图8. 哥德尔不完备性定理："在任何形式化的公理系统中，都有无法在系统内证明的真实语句，系统的一致性也无法由其自身的公理来证明"。
Gödel's incompleteness theorems: "In any formal system of axioms, there are true statements that cannot be proven within the system and the consistency of the system cannot be proven by its own axioms."
图9. 算术基本定理："每个大于1的正整数都可以唯一地表示为素数的乘积"。
The fundamental theorem of arithmetic: "Every positive integer greater than 1 can be represented uniquely as a product of prime numbers."
图10. Brouwer的固定点定理： "在欧几里得空间中一个紧凑的凸集的任何连续变换中，至少有一个点保持固定"。
Brouwer's fixed point theorem: "In any continuous transformation of a compact, convex set in Euclidean space, there is at least one point that remains fixed."
图11. 中心极限定理： "大量独立且相同分布的随机变量之和将近似于正态分布，而不考虑原始分布。"
The central limit theorem: "The sum of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the original distribution."
