Algorithms Quote by Jack Edmonds
![“The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. [...] I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) It is a legitimate…” quote by Jack Edmonds](https://sms4smile.com/quotes/img-quotes/43a/jack-edmonds-61996_algorithms_the-classes-of-problems-which-are-respec_50487.jpg)
“The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. [...] I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.”
About This Quote
The quote highlights the intrigue of classifying problems by algorithmic tractability and posits a conjecture about the inherent difficulty of the traveling salesman problem, emphasizing uncertainty as a legitimate basis for mathematical speculation.
In simple terms: It underscores the theoretical value of distinguishing solvable from intractable problems.
Key Takeaway
The TSP likely lacks a polynomial‑time solution.
Themes
computational complexity
algorithmic theory
NP‑hardness
conjecture
theoretical computer science
Mood
curiosity
skepticism
intellectual rigor
Type
theoretical statement
conjecture
observation
When to use this quote
- research on NP‑complete problems
- academic discussions on algorithm limits
- designing heuristics for TSP
- teaching complexity theory
- evaluating algorithm performance
Key Concepts
algorithmic tractability
complexity classes
hardness conjecture
mathematical uncertainty
Practical Applications
- guiding research priorities in optimization
- informing curriculum on computational complexity
Questions to Reflect On
- What evidence would shift this conjecture?
- How does uncertainty drive research in complexity?
![“Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last…” quote by Anonymous](https://sms4smile.com/quotes/img-quotes/948/anonymous-1_beautiful_some-mathematics-problems-look-simple-an_299446.jpg)
![“With recidivism algorithms, for example, I worry about racist outcomes. With personality tests [for hiring], I worry about filtering out people with mental health problems from jobs. And with a teacher value-added model algorithm [used in New York City to score teachers], I worry literally that…” quote by Cathy O'Neil](https://sms4smile.com/quotes/img-quotes/7df/cathy-o-neil-11478_algorithms_with-recidivism-algorithms-for-example-i_18212.jpg)
![“Object-oriented programming aficionados think that everything is an object… this [isn't] so. There are things that are objects. Things that have state and change their state are objects. And then there are things that are not objects. A binary search is not an object. It is an algorithm” quote by Alexander Stepanov](https://sms4smile.com/quotes/img-quotes/ef9/alexander-stepanov-55292_algorithms_object-oriented-programming-aficionados_89704.jpg)
![“[The Euclidean algorithm is] the granddaddy of all algorithms, because it is the oldest nontrivial algorithm that has survived to the present day.” quote by Donald Knuth](https://sms4smile.com/quotes/img-quotes/880/donald-knuth-8762_algorithms_the-euclidean-algorithm-is-the-granddadd_96085.jpg)
