The joke among bloggers over breakfast: What award *hasn’t* Atiyah won?

A Fields Medalist and Abel Prize recipient, he is a living legend: his index theorem (developed with Singer) revolutionized both mathematics and quantum physics.

In a sweeping talk on Monday morning, he leapt so nimbly from the upper echelons of abstraction to the gritty details of reality that you began to realize that they are one and the same. The purity of mathematics, the practicality of computer science—they’re interwoven.

Here are 23 quotes that capture the experience of hearing this knighted mathematician.

First, he introduced himself as our tour guide through the last century of theory in mathematics and computer science:

**I’m as ‘new’ as the hall.**

*(on lecturing in the so-called New University Building, built in 1929—the same year as Atiyah’s birth)*

**I’m going to be your tour guide of the last century. But don’t believe everything the tour guide says. They exaggerate.**

*(a self-effacing introduction to his far-ranging talk)*

**My first slide is Heidelberg in 1904. I don’t think many of you were here.**

**Among [Hilbert’s challenges] were questions like, ‘Find the mathematical foundations of physics.’ You know, small questions.**

*(on the ambitious questions laid out by David Hilbert in 1904)*

**There’s a picture of [Alan Turing’s code-breaking machine] the Colossus, with two young ladies doing all the work. There were lots of ladies doing all the work.**

*(on Alan Turing’s work in Bletchley Park)*

**You can’t get more famous than that: You win a million dollar prize and turn it down. You get even***more*publicity that way.

*(on Grigori Perelman turning down the Millennium Prize)*

**These are the grandfathers, the prophets, upon whose work computer science is based. They are almost gods.**

*(on legends like Turing, Kurt Gödel, and John Von Neumann, whose theoretical mathematics paved the way for computer science)*

Then, Atiyah began to explore the tensions between theory and practice.

**I had a banker who came into my office one day and said, ‘My shares went down 30 percent! I’m broke and it’s your fault!’ But mathematicians just give information. It’s not our fault.**

*(on the role of mathematics)*

**I’m sure up there**[*he points upwards*]—**I don’t mean in heaven, I mean up in the ceiling—there are bugs.**

*(on the ubiquity of governmental ‘data gathering’)*

**Astronomy: if you’re getting within 10 orders of magnitude, you’re okay.**

*(on the different meanings of “solution” in different fields)*

**What is a solution? It entirely depends on the customer.**

*(connecting the philosophical question ‘What is it to solve a problem?’ to the gritty practicalities of actual work)*

**Your computer’s fast, but it can’t actually travel faster than light.**

*(on the limits of computation)*

**‘Money’ is just a word to describe resources. Don’t think I’m being mercenary. Without resources, nothing happens.**

*(on practical considerations in research)*

**It’s worse than moving the goal-posts. In this game, you start playing football, and by the end you’re playing ping-pong. And the Chinese always win at ping-pong.**

*(on how new advances in computing can alter the playing field for research)*

He ended with a series of meditations on the purity and beauty of mathematics:

**Perfect spheres do not exist in the real world, but they do have reality. They exist in the human imagination—and that’s the most important world there is.**

*(on Platonism)*

**Plato has infinite time and money and can outrun Moore. In the ideal world, time has no boundaries, and we can travel faster than light.**

*(on the potential of theory to escape the constraints of practice)*

**You do it every day without realizing it: you break the barriers of space and time.**

*(on the power of human imagination)*

**We as mathematicians don’t have to be apologetic about saying we like beautiful things. We live on beautiful things.**

*(on aesthetics in mathematics)*

**You may have heard about it—there are things called spheres. The two-dimensional sphere has been known for a long time. You can play football with it.**

*(on the practical uses of low-dimensional geometry)*

**We mathematicians believe in brevity, so when I wrote a poem, it was a short poem. Don’t worry.**

*(introducing a poem to close the lecture)*

**Under the full moon, they dream.**

*(on mathematicians)*