Unsolvability (Noun)
Meaning
The property (of a problem or difficulty) that makes it impossible to solve.
Classification
Nouns denoting attributes of people and objects.
Examples
- The concept of unsolvability is a central theme in many areas of mathematics and computer science, particularly in the study of decision problems.
- The famous halting problem, which deals with the unsolvability of determining whether a program will halt or run forever, has far-reaching implications for the design of programming languages.
- The mathematical formulation of the traveling salesman problem has been shown to be an example of unsolvability, as there is no general solution that can be found in a reasonable amount of time.
- Researchers have long been interested in the unsolvability of certain problems in cryptography, particularly those related to encryption algorithms and secure data transmission.
- Gödel's incompleteness theorem is a well-known result that demonstrates the unsolvability of certain problems in formal systems, casting a doubt on the Hilbert program's goal of formalizing all of mathematics.