"I don't know how many people know this, but often it's mindblowing when you learn, that some infinities are bigger than others. The number of counting numbers...so 1, 2, 3, up to infinity...the numbers you would use to count things, that's infinite. The number of irrational numbers...so the numbers you cannot represent as a fraction, okay, there are more of those than there are counting numbers, by far. So these are orders of infinity. Then there are more transcendental numbers than there are irrational numbers. So that's a number you'll never find as a solution to an algebraic equation. So pi is a transcendental number. e is a transcendental number. These are magic numbers that show up in mathematics. And it turns out there's an even bigger infinity of those than there is of these other two classes of numbers. And they use the Hebrew letter aleph in ranking. So it's aleph-1, aleph-2, aleph-3, aleph-4. I think there are five levels of infinity."

“You don't take a dead cat to the vet. I mean you might, but why?”

“Yes, the universe had a beginning. Yes, the universe continues to evolve. And yes, every one of our body's atoms is traceable to the big bang and to the thermonuclear furnace within high-mass stars. We are not simply in the universe, we are part of it. We are born from it. One might even say we have been empowered by the universe to figure itself out — and we have only just begun.”

“This universality of physical laws drives scientific discovery like nothing else.”

“There are people who say "I'll never need this math, these trig identities from 10th grade or 11th grade," or maybe you never learned them. Here's the catch: whether or not you ever again use the math that you learned in school, the act of having learned the math established a wiring in your brain that didn't exist before and it's the wiring in your brain that makes you the problem solver.”

“During our brief stay on planet Earth, we owe ourselves and our descendants the opportunity to explore—in part because it's fun to do. But there's a far nobler reason. The day our knowledge of the cosmos ceases to expand, we risk regressing to the childish view that the universe figuratively and literally revolves around us. In that bleak world, arms-bearing, resource-hungry people and nations would be prone to act on their "low contracted prejudices." And that would be the last gasp of human enlightenment—until the rise of a visionary new culture that could once again embrace the cosmic perspective.”

“Some of the most productive times in the histories of nations have been when they were badly stressed — economically, politically, culturally or socially. It's possible to be stressed to a point that more creativity is stimulated than would otherwise be the case. I think it is true that necessity is the mother of invention.”