The Most Difficult Math Question, Ranked

Choose the math question you think is the most difficult!

Author: Gregor Krambs
Updated on Jun 11, 2024 06:31
Grasping the complexities of challenging math questions often requires more than individual effort; it can benefit from collective insights. By ranking these tough questions, learners can identify which problems have stumped others and perhaps gain clarity through shared struggles and solutions. This site offers users the opportunity to cast votes on what they consider the most daunting math questions. The rankings update in real time, reflecting the community's current views and providing a dynamic resource for anyone looking to understand the intricacies of mathematics more deeply.

What Is the Most Difficult Math Question?

  1. 2

    The Collatz Conjecture

    A conjecture in number theory that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1.
    • Proposed: 1937
    • Field: Number Theory
  2. 3

    The Goldbach Conjecture

    The conjecture that every even integer greater than 2 can be expressed as the sum of two prime numbers.
    • Proposed: 1742
    • Field: Number Theory
  3. 4

    The Hodge Conjecture

    A conjecture about the relationship between algebraic cycles and cohomology theory.
    • Field: Algebraic Geometry
    • Status: Unsolved
  4. 5

    P vs NP Problem

    A major unsolved problem in computer science, asking whether every problem whose solution can be quickly verified can also be solved quickly.
    • Field: Computer Science
    • Status: Unsolved
  5. 6

    The Poincaré Conjecture

    A conjecture about the characterization of the 3-dimensional sphere, which was solved by Grigori Perelman.
    • Field: Topology
    • Status: Solved
  6. 7

    The Yang-Mills Existence and Mass Gap

    A problem that involves proving the existence of a mass gap in the solution to the quantum versions of the Yang-Mills equations.
    • Field: Theoretical Physics
    • Status: Unsolved
  7. 8

    The Navier-Stokes Existence and Smoothness

    A millennium problem concerning the existence and smoothness of solutions to the Navier-Stokes equations.
    • Field: Fluid Mechanics
    • Status: Unsolved
  8. 9

    The Birch and Swinnerton-Dyer Conjecture

    A conjecture that relates the number of rational points on an elliptic curve to the behavior of the L-function of the curve at s=1.
    • Field: Number Theory
    • Status: Unsolved
  9. 10

    The Twin Prime Conjecture

    The conjecture that there are infinitely many prime numbers p such that p+2 is also prime.
    • Field: Number Theory
    • Status: Unsolved

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About this ranking

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


  • 66 votes
  • 10 ranked items

Voting Rules

A participant may cast an up or down vote for each Math question once every 24 hours. The rank of each Math question is then calculated from the weighted sum of all up and down votes.

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Additional Information

More about the Most Difficult Math Question

The Riemann Hypothesis
Rank #1 for the most difficult math question: The Riemann Hypothesis (Source)
Mathematics often presents challenges that push the limits of human understanding. Some questions in math remain unsolved for years, even centuries. These problems attract the brightest minds, who spend their lives trying to crack them.

Mathematicians approach these problems with a mix of curiosity and determination. They use logic, patterns, and abstract thinking. The difficulty of a math problem can lie in many factors. Sometimes, the problem involves complex concepts that are hard to grasp. Other times, it requires new methods or tools that have not yet been developed.

The journey to solve a difficult math question usually starts with understanding the problem. Mathematicians break it down into smaller parts. They look for connections to other known problems. Often, they will try to prove or disprove a small aspect of the problem. This process can take years and may involve many failed attempts.

Collaboration plays a key role in tackling these problems. Mathematicians share their work and ideas with others. They attend conferences and publish papers. This exchange of knowledge can lead to breakthroughs. Sometimes, a fresh perspective from someone in a different field can provide the missing piece.

History shows that the most difficult math questions often lead to significant advancements. Solving these problems can open new areas of research. It can also lead to practical applications in science, technology, and engineering. For example, the development of number theory has had a profound impact on cryptography.

The pursuit of these answers requires patience and persistence. Mathematicians must be willing to spend long hours working on a single problem. They must also be ready to face setbacks and continue despite them. This dedication is driven by a deep passion for discovery and understanding.

In some cases, the answer to a difficult math question can be simple and elegant. However, finding that answer can require complex and intricate work. The process of solving these problems often reveals new insights and deeper truths about mathematics.

The most challenging math questions remind us of the vastness and beauty of the mathematical world. They show that there is always more to learn and discover. These problems inspire future generations of mathematicians to keep exploring and pushing the boundaries of human knowledge.

In conclusion, the quest to solve difficult math questions is a testament to human ingenuity and perseverance. It highlights the collaborative nature of mathematical research and the importance of sharing knowledge. While the answers to these problems may be elusive, the journey to find them enriches our understanding of the world and drives progress in many fields.

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