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jedishrfu

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The first person to prove something or the first person to come up with a new idea in math and other fields often uses out of the box thinking. Others may have tried before but didn't think in the same way. There is no method to this style of thinking but you must be open to breaking the rules that you learned in order to see beyond then.

Some historical examples:

- Archimedes and his mathematical solutions to the surface area and volume of a sphere.

- Gallileo's observation about falling objects

- DaVinci's art, many inventions...

Sometimes ideas are extensions of existing ideas that are powerful in themselves:

- having counting numbers and then debit counting to negative numbers

- adding zero to the counting numbers

- fractional numbers to rational numbers to real numbers

Sometimes problems like the quadratic polynomial have no solution in real numbers:

- imaginary numbers then to complex numbers

- then to quaternions

- and octonians

These are just my personal feelings on these ideas.

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