The Most Difficult Math Equation, Ranked
Voting rules: Choose the math equation you think is the most difficult!
Updated on May 4, 2024 06:24
Mathematics often presents challenges that push the boundaries of understanding and problem-solving. Among these, certain equations stand out due to their complexity and the extensive cognitive effort required to solve them. By ranking these formidable math problems, individuals can appreciate the hierarchy of difficulty and the intellectual milestones in the field of mathematics.
This interactive listing allows users to engage by voting for what they consider the most challenging equations. This continuous input helps create a dynamic and updated ranking that reflects the collective opinion of a diverse audience. As more enthusiasts participate, the accuracy of the rankings improves, providing a clearer picture of the mathematical landscape's most demanding challenges.
What Is the Most Difficult Math Equation?
-
184votesThese equations describe the motion of fluids such as air and water. They are notoriously difficult to solve and are one of the seven Millennium Prize Problems.The Navier-Stokes equations are a set of partial differential equations that describe the motion of fluid substances such as liquids and gases.
- Equations: The equations consist of the continuity equation and the momentum equations.
- Continuity equation: Describes the conservation of mass for an incompressible fluid.
- Momentum equations: Describe the conservation of momentum for a fluid, taking into account pressure and viscous forces.
- Nonlinear nature: The equations are nonlinear, making them difficult to solve analytically.
- Important in fluid dynamics: They provide a mathematical description of the behavior of fluids in various scenarios.
Navier-Stokes Equations in other rankings- Position 1 of 10 in Most difficult equation
- Position 3 of 10 in Most difficult math question
- Position 4 of 10 in Most difficult unsolved mathematical problem
- Position 5 of 10 in Most advanced math problem
- Position 8 of 10 in Most advanced mathematical proof used in reasoning
-
232votes
Riemann Hypothesis
Bernhard RiemannThis is one of the most famous unsolved problems in mathematics. It deals with the distribution of prime numbers and has been a subject of research for over 150 years.The Riemann Hypothesis is one of the most significant unsolved problems in mathematics. It is a conjecture made by German mathematician Bernhard Riemann in 1859, regarding the distribution of prime numbers. Essentially, it provides information about the behavior of the Riemann zeta function, which is a complex-valued function that holds great importance in number theory. The Riemann Hypothesis suggests that all non-trivial zeros of the zeta function have a real part of 1/2.- Conjecture Type: Unsolved
- Field: Number Theory
- Conjectured Date: 1859
- Importance: Critical
- Significance: Determines prime numbers distribution
Riemann Hypothesis in other rankings- Position 1 of 10 in Most difficult unsolved mathematical problem
- Position 2 of 10 in Most difficult equation
- Position 3 of 10 in Most advanced mathematical proof used in reasoning
- Position 4 of 10 in Most difficult equation to solve
-
325votesThis is another Millennium Prize Problem that deals with computational complexity. It asks whether problems that are easy to verify can also be solved quickly.P vs. NP is one of the most famous unsolved problems in computer science and mathematics. It deals with the question of whether every problem whose solution can be verified quickly (in polynomial time) can also be solved quickly (in polynomial time).
- Problem Type: Computational complexity theory
- Problem Statement: Is P (problems solvable in polynomial time) equal to NP (problems whose solutions can be verified in polynomial time)?
- Importance: Considered one of the most important open problems in computer science and mathematics
- Applications: Relevant to many fields including cryptography, optimization, artificial intelligence, and algorithm design
- Difficulty: Listed as one of the Millennium Prize Problems by the Clay Mathematics Institute, with a $1 million prize for solving it
P vs. NP in other rankings- Position 2 of 10 in Most advanced math problem
-
419votes
Fermat's Last Theorem
Pierre de FermatThis theorem was famously solved by Andrew Wiles in 1995 after over 350 years of being unsolved. It deals with the equation xn + yn = zn and whether there are solutions when n is greater than 2.Fermat's Last Theorem is a famous mathematical statement that was first proposed by Pierre de Fermat in 1637. It states 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.- Conjecture: a^n + b^n = c^n has no integer solutions for n > 2
- Proof: The proof was completed by Andrew Wiles with assistance from Richard Taylor
- Year of Proof: 1994
- Field: Number Theory
- Significance: One of the most famous and long-standing unsolved problems in mathematics
Fermat's Last Theorem in other rankings- Position 1 of 10 in Most advanced mathematical proof used in reasoning
- Position 3 of 10 in Most difficult equation to solve
- Position 4 of 10 in Most difficult equation
- Position 5 of 10 in Most difficult math question
-
515votesThis conjecture deals with elliptic curves and has important implications for cryptography. It is another Millennium Prize Problem.The Birch and Swinnerton-Dyer Conjecture is a major unsolved problem in number theory, specifically in algebraic number theory and modular forms. It deals with the relationship between the solutions of certain elliptic curves and the behavior of their associated L-functions. The conjecture was first stated in 1965.
- Status: Unsolved
- Field: Number theory
- Focus: Algebraic number theory, modular forms
- Statement: Relates the rank of an elliptic curve to the order of its zero at s=1
- Importance: One of the seven Clay Mathematics Institute Millennium Prize Problems
The Birch and Swinnerton-Dyer Conjecture in other rankings- Position 7 of 10 in Most difficult equation
-
69votes
The Hodge Conjecture
William Vallancey Duff HodgeThis conjecture deals with algebraic geometry and asks whether certain geometric objects can be described in terms of simpler objects.The Hodge Conjecture is a major unsolved problem in algebraic geometry. It was proposed by Scottish mathematician William Vallancey Duff Hodge in 1950. The conjecture is concerned with the relationship between the topology and algebraic geometry of complex projective manifolds.- Problem type: Unsolved problem
- Field: Algebraic geometry
- Domain: Mathematics
- Difficulty: Very difficult
- Conjectured year: 1950
The Hodge Conjecture in other rankings- Position 9 of 10 in Most difficult math question
-
713votesThis theory describes the behavior of elementary particles and has important implications for quantum mechanics. It is also a Millennium Prize Problem.The Yang-Mills Theory is a mathematical framework that describes the behavior of elementary particles and their interactions using quantum field theory. It is a generalization of the Maxwell's theory of electromagnetism and plays a central role in the modern understanding of the fundamental forces of nature.
- Theory Type: Quantum Field Theory
- Fields: Gauge fields
- Equations: Yang-Mills equations
- Symmetry Group: Gauge symmetry group
- Particles: Gauge bosons
-
810votes
The Schrödinger Equation
Erwin SchrödingerThis equation describes the behavior of quantum mechanical systems and has important applications in chemistry and physics.The Schrödinger Equation is a fundamental equation in quantum mechanics that describes how the wavefunction of a physical system changes with time. It was first formulated by Erwin Schrödinger in 1925 as a non-relativistic approximation of the behavior of particles in quantum mechanical systems.- Mathematical Formulation: The equation is a partial differential equation that describes the time evolution of the wavefunction of a quantum system.
- Wavefunction: It involves a wavefunction, which is a mathematical representation of the state of a quantum system.
- Hamiltonian Operator: It incorporates the Hamiltonian operator, which represents the total energy of the system.
- Kinetic Energy Term: It includes a kinetic energy term that accounts for the motion of the particles in the system.
- Potential Energy Term: It includes a potential energy term that accounts for the interaction of the particles with their surroundings.
-
96votesThis equation is used to price financial derivatives and has important applications in finance.The Black-Scholes Equation is a mathematical equation that serves as the foundation for pricing options. It is a partial differential equation that models the dynamics of financial instruments, specifically the price of an option over time.
- Mathematical Model: The Black-Scholes Equation assumes that financial markets are efficient and that the price of the underlying asset follows geometric Brownian motion.
- Risk-Free Rate: The equation incorporates the concept of a risk-free interest rate, which represents the rate of return on a risk-free investment.
- Volatility: Volatility is a key input in the equation and represents the statistical measure of the price fluctuations of the underlying asset.
- Underlying Asset: The equation applies to options with underlying assets that do not pay dividends.
- Continuous Time: The equation is formulated in continuous time, assuming that the price of the option changes smoothly over time.
-
106votes
The Enigma Machine
Arthur ScherbiusThis machine was used by the Germans during World War II to encrypt messages. It was famously cracked by Alan Turing and his team at Bletchley Park.The Enigma Machine was an encryption device used during World War II to encode and decode secret messages. It was invented by German engineer Arthur Scherbius and was primarily used by the German military.- Encryption Algorithm: Polyalphabetic Substitution
- Rotors: Typically three or four
- Plugboard connections: Up to 10 pairs of letters
- Number of possible rotor positions: Approximately 10^19
- Reflector: Reflects electrical current back through the rotors
The Enigma Machine in other rankings- Position 5 of 10 in Most difficult puzzle
Missing your favorite math equation?
Graphs
Discussion
Ranking factors for difficult math equation
-
ComplexityThe level of complexity and intricacy of the equation. More complex equations tend to involve multiple variables, higher degrees, and various mathematical concepts.
-
Research-level knowledgeEquations that require a strong understanding of advanced mathematical concepts and cannot be easily understood by someone with a basic or intermediate understanding of mathematics should be ranked higher in difficulty.
-
Solve-abilityThe relative difficulty of solving the equation, particularly if it has no known closed-form solution or if the solution requires advanced techniques and methods.
-
Computational effortThe amount of computational effort required to solve the equation. If it requires large-scale computing resources, or if the computation takes a significant amount of time, this would make the equation more difficult.
-
NoveltyEquations that are not well-studied, or have fewer existing resources and solved examples to draw upon, can be more difficult to understand and solve.
-
Multidisciplinary natureIf solving the equation requires knowledge from multiple mathematical disciplines (e.g., algebra, calculus, topology, etc.), this can add to the difficulty.
-
ApplicationsEquations that have significant real-world applications might be considered more difficult, as they typically involve a higher level of abstraction and complexity.
-
Historical contextThe history of the equation and the challenges faced by mathematicians in solving it can also contribute to its perceived difficulty. For example, equations that have resisted solution for long periods or have only been solved by prominent mathematicians might be considered more difficult.
-
Necessity for proofsSome equations may only be considered solved once a formal proof has been presented for their solution, further adding to their difficulty.
About this ranking
This is a community-based ranking of the most difficult math 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
- 1681 views
- 218 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.
Trendings topics
Don't miss out on the currently trending topics of StrawPoll Rankings!
Mathematics
More information on most difficult math equation
Mathematics is often considered one of the most challenging subjects due to its complexity and abstract nature. Within the field, there are numerous equations that are notoriously difficult to solve, requiring advanced skills and knowledge. The quest to find the most difficult math equation is a topic of debate among mathematicians and enthusiasts alike, with many contenders vying for the title. Some of the most commonly cited equations include the Navier-Stokes equations, the Riemann hypothesis, and the P versus NP problem. Each of these equations presents unique challenges and has yet to be fully solved, making them fascinating subjects of study for anyone interested in the intricacies of mathematics.
Explore other rankings
Check out some of the other recommended rankings on StrawPoll and make your voice heard.
