I disagree with the complex reasoning aspect. Sure, Gemini will more often output a complete proof that is correct (likely because of the longer context training) but this is not particularly useful in math research. What you really want is an out-of-the-box idea coming from some theorem or concept you didn't know before that you can apply to make it further in a difficult proof. In my experience, GPT-5 absolutely dominates in this task and nothing else comes close.
Interesting, as that seems to mirror the way GPT-5 is often amazing at debugging code by simply reading it and spotting the deep flaws, or errata in libraries/languages which are being hit. (By carefully analysing what it did to solve a bug I often conclude that it suspected the cause immediately, it was just double-checking.)
