This is a bit of a cliche at this point, but my end goal for my career is to solve the problem of intelligence. It is unclear whether this is even possible in an early-21st century lifetime, but I'm going to give it my best shot. I've got a plan.
This is the shortest path I see towards machine intelligence: first, we develop ways to allow specialized AIs to manipulate formal concepts, write programs, run experiments, and at the same time develop mathematical intuition (even creativity) about the concepts they are manipulating. Then, we use our findings to develop an AI scientist that would assist us in AI research, as well as other fields. It would be a specialized superhuman artificial intelligence to be applied to scientific research. This would tremendously speed up the development of AI. At first we would apply it to solve well-scoped problems: for instance, developing agents to solve increasingly complex and open-ended games. By collaborating with humans and gradually improving themselves, such AI researchers would eventually go on to figure out the general problem of intelligence--both biological intelligence and machine intelligence.
So that's my long-term goal: getting AI to bootstrap itself. A side effect of this process would be the development of research assistants that would help solve many outstanding scientific problems. In the future, most scientific research will be performed by either AI itself, or by humans heavily relying on such AI assistants. With a generous definition of AI, one may even argue that this is already the case: all scientific research today relies on computers and software. The trend will only keep accelerating, and will soon extend to intelligent assistants abstracting away increasingly higher levels of our thought processes, including intuition and creativity.
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