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How can we rank and compare the difficulty of theorems in different fields?
cristo said:Why would one need to?
The difficulty of a theorem refers to the level of complexity and sophistication required to understand and prove it. Some theorems may be relatively simple and intuitive, while others may require advanced mathematical knowledge and techniques.
Theorems can be ranked and compared based on various factors, such as the level of mathematical background required, the length and complexity of the proof, and the significance and impact of the theorem in its respective field.
Some common measures of difficulty for theorems include the level of abstraction, the number of assumptions or conditions needed, and the amount of time and effort required to understand and prove the theorem.
Yes, the difficulty of a theorem can change over time as new techniques and knowledge are discovered. A theorem that was once considered difficult may become easier to prove with the development of new mathematical tools and theories.
Ranking and comparing theorems allows for a better understanding of the mathematical landscape and helps identify important and influential results. It also allows for the identification of gaps in knowledge and areas that require further research and development.