And she ended up spending her life developing mathematical proofs for the earliest computer.

她最终将自己的生命都贡献在了实现早期计算机的数学证明上。

No, Hippasus's transgression was a mathematical proof: the discovery of irrational numbers.

都不是 希帕索斯的罪源于一个数学证明：无理数的发现。

He was the first to discover the mathematical proof for what in physics is known as the force multiplier.

他是第一个发现物理学中所谓的力量倍增器的数学证明的人。

This is obvious for literature and history majors, but even engineers spend semesters on mathematical proofs that never come up on the job.

这对文史专业的学生尤为常见，但即使是工程专业也要花好几个学期的时间做那些工作中从不会出现的数学证明。

They’re able to do mathematical proofs.

他们能够进行数学证明。

At some point, we'll gather there, that it makes mathematical proofs about reality.

在某个时候，我们会聚集在那里，它对现实进行数学证明。

In fact, before computers were even built, she made mathematical proofs that can be characterized as the earliest computer programs for a machine called the difference engine and then the analytical engine.

实际上 早在计算机发明出来之前，她就先后为差分机和分析机做了数学证明，这个可以说是最早的计算机程序了。

In fact, mathematical proofs have shown that for any election with more than two options, it's impossible to design a voting system that doesn't violate at least some theoretically desirable criteria.

事实上，数学证明表明，对于任何有两个以上选项的选举，设计一个至少不违反某些理论上理想标准的投票系统是不可能的。