The Most Difficult Equation, Ranked

Choose the equation you think is the most difficult!

Author: Gregor Krambs
Updated on Jul 14, 2024 06:30
Determining the difficulty of equations has long been a subject of interest among mathematical enthusiasts and professionals alike. It is important to highlight these challenges, as it allows a deeper understanding and appreciation for the complexities involved in various fields of math and science. By ranking these equations, we gain insights into the intellectual hurdles that continue to intrigue and challenge the brightest minds. This space provides a unique opportunity for people passionate about mathematics to engage actively by voting for what they consider the most perplexing equations. Each vote contributes to a dynamic ranking that reflects current opinions and debates within the community. Engaging with this ranking not only fuels a broader discussion but also enhances collective knowledge by highlighting which problems are viewed as most formidable.

What Is the Most Difficult Equation?

  1. 1
    89
    points
    Navier-Stokes Equations

    Navier-Stokes Equations

    A set of equations that describe the motion of viscous fluid substances.
    • Field: Fluid Dynamics
    • Millennium Prize Problem: Yes
  2. 2
    65
    points
    Riemann Hypothesis

    Riemann Hypothesis

    A conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2.
    • Field: Number Theory
    • Millennium Prize Problem: Yes
  3. 3
    18
    points
    Fermat's Last Theorem

    Fermat's Last Theorem

    A theorem stating 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.
    • Field: Number Theory
    • Proven: Yes
  4. 4
    2
    points
    General Relativity Equations

    General Relativity Equations

    A set of ten interrelated differential equations that describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy.
    • Field: Physics
    • Introduced by: Albert Einstein
  5. 5
    1
    points

    Yang-Mills Existence and Mass Gap

    A problem that involves proving the existence of a gap between the lowest energy state and the vacuum state in quantum field theories.
    • Field: Theoretical Physics
    • Millennium Prize Problem: Yes
  6. 6
    1
    points
    Hodge Conjecture

    Hodge Conjecture

    A conjecture that predicts a relationship between the algebraic cycles and the cohomology groups of a non-singular projective algebraic variety.
    • Field: Algebraic Geometry
    • Millennium Prize Problem: Yes
  7. 7
    0
    points
    Four Color Theorem

    Four Color Theorem

    A theorem stating that any map in a plane can be colored using four colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color.
    • Field: Graph Theory
    • First computer-aided proof: Yes
  8. 8
    0
    points
    Birch and Swinnerton-Dyer Conjecture

    Birch and Swinnerton-Dyer Conjecture

    A conjecture that deals with the number of solutions to certain types of equations, known as elliptic curves, over rational numbers.
    • Field: Number Theory
    • Millennium Prize Problem: Yes
  9. 9
    0
    points
    Poincaré Conjecture

    Poincaré Conjecture

    A theorem that characterizes the 3-dimensional sphere among 3-dimensional manifolds.
    • Field: Topology
    • Millennium Prize Problem: Yes, Solved
  10. 10
    0
    points
    P vs NP Problem

    P vs NP Problem

    A major unsolved problem in computer science asking if every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
    • Field: Computer Science
    • Millennium Prize Problem: Yes

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About this ranking

This is a community-based ranking of the most difficult equation. 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

  • 4308 views
  • 176 votes
  • 10 ranked items

Movers & Shakers

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.

Additional Information

More about the Most Difficult Equation

Navier-Stokes Equations
Rank #1 for the most difficult equation: Navier-Stokes Equations (Source)
Mathematics has always fascinated humans. It is a field where logic meets creativity. Within this realm, some equations stand out as particularly challenging. These equations require deep understanding and innovative thinking. They often involve complex concepts that stretch the limits of human knowledge.

The most difficult equations often arise in the context of theoretical physics. They attempt to describe the fundamental forces of nature. These equations seek to explain phenomena that we observe in the universe. They try to unify different aspects of physical reality into a single framework. This quest for unification drives much of modern physics.

In mathematics, difficult equations often come from abstract areas. These areas include number theory, algebraic geometry, and topology. These fields study properties and structures that are not always visible in the physical world. They require a high level of abstraction and imagination. Mathematicians working in these fields often deal with concepts that are hard to visualize.

Solving these equations can take years, decades, or even centuries. It requires collaboration among many brilliant minds. The process involves trial and error, intuition, and rigorous proof. Often, solving a difficult equation leads to new questions and deeper mysteries. This is the nature of mathematical inquiry.

The history of mathematics is full of stories of perseverance. Mathematicians often dedicate their lives to solving a single problem. They spend countless hours thinking, calculating, and testing ideas. Their work can lead to breakthroughs that change our understanding of the world.

One reason these equations are so challenging is their complexity. They often involve many variables and parameters. They may require advanced techniques from various branches of mathematics. Understanding these techniques takes years of study and practice. Even then, the solution may remain elusive.

Another reason is the level of precision needed. In mathematics, a solution must be exact. There is no room for approximation or error. This precision demands a high level of rigor and attention to detail. Mathematicians must ensure that every step of their reasoning is correct.

The impact of solving a difficult equation can be profound. It can lead to new technologies and advancements in science. It can also deepen our understanding of the universe and our place in it. The pursuit of these solutions drives progress in many fields.

Despite the challenges, mathematicians continue to tackle these equations. They are motivated by curiosity and the desire to uncover hidden truths. Their work is a testament to the power of human intellect and perseverance. It shows that even the most difficult problems can be solved with dedication and effort.

In conclusion, the most difficult equations in mathematics and physics represent the pinnacle of human intellectual achievement. They challenge our understanding and push the boundaries of knowledge. Solving them requires a combination of creativity, rigor, and collaboration. The journey to find these solutions is as important as the solutions themselves. It is a journey that continues to inspire and motivate mathematicians around the world.

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