The Most Difficult Unsolved Mathematical Problem, Ranked

Voting rules: Choose the unsolved mathematical problem you think is the most difficult!

Updated on Jun 1, 2024 06:34

Ranking the most challenging unsolved mathematical problems serves a distinct purpose in the academic community. It highlights areas where curiosity and expertise can combine to push the boundaries of knowledge. By identifying which problems are deemed the most formidable, both aspiring and seasoned mathematicians can see where their efforts might contribute most significantly. This voting system allows everyone, from novices to experts in the field, to express their views on which mathematical conundrums they believe should be prioritized or are of greatest interest. This collective insight not only enriches the mathematical community but also guides future explorations. It's an opportunity for all to engage with the frontiers of mathematical thought and to potentially influence the direction of future research.

What Is the Most Difficult Unsolved Mathematical Problem?

1

97
votes
Source

Riemann Hypothesis

Proposes that all non-trivial zeros of the Riemann zeta function have their real parts equal to 1/2.
- Proposed by: Bernhard Riemann in 1859
- Field: Number Theory
In other topics
2

28
votes
Source

Birch and Swinnerton-Dyer Conjecture

Predicts a way to determine the number of rational points on a given elliptic curve based on the behavior of the curve's L-function at s=1.
- Field: Number Theory
In other topics
3

18
votes
Source

Hodge Conjecture

Concerns the relationship between algebraic cycles and cohomology, specifically predicting which de Rham cohomology classes are algebraic.
- Field: Algebraic Geometry
In other topics
4

12
votes
Yang-Mills Existence and Mass Gap

Involves proving the existence of a quantum field theory for Yang-Mills fields and establishing a non-zero mass gap for the theory.
- Field: Theoretical Physics
In other topics
5

4
votes
Source

Goldbach's Conjecture

Asserts that every even integer greater than 2 can be expressed as the sum of two prime numbers.
- Proposed by: Christian Goldbach in 1742
- Field: Number Theory
In other topics
- Position 4 in the ranking of the most advanced math problem
- Position 7 in the ranking of the most difficult math equation
6

3
votes
Twin Prime Conjecture

Suggests that there are infinitely many prime pairs that have a difference of 2.
- Field: Number Theory
In other topics
- Position 5 in the ranking of the most advanced math problem
- Position 5 in the ranking of the most difficult equation to solve
7

0
votes
Source

Poincaré Conjecture

Proposed that every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. It has been proven, thus no longer unsolved.
- Proposed by: Henri Poincaré in 1904
- Solved by: Grigori Perelman in 2003
- Field: Topology
In other topics
- Position 10 in the ranking of the most difficult equation
8

0
votes
Source

Collatz Conjecture

Posits that the Collatz sequence for any positive integer will eventually reach the number 1.
- Proposed by: Lothar Collatz in 1937
- Field: Number Theory
In other topics
- Position 7 in the ranking of the most advanced math problem
- Position 2 in the ranking of the most difficult math equation
9

0
votes
Source

P vs NP Problem

Asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- Field: Computational Complexity Theory
In other topics
10

0
votes
Source

Navier-Stokes Existence and Smoothness

Concerns the existence and smoothness of solutions to the Navier-Stokes equations, which describe the motion of fluid substances.
- Field: Fluid Dynamics
In other topics

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About this ranking

This is a community-based ranking of the most difficult unsolved mathematical problem. We do our best to provide fair voting, but it is not intended to be exhaustive. So if you notice something or puzzle is missing, feel free to help improve the ranking!

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162 votes
10 ranked items

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More about the Most Difficult Unsolved Mathematical Problem

Rank #1 for the most difficult unsolved mathematical problem: Riemann Hypothesis (Source)

Mathematics has always been a field of great challenges. Among these challenges, some problems remain unsolved. These problems intrigue mathematicians and spark their curiosity. They push the boundaries of human knowledge and understanding.

These problems often have simple statements. Yet, their solutions elude even the brightest minds. They involve basic concepts but require deep insights. The search for solutions drives much of mathematical research. It leads to new methods and theories.

One reason these problems are hard is their abstract nature. They often deal with infinite sets or complex structures. Understanding these requires advanced tools. Developing these tools can take years or even decades.

Another reason is the interconnectedness of mathematics. Solving one problem can depend on progress in many areas. This requires a broad knowledge base. Mathematicians must collaborate and share ideas. This collective effort is crucial.

These unsolved problems also have practical implications. They can impact fields like cryptography, physics, and computer science. Solving them can lead to technological advances. This adds to their importance and urgency.

Despite the challenges, progress is made. Mathematicians develop new techniques and approaches. They refine existing theories and uncover new connections. This slow, steady progress is part of the beauty of mathematics.

Students and researchers are drawn to these problems. They represent the frontier of human knowledge. Solving one can bring great recognition. It can also bring a sense of accomplishment and satisfaction.

The history of mathematics shows that no problem is unsolvable. Many problems once thought impossible have been solved. This gives hope and motivation to those working on today’s unsolved problems. They know that persistence and creativity can lead to breakthroughs.

In the end, the pursuit of these problems is about more than finding solutions. It is about the journey of discovery. It is about pushing the limits of what we know. It is about the joy of exploring the unknown. This is what makes mathematics a living, evolving field.