The Most Difficult Equation to Solve, Ranked

Choose the equation you think is the most difficult!

Author: Gregor Krambs
Updated on Jun 3, 2024 06:30
Mathematics encompasses a wide array of equations, some notorious for their complexity and the intellectual challenge they present. Ranking these equations based on difficulty can be a valuable resource for students, educators, and mathematics enthusiasts. It aids in identifying which problems require more focus and preparation, and serves as a gauge of the mathematical landscape's challenging territories. This dynamic ranking relies heavily on community input, where votes cast by users like you shape the list. Your participation not only reflects your personal experience but also contributes to a broader understanding of mathematical complexities. By voting, you help paint a clearer picture of which equations are deemed most daunting by your peers, enhancing the resource for everyone.

What Is the Most Difficult Equation to Solve?

  1. 1
    21
    points

    Fermat's Last Theorem

    The statement that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
    • Problem Type: Theorem
    • Field: Number Theory
    • Status: Solved
  2. 2
    16
    points

    Riemann Hypothesis

    A conjecture about the distribution of the zeros of the Riemann zeta function.
    • Problem Type: Millennium Prize Problem
    • Field: Number Theory
  3. 3
    7
    points

    Birch and Swinnerton-Dyer Conjecture

    A conjecture that describes the set of rational solutions to equations defining an elliptic curve.
    • Problem Type: Millennium Prize Problem
    • Field: Algebraic Geometry
  4. 4
    0
    points

    Hodge Conjecture

    A conjecture about the relationship between algebraic cycles and cohomology theory.
    • Problem Type: Millennium Prize Problem
    • Field: Algebraic Geometry
  5. 5
    0
    points

    Hilbert's Sixteenth Problem

    A problem related to the number and position of limit cycles in polynomial vector fields.
    • Problem Type: Hilbert's Problems
    • Field: Differential Equations
  6. 6
    0
    points

    Twin Prime Conjecture

    The conjecture that there are infinitely many prime numbers p such that p + 2 is also prime.
    • Problem Type: Conjecture
    • Field: Number Theory
  7. 7
    0
    points

    Navier-Stokes Existence and Smoothness

    A set of equations that describe the motion of viscous fluid substances.
    • Problem Type: Millennium Prize Problem
    • Field: Fluid Dynamics
  8. 8
    0
    points

    Four Color Theorem

    The assertion that any planar map can be colored with no more than four colors in such a way that no two adjacent regions have the same color.
    • Problem Type: Theorem
    • Field: Graph Theory
    • Status: Solved
  9. 9
    0
    points

    P vs NP Problem

    A major unsolved problem in computer science regarding the relationship between two classes of computational problems.
    • Problem Type: Millennium Prize Problem
    • Field: Computer Science
  10. 10
    0
    points

    Yang-Mills Existence and Mass Gap

    A problem that involves proving the existence of a mass gap in quantum field theories.
    • Problem Type: Millennium Prize Problem
    • Field: Theoretical Physics

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About this ranking

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

Statistics

  • 2346 views
  • 44 votes
  • 10 ranked items

Voting Rules

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

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Additional Information

More about the Most Difficult Equation to Solve

Fermat's Last Theorem
Rank #1 for the most difficult equation to solve: Fermat's Last Theorem (Source)
Mathematics has always posed challenges. Among these, some equations stand out due to their complexity. These equations often baffle even the most skilled mathematicians. They can take years, even decades, to solve. The journey to understand and solve them is both fascinating and arduous.

Mathematicians approach these problems with various techniques. They break down the equation into smaller parts. They look for patterns. They test different methods. Sometimes, they need to create new tools or theories. Collaboration plays a crucial role. Mathematicians often work in teams. They share ideas and insights. This collective effort can lead to breakthroughs.

The difficulty of an equation can stem from various factors. It might involve many variables. It could require advanced concepts from different branches of mathematics. Some equations are rooted in real-world problems. These problems might be in physics, engineering, or economics. The complexity of the real-world scenario adds to the challenge.

Historical context also plays a role. Some equations have been around for centuries. They have resisted numerous attempts at solutions. Over time, they gain a reputation. They become symbols of the limits of human knowledge. Solving such an equation is a significant achievement. It often leads to recognition and accolades.

The process of solving a difficult equation is not just about finding the answer. It's about the journey. Mathematicians learn a lot along the way. They develop new techniques. They gain a deeper understanding of mathematics. This progress benefits the broader field. It opens up new areas of research.

The impact of solving a difficult equation can be profound. It can lead to advancements in science and technology. It can provide insights into natural phenomena. It can improve our understanding of the universe. The ripple effects are far-reaching.

Despite the challenges, mathematicians remain undeterred. They are driven by curiosity and a passion for discovery. They take on these equations with determination. They know that the journey, though tough, is rewarding. The pursuit of solving difficult equations continues to push the boundaries of human knowledge.

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