"Proof" and "evidence" are almost interchangeable, though in official language, "evidence" is used, especially for court cases. One exception: In mathematics, the word "proof" is always used. "Proof" and "evidence" can refer to both abstract ideas and concrete things. However, "Testament" almost always refers to something abstract, not physical -- in other words, evidence that something is a certain way, or has certain qualities (ex: "testament to his strength," "testament to the group's commitment," etc.)
1. I need a proof to solve this math problem.
(You cannot use "testament" or "evidence" here.)
aevidence that you did it.
You can also say: There's proof that you did it.
(You cannot say: There's a testament that you did it.)
3. Good product means a testament that you worked hard.
I would say: This quality product is a testament to your hard work.
You could say: This quality product is evidence of your hard work.
You could say: This quality product is proof of your hard work.
Student or Learner