Carl Jacobi was a renowned 19th-century German mathematician who made profound contributions to the field of differential equations. One aspect that set Jacobi apart was his unique problem-solving approach. Jacobi believed that when one inverts known facts in a particular discipline, additional knowledge can be revealed that was previously unknown. He always encouraged his graduate students to invert the known confines of the field and examine what they found there.
Jacobi’s approach, known as “inversion,” involves thinking in a contrarian way and challenging assumptions. By asking questions that invert a problem, such as “What would happen if we did the opposite?” or “How can we make the problem worse?”, one can identify the things that are preventing them from achieving their goals and find new solutions and insights that they may have missed otherwise. Inversion is now considered an analytic strategy fundamental to scientific and mathematical thinking, and it can be applied to many other areas of life, such as business, personal relationships, and self-improvement.
Inversion is not just about thinking differently but also about challenging one’s assumptions. By questioning preconceived ideas and beliefs, one can identify the things that are preventing them from achieving their goals. Inversion can thus help people to break free from the constraints of conventional thinking and achieve success in many areas of life.