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"Every failure in the lab is a lesson in disguise, guiding us toward the right path."
"Science is about asking the right questions and being persistent in finding the answers."
The true challenge in mathematics is not solving problems, but asking the right questions.
The key to solving complex problems is often to find the right abstraction that simplifies the problem without losing its essential features.
To solve a problem, one must first understand its nature and then find the right tools to tackle it.
The most important thing in science is not to solve problems, but to ask the right questions.
"The challenge in computer science is not just to solve problems, but to find the right problems to solve."
In the context of computational learning, the concept of 'probably approximately correct' (PAC) learning provides a framework for understanding the efficiency and feasibility of learning algorithms.
"Model checking is a powerful technique for verifying the correctness of finite-state concurrent systems."
The real test of an algorithm is not just its correctness, but its scalability and robustness.
The most important thing in science is not to solve problems, but to ask the right questions.
Mathematical intuition often guides the development of algorithms, but it is the rigorous proof that ensures their correctness and efficiency.
The concept of probably approximately correct (PAC) learning has been foundational in computational learning theory.
The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.
The Liskov Substitution Principle is a fundamental concept in object-oriented programming, stating that objects of a superclass should be replaceable with objects of a subclass without affecting the correctness of the program.
A good system design is one that makes it easy to do the right thing and hard to do the wrong thing.
"The most important thing in science is not to be right, but to be curious."
The goal of computer architecture is to make the common case fast and the rare case correct.
The key to solving complex problems is to ask the right causal questions.
The Liskov Substitution Principle is a fundamental concept in object-oriented programming, ensuring that derived classes can be used in place of their base classes without altering the correctness of the program.