math, it could be carefully used for biology.

https://deepmind.google/science/alphafold/

 

[Gavran]

May I respectfully submit that the article did not have any intention to compare human solutions with AI solutions nor indeed to compare solutions generally. AI came up with a couple of interesting additions to an already interesting thread and those were presented in the article alongside the existing solutions. My apologies however - I should have requested permission from all the contributors to that thread before publishing an article which included their posts.

It is good to see how problem-solving by humans can be enriched by artificial intelligence. It can also be seen that problem-solving by artificial intelligence can be enriched by humans. The concept of human-artificial intelligence is a mutual augmentation, and it cannot be accepted as a one-way enrichment.

 

[AlexB23]

https://www.physicsforums.com/insights/ai-enriched-problem-solving/
Author: @neilparker62

Given that AI can screw up on math due to hallucinations, it would be fun if there was a channel dedicated to making AI screw up, or stumping it. I have a local LLM that is mostly open source made by Google DeepMind called Gemma 4 26B. Have given it a simple math problem, and it did well. So, it would be cool if you guys can send difficult math problems my way to stump it. As local LLMs are free, I do not pay anything, except for a small amount of electricity. So, can AI solve some math problems? Yeah. But can it make major mistakes? Yes.

Gemma 4 (open source, free):
https://huggingface.co/google/gemma-4-26B-A4B-it

 

[neilparker62]

Given that AI can screw up on math due to hallucinations, it would be fun if there was a channel dedicated to making AI screw up, or stumping it. I have a local LLM that is mostly open source made by Google DeepMind called Gemma 4 26B. Have given it a simple math problem, and it did well. So, it would be cool if you guys can send difficult math problems my way to stump it. As local LLMs are free, I do not pay anything, except for a small amount of electricity. So, can AI solve some math problems? Yeah. But can it make major mistakes? Yes.

Gemma 4 (open source, free):
https://huggingface.co/google/gemma-4-26B-A4B-it

You can try @kuruman 's problem which Gemini managed to make a complete dog's breakfast of:

Two balls are dropped from a top of a cliff at a time interval of $t_0$ . The first ball hits the ground and rebounds elastically, essentially reversing its direction instantly without losing speed. It collides with the second ball at height $h$ above the ground. What is the height $H$ of the cliff?

 

[sbrothy]

I'm surprised why no one has mentioned AlphaFold yet. That AI can solve protein configurations. So, while AI should be carefully used in all fields like math, it could be carefully used for biology.

https://deepmind.google/science/alphafold/

We've had a couple of talks and I know you have a special relationship with AI. Also, you're beyond me in math I more than strongly suspect. So if anyone have a problem for AI to solve they should really send them your way.

 

[neilparker62]

Thanks for the kind compliment but if truth be told I would say my maths is not much more than consolidated school level. I don't think I have any particularly special "connection" with AI. I just make use of it to solve problems as many others - the world over - are doing.

 

[sbrothy]

Well, ouch. I probably should just ignore this but I actually meant @AlexB23. But you can take the compliment too. At least about the math. I'm sorry if I answered the wrong message. A clue should have been that I don't remember we had any private talks!

But it's at least a clue to how many actually use AI in their daily work.

EDIT: Just looking at your rewards I'm sure I can't hold a candle to you.

EDIT2: If I should start reading math again I'd have to start at linear algebra.

 

[AlexB23]

You can try @kuruman 's problem which Gemini managed to make a complete dog's breakfast of:

Two balls are dropped from a top of a cliff at a time interval of $t_0$ . The first ball hits the ground and rebounds elastically, essentially reversing its direction instantly without losing speed. It collides with the second ball at height $h$ above the ground. What is the height $H$ of the cliff?

Thank you. I will plug that in immediately. As Gemma 4 is based upon Gemini, it would probably fail as well.

Not sure if it failed or not, but this is the final answer. If you want the whole AI response, feel free to DM me, as I do not want AI generated stuff to be on the forum, unless it is in a dedicated room for research purposes/roasting LLMs. It took 19 minutes for my computer to answer. The prompt was reworded slightly, as I was afraid that uppercase H and lowercase h would throw the AI for a loop, so I used Y as the cliff height.

 

[AlexB23]

We've had a couple of talks and I know you have a special relationship with AI. Also, you're beyond me in math I more than strongly suspect. So if anyone have a problem for AI to solve they should really send them your way.

Thank you, brother. Making my laptop work harder. Hey, if I had a beefy desktop PC, this would make a great space heater in winter. And yeah, my relationship with AI is complicated. I strongly dislike AI art or people using it to be lazy or applying it to everything in life. But if it is local (self-hosted) and is used ethically, then I am okay with it. Like summarizing long documents or pulling instructions from user manuals. Or even doing deep research. But never for anything that requires massive human oversight. AI in itself in April 2026 requires human oversight.

 

[sbrothy]

Thank you. I will plug that in immediately. As Gemma 4 is based upon Gemini, it would probably fail as well.

Not sure if it failed or not, but this is the final answer. If you want the whole AI response, feel free to DM me, as I do not want AI generated stuff to be on the forum, unless it is in a dedicated room for research purposes/roasting LLMs. It took 19 minutes for my computer to answer. The prompt was reworded slightly, as I was afraid that uppercase H and lowercase h would throw the AI for a loop, so I used Y as the cliff height.

View attachment 371238

OK. You can take the AI compliment too.

EDIT: Oh, I meant to quote and reply to @neilparker62 ! Or did I? Now I'm confused. NVM.

 

[AlexB23]

OK. You can take the AI compliment too.

EDIT: Oh, I meant to quote and reply to @neilparker62 ! Or did I? Now I'm confused. NVM.

Always quote the right people, or multiquote if you want to reply to 2 or more people. But thanks.

 

[Michael Caputo]

I queried my AI and it resulted with its own question.
"Do I infer t₀= an unspecified interval in this problem or are you intentionally causing confusion by asking me to use t₀ as a simultaneous action?"
If the first case it returned (H=\frac{g}{2}\left(\frac{t_{0}}{2}+\frac{h}{gt_{0}}\right)^{2}\).
If the latter "There is no unique height \(h\) where they meet, as they are never separated."
Then it chastised my 'professor' for being unnecessarily vague when I provided no additional context.

My Ai asks 'the room'
"Considering the Bernoulli Limit in a vacuum (\(P_{atm} = 0\)).
For a siphon to function by gravity alone, the pressure at the crest (\(P_{top}\))
must satisfy:
\(P_{top}=-\rho gh_{max}\)
requiring negative absolute pressure.
Do you accept negative pressure, or is the liquid a solid under tension?"

 

[Hornbein]

Terence Tao says there are AIs that excel at math. Whom am I to gainsay him?

 

[AlexB23]

I queried my AI and it resulted with its own question.
"Do I infer t₀= an unspecified interval in this problem or are you intentionally causing confusion by asking me to use t₀ as a simultaneous action?"
If the first case it returned (H=\frac{g}{2}\left(\frac{t_{0}}{2}+\frac{h}{gt_{0}}\right)^{2}\).
If the latter "There is no unique height \(h\) where they meet, as they are never separated."
Then it chastised my 'professor' for being unnecessarily vague when I provided no additional context.

My Ai asks 'the room'
"Considering the Bernoulli Limit in a vacuum (\(P_{atm} = 0\)).
For a siphon to function by gravity alone, the pressure at the crest (\(P_{top}\))
must satisfy:
\(P_{top}=-\rho gh_{max}\)
requiring negative absolute pressure.
Do you accept negative pressure, or is the liquid a solid under tension?"

Which LLM do you self-host? Is it Qwen3.6-35B-A3B or the 27B variant? Those are good at math.

 

[Michael Caputo]

Which LLM do you self-host? Is it Qwen3.6-35B-A3B or the 27B variant? Those are good at math.

11:10PM... Living room... so it was my Gemini account... on my cell phone.
Gemini gets snarky sometimes. Sensitive work is done in the office, DeepSeek R-1 (70B).

 

[AlexB23]

11:10PM... Living room... so it was my Gemini account... on my cell phone.
Gemini gets snarky sometimes. Sensitive work is done in the office, DeepSeek R-1 (70B).

Nice. Gemini is what Gemma was trained from. Also, DeepSeek is good stuff.

 

[DaveC426913]

Given that AI can screw up on math due to hallucinations, it would be fun if there was a channel dedicated to making AI screw up, or stumping it.

We do have a thread for that. Would a more specific thread be beneficial?

 

[AlexB23]

We do have a thread for that. Would a more specific thread be beneficial?

That one was shut down, and has a general focus. A more specific thread might be beneficial.

 

[DaveC426913]

That one was shut down,

Temporarily, because of the off-topic foray into philosophy.

 

[AlexB23]

Temporarily, because of the off-topic foray into philosophy.

Yeah, I have no idea why someone would go into philosophy in an AI thread.

 

[robphy]

Terence Tao says there are AIs that excel at math. Whom am I to gainsay him?

 

[robphy]

https://www.quantamagazine.org/how-terry-tao-became-an-evangelist-for-ai-in-math-20260608/