Always Start With End In Mind

“It is more important to know where you are going than to get there quickly. Do not mistake activity for achievement(/accomplishment).” — Isocrates

“There is nothing so useless as doing efficiently that which should not be done at all.” — Peter Drucker

= 以終為始

Complex problems are sometimes better solved backwards

• Invert the problem
• Inversion
• Reverse Engineering
• Work backwards

In linear algebra, proofs often require working with the inverse of a matrix to arrive at the solution. However, determining the inverse itself usually starts with the end goal in mind: verifying properties like $A^{-1}A = I$ or solving $AX = B$, the steps to constructing or applying the inverse become more focused and straightforward. Similarly, in any task, starting with the end in mind provides clarity and direction, making the process more efficient and focused.