Most people learn to avoid that person that is wrong/has bad judgment and is arrogant about it.
Not only do LLMs not know some things, they don't know that they don't know because of a lack of true reasoning ability, so they inevitably end up like Peter Zeihan, confidently spouting nonsense
That heavily depends on the individual grader/instructor. A good grader will take into account the amount of progress toward the solution. Restating trivial facts of the problem (in slightly different ways) or pursuing an invalid solution to a dead end should not be awarded any marks.
impressive attempt though, it used number of wraps which I found quite clever
It has gotten quite impressive at handling calculus word problems. GPT-4 (original) failed miserably on this problem (attempted to set it up using constant acceleration equations); GPT-4O finally gets it correct:
> I am driving a car at 65 miles per hour and release the gas pedal. The only force my car is now experiencing is air resistance, which in this problem can be assumed to be linearly proportional to my velocity.
> When my car has decelerated to 55 miles per hour, I have traveled 300 feet since I released the gas pedal.
> How much further will I travel until my car is moving at only 30 miles per hour?
"Consider the following word problem: "A 100 meter long chain is hanging off the end of a cliff. It weighs one metric ton. How much physical work is required to pull the chain to the top of the cliff if we discretize the problem such that one meter is pulled up at a time?" Note that the remaining chain gets lighter after each lifting step. Find the equation that describes this discrete problem and from that, generate the continuous expression and provide the Latex code for it."