iwtl problem solving like Oppenheimer | mostly for math but for applications in STEM and beyond

About two years ago, I was reading this book, "Countdown 1945," which describes all the decision-making that preceded the nuclear bombardment of Japan. The book provided a very diverse background story of the Manhattan Project and the people involved. The book described Oppenheimer as a person who was a brilliant problem-solver (besides being a brilliant person in so many aspects) by perceiving the core of any problem. That made me think about how they advise solving complex math by breaking it down into smaller components until you can figure it out.

Can someone explain a general algrithm for this and how this can be applied not only in math but in other things as well. An example would be valuable. Also, I believe doing the math is actually a great tool for exercising this skill, but is there anything else to train on?