The funny thing is that I was looking 3 days ago for sign mistakes in some heavy quantum field theoretical calculations. There were two subtle mistakes (leaving thus the final result unaffected). ChatGPT and Perplexity both failed dramatically in finding what was wrong with my reasoning (even inventing mistakes), but Gemini was not too bad. He identified the right spots but proposed wrong corrections and directions, together with identifying non mistakes too. Conclusion: Gemini helped but all these tools are still not fully perfect. This being said, I am using only free versions.
I have another good complex QFT calculation in mind, which I plan to ask to AI tools to see where this brings us. This will tell me whether this is a good exam question or not (i.e. I want the AI to fail).
Gemini new model is quite good. I am very happy with it.
I was doing some political what if scenario logic with oil supply and demand with it, and it is rather good :)