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- TL;DR Summary
- How are research-level proofs written?

I watched an interview of Yitang Zhang and he said "the way to prove a finite limit of bounded gaps between primes came to him during ##30## minutes in an afternoon", and he worked alone and did not collaborate with others during his research time.

After looking up the proof, I am in disbelief he worked alone. What baffles is how one person could write ##50## pages of what feels like an enormously complicated and difficult mathematical maze to end up with the final result "so and so is the lower limit of so and so". I can't believe that so much work is done just to prove the final result because so many independent steps are taken, that don't seem to be obviously connected to the final result at all. But every step is nit-picky, deliberate, and brings the logic one step closer to the desired result. Are there mathematicians who could even read the entire proof and understand everything in it?

My main question is, do research-level proofs in mathematics such as "bounded gaps between primes", or "Harnack's Inequality for the Ricci Flow" or "Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere." really come as a result of a one-person's genius, like everyone makes them out to be?

After looking up the proof, I am in disbelief he worked alone. What baffles is how one person could write ##50## pages of what feels like an enormously complicated and difficult mathematical maze to end up with the final result "so and so is the lower limit of so and so". I can't believe that so much work is done just to prove the final result because so many independent steps are taken, that don't seem to be obviously connected to the final result at all. But every step is nit-picky, deliberate, and brings the logic one step closer to the desired result. Are there mathematicians who could even read the entire proof and understand everything in it?

My main question is, do research-level proofs in mathematics such as "bounded gaps between primes", or "Harnack's Inequality for the Ricci Flow" or "Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere." really come as a result of a one-person's genius, like everyone makes them out to be?