One thing I learned from the obituary on Scott Aaronson's blog (https://scottaaronson.blog/?p=6622 https://scottaaronson.blog/?p=6622) is that Juris Hartmanis p

One thing I learned from the obituary on Scott Aaronson's blog (https://scottaaronson.blog/?p=6622 https://scottaaronson.blog/?p=6622) is that Juris Hartmanis proved in 1965 (as a very early result in his career) that there are infinitely many separate complexity classes (both for time complexity and space complexity) for decidable computational problems. That is, for every problem that takes a certain amount of computational resources to solve correctly in general, there is always a harder (still solvable) problem that takes asymptotically more resources than that one. There is no hardest problem. That doesn't necessarily say anything about whether these problems would be of practical interest to human beings, but conceptually, there is an infinite hierarchy of complexity classes, and there can never been an algorithmic discovery that would make all of them equally hard to solve. https://en.wikipedia.org/wiki/Time_hierarchy_theorem https://en.wikipedia.org/wiki/Time_hierarchy_theorem https://en.wikipedia.org/wiki/Space_hierarchy_theorem https://en.wikipedia.org/wiki/Space_hierarchy_theorem Aaronson says that this guaranteed that "that the [then] new field of computational complexity theory would have a subject matter". He also notes that Richard Lipton and Ken Regan say that Hartmanis actually pioneered the concept of studying problems systematically in terms of the complexity classes they fall into. Hartmanis's original co-author, Richard Stearns, is still alive. https://en.wikipedia.org/wiki/Richard_E._Stearns https://en.wikipedia.org/wiki/Richard_E._Stearns