- #61
phoenixthoth
- 1,600
- 2
Here's one that I think is hard:
math = ?
math = ?
The most difficult equation in mathematics
- Context: Graduate
- Thread starter Demystifier
- Start date
-
- Tags
- Mathematics
Click For Summary
Discussion Overview
The discussion revolves around identifying what participants consider to be one of the most difficult equations in mathematics. The scope includes theoretical aspects of set theory, mathematical logic, and the continuum hypothesis, as well as broader considerations of mathematical difficulty and problem-solving.
Discussion Character
- Debate/contested
- Exploratory
- Conceptual clarification
- Mathematical reasoning
Main Points Raised
- One participant suggests the equation $$2^{\aleph_0}=\aleph_k$$ as a candidate for the most difficult equation.
- Another participant challenges the notion of a "most difficult equation," arguing that such a concept may not exist in mathematics.
- Discussion includes the generalization of the equation to $$2^{\aleph_m}=\aleph_k$$ and the implications of finding k for a given m.
- Participants explore the difficulty of finding k versus finding m, questioning whether these problems have been solved or considered.
- The undecidability of the continuum hypothesis is mentioned, with references to Gödel's and Cohen's theorems, highlighting the complexity of the topic.
- Some participants express interest in the foundational aspects of mathematical logic and set theory, while others prioritize applications to physics.
- There is a discussion about the base of the exponent in the equations, with questions about whether it must be 2 or if other bases can be used.
- Several participants propose other difficult problems, including those related to Hilbert's problems and the P vs NP problem, emphasizing the challenge of defining mathematical difficulty.
- The difficulty of solving first-order ordinary differential equations is also raised, with acknowledgment that no single algorithm exists for finding integrals in general.
Areas of Agreement / Disagreement
Participants express a range of opinions on what constitutes the most difficult equation, with no consensus reached. Some agree on the significance of the continuum hypothesis, while others propose alternative equations and problems, indicating multiple competing views.
Contextual Notes
Participants note that the difficulty of mathematical problems can be subjective and context-dependent, with discussions about the limitations of definitions and the criteria for measuring difficulty.
Who May Find This Useful
This discussion may be of interest to those studying advanced mathematics, particularly in set theory and mathematical logic, as well as individuals curious about the nature of mathematical difficulty and problem-solving.
Similar threads
- · Replies 24 ·
High School
The Paradox of 1 – 1 + 1 – 1 + 1 – 1 + …
- · Replies 5 ·
- · Replies 6 ·
- · Replies 6 ·
- · Replies 6 ·
Foundations
A rigorous approach to learn Mathematics
- · Replies 20 ·
- · Replies 34 ·
- · Replies 1 ·
- · Replies 1 ·
- · Replies 2 ·