I prefer LLMs as opposed to AI. AI has the word 'intelligence' preceded by the word 'artificial'; meaning not natural, not real. I am not as sanguine about the intelligence aspect as you are. LLMs are excellent tools due to their ability to sort and analyze extremely large data sets, but they cannot perform abstract or critical thinking. You dwell on math solutions, which are a special subset of STEM. Math is a tool used in the sciences to bring clarity to complex or abstract theories. One of the problems behind the current stagnation in theoretical physics is that many physicists let math drive their theories instead of using it as a tool. This causes theories such as 'string', 'multiverse', and 'dark matter/energy' to dead-end.
LLMs can only do what they have been programmed to do. Humans are still the only ones able to perform imaginative, abstract, critical thinking.
I would humbly disagree - finding a counterexample to the Keller's Jacobian conjecture for C3 to C3 and beyond is very impressive. Math does play an existential role in physics. For example, Dirac found positrons not via observation but through pure math, looking for matrix solutions of energy levels under conditions of special relativity.
The use of the term 'existential' is overstated; perhaps essential would be better.
"For example, Dirac found positrons not via observation but through pure math, looking for matrix solutions of energy levels under conditions of special relativity."
But the concept and theory of special relativity were already formed.
The example of Einstein is overused, but I will do it anyway. Einstein's theories of relativity were not conceived in math, but in imaginative, abstract, critical thinking.
Einstein later used math to provide a succinct base for understanding.
I prefer LLMs as opposed to AI. AI has the word 'intelligence' preceded by the word 'artificial'; meaning not natural, not real. I am not as sanguine about the intelligence aspect as you are. LLMs are excellent tools due to their ability to sort and analyze extremely large data sets, but they cannot perform abstract or critical thinking. You dwell on math solutions, which are a special subset of STEM. Math is a tool used in the sciences to bring clarity to complex or abstract theories. One of the problems behind the current stagnation in theoretical physics is that many physicists let math drive their theories instead of using it as a tool. This causes theories such as 'string', 'multiverse', and 'dark matter/energy' to dead-end.
LLMs can only do what they have been programmed to do. Humans are still the only ones able to perform imaginative, abstract, critical thinking.
I would humbly disagree - finding a counterexample to the Keller's Jacobian conjecture for C3 to C3 and beyond is very impressive. Math does play an existential role in physics. For example, Dirac found positrons not via observation but through pure math, looking for matrix solutions of energy levels under conditions of special relativity.
"Math does play an existential role in physics."
The use of the term 'existential' is overstated; perhaps essential would be better.
"For example, Dirac found positrons not via observation but through pure math, looking for matrix solutions of energy levels under conditions of special relativity."
But the concept and theory of special relativity were already formed.
The example of Einstein is overused, but I will do it anyway. Einstein's theories of relativity were not conceived in math, but in imaginative, abstract, critical thinking.
Einstein later used math to provide a succinct base for understanding.
There are two types of math: pure and applied.