We were studying geometry - my adviser was the great Branko Grünbaum: https://en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaum

The conjecture had to do with whether one convex polygon could be continuously deformed into another while remaining convex, under certain conditions and constraints. The answer turns out to be no, but surprise and disappointment are understandable reactions to that outcome. It was indeed much more practical for a young grad student to look for a clever misbehaving polygon than to try to prove something about all of them at once.

How interesting I was just reading yesterday his paper "An enduring error" about how we have been miscounting the Archimedean solids for two thousand years.

But also, for this conjecture to be wrong is quite surprising to me. Intuitively I would think any convex polygon to be topologically equivalent to a circle, and any convex n-gon should be deformable into its regular version, then back to the other one…

Thanks! It makes sense.