The idea that all of this is completely mathematical sounds pretty nutty at first since it doesn't seem mathematical at all, but actually, when we look closer, there is mathematics everywhere.

所有這一切都完全是數學的 這想法一開始聽起來非常古怪 因為它看起來一點也不像是數學的 但其實 如果我們看得更仔細些 數學無處不在

I prefer finite mathematics much more to infinite mathematics.

我更愿相信有限數范圍內的數學 而不是無窮數數學

And then, because, if something is true in mathematics, it's always true, there's a sense in which mathematics is timeless, is timefree.

之后 因為如果某件事 在數學中證明為真 那就永遠為真 所以我們感覺數學是永恒的 是不為時間所左右的

Here we see some beautiful mathematical circles forming, and whose spreading over the water is perfectly described by a mathematical equation called the wave equation.

這里我們看到美麗的數學的圓正在形成 一種叫做波動方程的數學方程 完美地描述了它們在水面上的擴散過程

This tree here doesn't look very mathematical at first sight, but if we look really closely at this bark, it's made of cells, that are made of molecules, that are made of atoms, that are made of quarks and electrons, and as far as we can tell, neither the electrons nor the quarks, nor any of the other particles that make up all of this have any properties at all, except for mathematical properties.

第一眼看去 這棵樹也不像是數學的 然而如果我們仔細看這塊樹皮 它是由細胞構成的 細胞由分子構成 分子由原子構成 原子由夸克和電子構成 據我們所知 無論是電子還是夸克 還是構成這些的其它任何粒子 除了具有數學上的性質之外 不具備別的任何性質

I'm a very big believer that maths can offer you a new way of looking at almost anything, because I think if you take the time to look, thank you very much, there are mathematical patterns hiding behind almost everything, even things that feel like they are very far away from being mathematical, even things that you think should be completely random.

我非常相信數學可以給你 一種看待幾乎一切事物的新方法 因為我認為假如你花時間仔細看 非常感謝 幾乎所有東西背后都隱藏著數學規律 甚至是那些你感覺跟數學 扯不上關系的東西 那些你覺得應該是完全隨機的東西

a place in which you do mathematics.

一道你做數學研究時不可或缺的風景

I think they had her doing mathematics.

我覺得他們在讓她做一些算數

More of a misunderstood mathematics, I think.

更算是被誤解的數學 我認為

Nobel doesn't have a prize for mathematics.

諾貝爾獎沒頒發獎項給數學