ChatGPT 4 has a significant improvement in Math over ChatGPT 3.5 but there is a significant problem with solving e.g. differential equations or not “understanding” that imagination that a substitution that x = dυ/dt drives to a simle equation of 1st order as to x. There are two points in mathematics:

- Inspiration, e.g. to set x = dυ/dt and then we solve as to x, that is as to dυ/dt. This inspiration is a simple IDEA that a mediocre mathematician comes up with during the solving. And
- Checking the results at each step, where each step is defined as each part of the solution that must be correct so we can go to the next step.

Now there are 3 categories of IDEAS as products of inspiration or intuition (due to statistical subconscious psychizing of observations in the data):

a) The very simple ideas, like the one I mentioned before. Or e.g. if the unknown x in a differential equation is in the exponent eg e^(kx), then we have to come up with the idea that I can set the entire exponent in all relations equal to z , ie z = e^(kx) then calculate the z , let it be z = 0.1 and then I easily find the unknown x I am looking for, in a logarithm form: x = [log(0.1)]/k.

b) The difficult IDEAS, like those that unlock Mathematical Olympiad problems for students and are the feat of only good Mathematicians. These I imagine correspond to AGI, perhaps in the future. And finally

c) the extremely difficult IDEAS, very high-level ideas of great mathematicians that surprise us or of physicists, for example Einstein’s idea of the curvature of space-time or other physists as it is the idea of the existence of parallel worlds in quantum computers. Such ideas are after AI singularity and correspond to ASI. I think the ChatGPT 5 model can complete (a) and show how far AGI is. Here we are now, that is, we need a global system of personalized education with the help of schools to save humanity etc. The risk is less than the gain and AI is probably one of the few weapons we have to solve global problems.