Difficulty of Theorems: Ranking & Comparing

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Discussion Overview

The discussion revolves around the ranking and comparison of the difficulty of theorems across different fields of study. Participants explore the motivations for such comparisons and the implications of difficulty levels in various research areas.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the necessity of ranking theorems by difficulty, prompting others to consider the potential interest in such an endeavor.
  • Another participant asserts that every actively researched field contains theorems of varying difficulty, suggesting a universal property of theorems across disciplines.
  • Some participants express curiosity about how one might approach the task of ranking theorems, indicating a lack of consensus on methodology.

Areas of Agreement / Disagreement

There is no clear consensus on the necessity or methodology for ranking theorems by difficulty, with multiple viewpoints and questions remaining unresolved.

Contextual Notes

The discussion does not clarify specific criteria for measuring difficulty or the implications of such rankings, leaving these aspects open to interpretation.

tgt
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How can we rank and compare the difficulty of theorems in different fields?
 
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Why would one need to?
 
cristo said:
Why would one need to?

Don't know but one might find it interesting to do so and wonders how?
 
The answer is that every actively researched field has theorems of any desired difficulty i.e. for all fields of research F and for all levels of difficulty D there is at least one theorem T in F such that the difficulty of F is greater then D.
 

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