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Technology is a tool that can empower people, but it must be designed with inclusivity in mind.
A problem is in P if it can be solved quickly by a computer, and in NP if a solution can be verified quickly.
The concept of computational complexity is not just about how fast we can compute, but also about understanding the limits of what can be computed.
"Theoretical insights can lead to practical breakthroughs, bridging the gap between abstract ideas and real-world applications."
Shor's algorithm demonstrates that quantum computers can solve certain problems exponentially faster than classical computers.
Factoring large numbers is believed to be hard for classical computers, but quantum computers can do it efficiently.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
Every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it.
The key to solving complex problems is often to find the right abstraction that simplifies the problem without losing its essential features.
The power of randomness in algorithms is that it can help us find solutions that are difficult to discover through deterministic methods.
In quantum mechanics, the act of measurement can change the state of the system being measured.
"We need to think of software not just as code, but as a mathematical object that can be analyzed and verified."
Every problem in NP can be reduced to the satisfiability problem, which is the cornerstone of computational complexity theory.
The essence of computational complexity is to understand the limits of what can be computed efficiently.
The Internet is a place where people can connect, share, and learn.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
I can accept failure, everyone fails at something. But I can't accept not trying.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.
Mathematics is the language of the universe, and through it, we can understand the fundamental principles that govern our world.