证明
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.
I have already carried out my duty. I have proved the Poincaré conjecture and I have nothing more to do in mathematics.
The genetic code is a testament to the complexity and elegance of biological systems.
Every child born through IVF is a miracle, a testament to the resilience of life.
The success of IVF is a testament to the power of collaboration between scientists and clinicians.
The elegance of a mathematical proof is in its simplicity and clarity.
I don't have any particular recipe [for developing new proofs] ... It is the reason why doing research is challenging as well as attractive. It's like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.
If you do something once, people will call it an accident. If you do it twice, they call it a coincidence. But do it a third time and you've just proven a natural law.
A proof is a device for convincing someone else that a mathematical statement is true.
A proof tells us where to concentrate our doubts.
The power of randomization in algorithms is a testament to the unpredictability and richness of the computational world.
In computational complexity, we are not just dealing with the limits of what we can compute, but also with the limits of what we can prove.
A proof that P = NP would have profound implications for mathematics, cryptography, and algorithm design.
"Approximation algorithms are a testament to the power of compromise in achieving practical solutions."
A proof is a repeatable experiment in persuasion.
A proof tells us where to concentrate our doubts.