> > In my feeling truly innovative opportunities are still rather easy to find.
> Such as? Can you name a few?
Naming them would need long explanations (and a lot of my thoughts are still in an early phase), but I can give you a rough sketch of one possible way how one can find them (but note that there exists an insane amount of other possible ways to find great innovative opportunities):
Simply read sophisticated scientific literature about mathematics and related areas, in particular about insanely deep results that were (possibly) honored with high awards (which gives you a strong evidence that there is indeed something deep to find in these results). Then find cool, exciting applications of these results in an area of your choice.
Why does this simple approach work? Answer: the state of the art in mathematics is in many cases simply working with science-fiction technologies from, say, 50 years in the future already today.
Honestly, this way I find raw ideas for possibly cool, exciting opportunities basically every few days.
> Such as? Can you name a few?
Naming them would need long explanations (and a lot of my thoughts are still in an early phase), but I can give you a rough sketch of one possible way how one can find them (but note that there exists an insane amount of other possible ways to find great innovative opportunities):
Simply read sophisticated scientific literature about mathematics and related areas, in particular about insanely deep results that were (possibly) honored with high awards (which gives you a strong evidence that there is indeed something deep to find in these results). Then find cool, exciting applications of these results in an area of your choice.
Why does this simple approach work? Answer: the state of the art in mathematics is in many cases simply working with science-fiction technologies from, say, 50 years in the future already today.
Honestly, this way I find raw ideas for possibly cool, exciting opportunities basically every few days.