Your demand — why are some equations unsolvable?

Some equations are unsolvable because they lack a solution within the conventional mathematical framework or because the problem is too complex to be solved with current mathematical techniques.

More detailed answer to your request

Some equations are unsolvable due to various reasons. One reason is that they lack a solution within the conventional mathematical framework. For example, imaginary numbers like the square root of negative numbers cannot be represented on a number line, making some equations unsolvable using only real numbers. Another reason is that the problem is too complex to be solved with current mathematical techniques. Mathematicians continue to develop new methods to solve more complicated problems, but some remain unsolvable.

In the words of mathematician Ian Stewart, “The equations that can be solved tell us less than the ones that can’t.” Unsolved equations have spurred advancements in mathematics throughout history, such as Fermat’s Last Theorem, which took over 300 years to solve and led to the development of new mathematical fields.

Some interesting facts on the topic:

  • The Halting Problem, a famous mathematical problem from computer science, is known to be unsolvable. It asks whether a given computer program will eventually halt or run forever.
  • In 2016, a team of researchers announced the discovery of a 78-digit prime number, which is the largest known prime number to date. However, the discovery of prime numbers remains a difficult problem since there is no known formula to generate them.
  • Unsolved equations have even been the subject of popular fiction, such as the mystery novel “The Oxford Murders” by Guillermo Martinez and the film “Good Will Hunting.”


Reason for Unsolvability Example
Lack of solution within conventional framework Equations involving imaginary numbers
Problem is too complex Fermat’s Last Theorem
Not computationally solvable Halting Problem

Watch a video on the subject

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.

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Other approaches of answering your query

An equation can be unsolvable if it is too complex, has too many variables, or yields an irrational or infinite number. Examples of unsolvable equations include those with transcendental numbers, multiple unknowns, certain shapes, radicals, multiple solutions, or incomplete data. Fermat’s Last Theorem and the Diophantine Equation are examples of unsolved math problems. Other unsolved problems include the Goldbach conjecture, the Riemann hypothesis, the Hadamard matrix conjecture, and the twin prime conjecture.

An equation can be unsolvable when it is either too difficult or impossible to solve. This usually occurs when the equation is too complex, with too many variables, or when the equation yields an irrational number or a number that cannot be expressed in a finite form. Examples of unsolvable equations include equations that involve

Fermat’s Last Theorem went unsolved for hundreds of years. It said that no three positive integers a, b and c can satisfy ax + bx = cx when integer x is greater than two.

What is the hardest maths equation in the world? In 2019, mathematicians finally solved a math puzzle that had stumped them for decades. It’s called a Diophantine Equation, and it’s sometimes known as the “summing of three cubes”: Find x, y, and z such that x³+y³+z³=k, for each k from one to 100.

For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that’s sometimes known as "summing of three cubes." When there are two or more unknowns, as is the case here, only the integers are studied. The trick is

Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. 2. The Riemann hypothesis. 3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4. 4. The twin prime conjecture (i.e., the conjecture that there are an

In January 2013, Elisa Lam, a 21-year-old Canadian student, set off on a solo trip across the West Coast.

The first few days, she regularly contacted family and updated social media. She looked and sounded content.

However, things took a turn for the worse on January 26th when Lam arrived in Los Angeles and checked into the Cecil Hotel.

Originally, she was supposed to share a room with a few others, but her roommates complained she was behaving oddly, so she was forced to change rooms.

Then, on January 31st, Elisa Lam disappeared.

Her posts on Facebook and Tumblr abruptly ceased.

Her daily calls to her parents stopped without explanation.

To speak in cliché, it seemed Lam had fallen off the face of the earth.

Initially, there were no clues, no evidence. Hotel staff reported that Lam had been alone that day, but in good spirits.

Other than that, nothing.

Her face was on fliers across the city and her parents flew out to help the investigation.

Soon however, a strange video su…

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Also question is, What makes an equation unsolvable?
As an answer to this: If your vector b (which consists of all the entries to the RIGHT of the equals sign) is not in the column space of A (which is a matrix consisting of all of the coefficients of x, y, and z in this example), the system is unsolvable.

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People also ask, Are some equations unsolvable? Answer will be: Some equations have no solutions, others have plenty! Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

One may also ask, Why some math problems are unsolved?
Response to this: Unsolved problems are not just arithmetic problems no one can find the answers to. They are usually conjectures about some mathematical structure or group of structures, and they are usually impossible to solve by brute force because the structures involved are usually infinite. For example: The Collatz conjecture.

What are the 7 unsolved math problems?
Answer to this: Clay “to increase and disseminate mathematical knowledge.” The seven problems, which were announced in 2000, are the Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture.

Are n equations solvable? In reply to that: Specifically if the n equations are not independent (we can derive one of them from a combination of the other two), it is not solvable. However, you may run in to two scenarios. One is the system is dependent and thus can’t be solved uniquely. The other is that the system is overdetermined and can’t be solved AT ALL.

Accordingly, What happens if there is no solution? As an answer to this: In other words, if there is no solution, then you can find a linear combination of the equations, so that the left hand side coefficients are all zeros, while the right hand side is not zero. Verifying these certificates takes time linear in the size of A, which is much faster than actually solving the system.

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Are there any mathematical problems that have never been solved?
The response is: So Far this has never been solved. As you can see in the equations above, there are several seemingly simple mathematical equations and theories that have never been put to rest. Decades are passing while these problems remain unsolved. If you’re looking for a brain teaser, finding the solutions to these problems will give you a run for your money.

How do you know if a linear algebra system is solvable? 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. That’s one of the main reasons why linear algebra was invented!

Also question is, Are all differential equations unsolvable?
In the real world, almost all of the differential equations that you encounter will be unsolvable, or at least very difficult to solve using the kinds of analytical methods found in textbooks.

Likewise, Who solved an equation that was considered unsolvable?
Response to this: After 10 years, Prof. Raimar Wulkenhaar from the University of Münster’s Mathematical Institute and his colleague Dr. Erik Panzer from the University of Oxford have solved a mathematical equation which was considered to be unsolvable. The equation is to be used to find answers to questions posed by elementary particle physics.

Are n equations solvable?
The reply will be: Specifically if the n equations are not independent (we can derive one of them from a combination of the other two), it is not solvable. However, you may run in to two scenarios. One is the system is dependent and thus can’t be solved uniquely. The other is that the system is overdetermined and can’t be solved AT ALL.

Correspondingly, Why are some problems not solvable? The reply will be: Some problems are now known to not be solvable, because the answer to the question they ask depend on what assumptions you want to make (what set of axioms you wish to start from). For example, there are theorems that work in Euclidean geometry but not in spherical geometry. What mathematical equation represents death? Indian Revenue Service.

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