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A universal way to solve problems, from a mathematical genius
Problems have to be understood fundamentally before they are to be solved.
A problem may not just be a question requiring an answer but may require a process, and a methodology to see what cannot be seen easily.
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Key Ideas
If life were all about luck, the same people wouldn’t repeatedly do great things(Einstein, Elon Musk, Newton). When someone repeatedly does great things it is because they prepared in advance to recognize, work on, and fill in the blanks when necessary.
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Key Ideas
Having a systematic approach to how you deal with problems, as opposed to just going by gut and feelings, can make a big difference in how you creatively find answers to your obstacles.
Detectives and investigators use the process. They ask both obvious and unthinkable questions.
Get close and collect information about how the problem is manifesting. Understand where the problem does and doesn’t happen, when the problem started, and how often the problem occurs to generate critical insight for the problem-solving effort.
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Key Ideas
Genius is not about having an extraordinarily high IQ, or even about being smart. It is not about finishing Mensa exercises in record time or mastering fourteen languages at the age of seven.
Geniuses think productively, not reproductively. They ask "How many different ways can I look at it?" not "What have I been taught by someone else on how to solve this?"
Leonardo da Vinci believed you begin by learning how to restructure the problem by looking at it from many different angles.
In order to creatively solve a problem, the thinker should not use the usual approach that is based on past experience. Geniuses use several different perspectives to solve an existing problem and thereby also identify new ones.
_Galileo Galilei revolutionized science by making his idea visible with diagrams, maps, and drawings. Einstein believed that words and numbers as they are spoken did not play a significant role in his thinking process.
Geniuses seem to develop a skill to display information in visual and spatial forms, rather than only mathematical or verbal lines.