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定理是自由的吗？Are theorems freedom?
这就是动能定理。This is the work-energy theorem.
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柯西不等式、刘维尔定理。Cauchy inequalities, Liouville's Theorem.
那么散度定理究竟讲的是什么？So, what does the divergence theorem say?
将二项式扩展到规定幂的定理。This is nothing but the binomial expansion.
正、余弦定理内在丰厚，用处普遍。Is, Cosine rich content, wide range of uses.
阿罗悖论是经济理论界的哥德尔定理。Arrow paradox is the economics Godel theorem.
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在毕达哥拉斯定理中还有更复杂的例子。More complicated example Pythagoras's theorem.
我们还有很多有关的定理。Now we have a bunch of theorems relating them.
它的逆命题就是下面这个定理。So, now, the converse is the following theorem.
很快也会看到关于通量的定理。And we will see theorems about flux pretty soon.
有些程序可以证明数学定理There are mathematical theorem-proving programs.
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著名的定理决定数学的风景。Famous Theorems define the mathematical landscape.
代数，数论，费尔马大定理等介绍。Algebra, Number Theory, Fermat's Last Theorem, etc.
特征多项式和那个定理。Characteristic polynomial, Cayley-Hamilton theorem.
现在他要演示能量守恒定理。Now he will demonstrate the conservation of energy.
我们相信,机械能守恒定理。We believe in the conservation of mechanical energy.
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本文给出了该定理的一个直接证明。A direct proof of the theorem is given in this paper.
理解欧几里得对毕德哥拉斯定理的证明。Understand Euclid's proof of the Pythagorean Theorem.
给出该类半群的一个构造定理。A construction theorem for such semigroup is obtained.