Sure, here's definition for "brute force" from university textbook material written by pllk, who has taught algorithms for 20 years and holds a 2400 rating on Codeforces:
"Complete search is a general method that can be used to solve almost any algorithm problem. The idea is to generate all possible solutions to the problem using brute force ..."
And a bit further down chapter 5:
"We can often optimize backtracking by pruning the search tree. The idea is to add ”intelligence” to the algorithm so that it will notice as soon as possible if a partial solution cannot be extended to a complete solution. Such optimizations can have a tremendous effect on the efficiency of the search."
Your mistake is that you for some reason believe that any search over solution space is a brute force solution. But there are many ways to search over a solution space. A "dumb search" over solution space is generally considered to be brute force, whereas a "smart search" is generally not considered to be brute force.
Ok now I think I understand what causes your confusion. When an author writes "One way to speed up a brute-force algorithm ..." you think that the algorithm can still be called "brute force" after whatever optimizations were applied. No. That's not what that text means. This is like saying "One way to make a gray car more colorful is by painting it red". Is it still a gray car after it has been painted red? No it is not.
Sure, here's definition for "brute force" from university textbook material written by pllk, who has taught algorithms for 20 years and holds a 2400 rating on Codeforces:
https://tira.mooc.fi/kevat-2024/osa9/
"Yleispätevä tapa ratkaista hakuongelmia on toteuttaa raakaan voimaan (brute force) perustuva haku, joka käy läpi kaikki ratkaisut yksi kerrallaan."
edit:
Here's an English language book written by the same author, though the English source does not precisely define the term:
https://cses.fi/book/book.pdf
In chapter 5:
"Complete search is a general method that can be used to solve almost any algorithm problem. The idea is to generate all possible solutions to the problem using brute force ..."
And a bit further down chapter 5:
"We can often optimize backtracking by pruning the search tree. The idea is to add ”intelligence” to the algorithm so that it will notice as soon as possible if a partial solution cannot be extended to a complete solution. Such optimizations can have a tremendous effect on the efficiency of the search."
Your mistake is that you for some reason believe that any search over solution space is a brute force solution. But there are many ways to search over a solution space. A "dumb search" over solution space is generally considered to be brute force, whereas a "smart search" is generally not considered to be brute force.
Here's the Codeforces profile of the author: https://codeforces.com/profile/pllk
edit 2:
Ok now I think I understand what causes your confusion. When an author writes "One way to speed up a brute-force algorithm ..." you think that the algorithm can still be called "brute force" after whatever optimizations were applied. No. That's not what that text means. This is like saying "One way to make a gray car more colorful is by painting it red". Is it still a gray car after it has been painted red? No it is not.