# Ideal answer to – which equation is unsolvable?

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There is no specific equation that is universally unsolvable, as the difficulty of solving an equation depends on various factors such as the type of equation and the available mathematical methods.

## Extensive response

Equations can vary in complexity and some may require more advanced methods to solve. While there is no specific equation that is universally unsolvable, some equations may be extremely difficult or impossible to solve using current mathematical methods. As mathematician J.E. Littlewood once stated, “Every problem is trivial once you know how to solve it.” The difficulty lies in finding the solution.

One example of such an equation is the famous Fermat’s Last Theorem, which took nearly 350 years to solve. The theorem states that for any integer value of n greater than two, there are no three positive integers a, b and c that can satisfy the equation a^n + b^n = c^n. Fermat’s Last Theorem was finally solved by Andrew Wiles in 1995 using advanced mathematical techniques.

Another example of a difficult equation is the Navier-Stokes equations, which describe the motion of fluids such as air and water. These equations involve non-linear partial differential equations that are notoriously difficult to solve. As of yet, no general solution exists for the Navier-Stokes equations, although various solutions have been found for specific cases.

While there are no universally unsolvable equations, some equations may be more difficult to solve than others. A helpful tool for classifying equations is the table below, which shows various types of equations and their corresponding difficulty levels.

Equation Type Difficulty Level
Linear Easy
Cubic Hard
Quartic Very Hard
Quintic and Above Insoluble

Overall, the difficulty of solving an equation depends on various factors such as the type of equation and the available mathematical methods. As Albert Einstein once said, “Everything should be made as simple as possible, but not simpler.” While challenging equations can lead to breakthroughs in mathematics and science, simplifying and finding elegant solutions is often the ultimate goal.

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See the answer to “Which equation is unsolvable?” in this video

The “4 Weird Unsolved Mysteries of Math” video has presented four intriguing mathematical problems that have yet to be solved, starting with the Moving Sofa Problem, which focuses on finding the largest sofa that can be turned around a 90-degree corner without lifting it. The video also mentioned the Worm Problem or the Mother Worm’s Blanket, which involves finding the smallest blanket that can cover a sleeping baby worm in any position. Another problem is the shortest forest path, which aims to find the shortest path out of a specific shape of the forest, while the Magic Square of Squares problem is to find a functional 3×3 magic square made solely of square numbers. Despite the endless efforts of scientists and mathematicians alike, these challenges still remain unresolved, and many believe that they may never be solved in the future.

The Euler-Mascheroni Constant The character y is what is known as the Euler-Mascheroni constant and it has a value of 0.5772. This equation has been calculated up to almost half of a trillion digits and yet no one has been able to tell if it is a rational number or not.

10 Math Equations That Have Never Been Solved

• 1. The Riemann Hypothesis Equation: σ (n) ≤ Hn +ln (Hn)eHn
• 2. The Collatz Conjecture Equation: 3n+1
• 3. The Erdős-Strauss Conjecture Equation: 4/n=1/a+1/b+1/c

Here is a list of some of the most complicated, unsolved math problems the world has ever seen:

• Goldbach Conjecture: Goldbach asserts that all positive even integers >=4 can be expressed as the sum of two primes.

That’s one of the main reasons why linear algebra was invented!

First we translate the problem into matrices: if
A=x=[xyz]b=[13−1]

then the system can be rewritten as Ax=b. This is not really a great simplification, but allows using the unknowns as a “single object”.

A big advance is obtained by interpreting this in terms of linear maps. The matrix A induces a linear map fA:R3→R3 defined by
fA(v)=Av

and now solvability of the linear system becomes the question

does the vector b belong to the image of fA?

The image Im(fA) is a vector subspace of R3; if it has dimension 3, then clearly the system is solvable. But what if the dimension is less than 3?

This is the “obstruction” for the solvability: when the dimension of the image (the rank of the linear map and of the matrix A) is less than the dimension of the codomain (in your case 3) the system can be solvable or not, depending on whether b belongs to the image or not.

There is no “general answer” that allows just loo…

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How do you know if an equation is unsolvable? As a response to this: When you have an equal number of equations and unknowns, put the coefficients on the variables into a matrix and take the determinant of the matrix. If the determinant does NOT equal zero, the system is solvable. If it DOES equal zero, it is not uniquely solvable.

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Regarding this, What equation Cannot be solved? Response: Linear and nonlinear equations
they are called transcedental equations because they are non-algebraic and never can be solved analytically.

Besides, Why is 3x 1 unsolvable? The 3x+1 Conjecture asserts that, starting from any positive integer n, repeated iteration of this function eventually produces the value 1. The 3x+1 Conjecture is simple to state and apparently intractably hard to solve.

What’s the answer to x3 y3 z3 K?
In mathematics, entirely by coincidence, there exists a polynomial equation for which the answer, 42, had similarly eluded mathematicians for decades. The equation x3+y3+z3=k is known as the sum of cubes problem.

What are the 7 unsolvable math problems? In reply to that: What are the 7 unsolved problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.

Keeping this in view, What are the 7 unsolved math problems? What are the 7 unsolvable math problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.

What is the world’s hardest math equation? Response to this: The Navier-Stokes equation, for me is the hardest of all. This is the full Navier-Stokes equation in conservative form. It looks pretty simple, but as one will dig in, they will notice why it is the hardest one.

Then, What are the 7 unsolvable math problems? Response: What are the 7 unsolved problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.

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Besides, What are the 7 unsolved math problems?
What are the 7 unsolvable math problems? The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.

In respect to this, What is the world’s hardest math equation?
In reply to that: The Navier-Stokes equation, for me is the hardest of all. This is the full Navier-Stokes equation in conservative form. It looks pretty simple, but as one will dig in, they will notice why it is the hardest one.

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