Search results
- In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.
en.wikipedia.org/wiki/Proof_of_impossibility
People also ask
Is it possible to prove that something is impossible?
How does an impossible theorem solve a problem?
What are some examples of proofs of impossibility?
What if it's not possible to prove that something can't be done?
But there are still some math equations that have managed to elude even the greatest minds, like Einstein and Hawkins. Other equations, however, are simply too large to compute. So for whatever reason, these puzzling problems have never been solved.
- The Twin Prime conjecture. Prime numbers are those magical unicorns that are only divisible by themselves and 1. As far as we know, there's an infinite number of primes, and mathematicians are working hard to constantly find the next largest prime number.
- The Moving Sofa Problem. Claudio Rocchini. This is something most of us have struggled with before - you're moving into a new apartment and trying to bring your old sofa along.
- The Collatz conjecture. XKCD. The Collatz conjecture is one of the most famous unsolved mathematical problems, because it's so simple, you can explain it to a primary-school-aged kid, and they'll probably be intrigued enough to try and find the answer for themselves.
- The Beal conjecture. The Beal conjecture basically goes like this… If A+ B= C. And A, B, C, x, y, and z are all positive integers (whole numbers greater than 0), then A, B, and C should all have a common prime factor.
- Benjamin Skuse
- Separatrix Separation. A pendulum in motion can either swing from side to side or turn in a continuous circle. The point at which it goes from one type of motion to the other is called the separatrix, and this can be calculated in most simple situations.
- Navier–Stokes. The Navier-Stokes equations, developed in 1822, are used to describe the motion of viscous fluid. Things like air passing over an aircraft wing or water flowing out of a tap.
- Exponents and dimensions. Imagine a squirt of perfume diffusing across a room. The movement of each molecule is random, a process called Brownian motion, even if the way the gas wafts overall is predictable.
- Impossibility theorems. There are plenty of mathematical expressions that have no exact solution. Take one of the most famous numbers ever, pi, which is the ratio of a circle’s circumference to its diameter.
Problems in Latin squares – open questions concerning Latin squares; The lonely runner conjecture – if runners with pairwise distinct speeds run round a track of unit length, will every runner be "lonely" (that is, be at least a distance / from each other runner) at some time? [28]
Four famous questions asked how to construct: a pair of lines trisecting a given angle; a cube with a volume twice the volume of a given cube; a square equal in area to that of a given circle; an equilateral polygon with an arbitrary number of sides.
Sep 25, 2014 · Technically, you can prove that something can't be done, provided that you choose an appropriate "something" to prove impossible. Several examples have been cited in answers.
The problem, restricted to the case of an incompressible flow, is to prove either that smooth, globally defined solutions exist that meet certain conditions, or that they do not always exist and the equations break down.
