I still remember Gowers doing a live problem-solve as a lecture on what he calls "splitting questions" (that is, a sub-question whose resolution would ~halve th

I still remember Gowers doing a live problem-solve as a lecture on what he calls "splitting questions" (that is, a sub-question whose resolution would ~halve the search space for a proof). He was given an unseen IMO problem and tried to demonstrate the process of solving it this way. I would have called this astonishingly brave, to live-solve a problem that you know in advance is extremely difficult; in fact he didn't succeed. It reminds me of something one of my schoolteachers once arranged a lesson to teach, to the effect of "you'll learn fastest if you're able to guess and be publicly wrong". It's brilliant to get more examples of this.