Mario Livio ranks among pop science's brightest stars. The senior astrophysicist heads the Office of Public Outreach at the Hubble Space Telescope Science Institute in Baltimore. His books *The Golden Ratio*, *The Equation That Couldn't Be Solved*, and *The Accelerating Universe* have paved the way for his latest feat—*Is God a Mathematician?*

"Not everybody needs to be a working mathematician. God forbid. This would be a disaster."

Released in January, the book confronts "the unreasonable effectiveness of mathematics" for formulating the laws of nature. In it, Livio divines whether math was "invented" by human minds or "discovered" by uppity apes tapping into the abstract, non-local super-nature of the cosmos.

In short, the answer is both, but that's not exactly a cop-out. In the interview below, edited for length and clarity, Livio goes into detail on that subject and tells Gelf about the importance of the Hubble telescope and opines on the future of math in America.**Gelf Magazine:** How do you pitch a mainstream book on math's history when America almost feels like it's at the nadir of mathematical cognition?

**Mario Livio:** Well, it's not easy. I have a very excellent agent and she's very experienced.

**Gelf Magazine:** What do you see as the state of math in America? It seems like we've lost our way compared to India or China. Is there hope for us?

**Mario Livio:** There's definitely is hope. But I think we need to take the right steps. I completely agree with you that we have a rather sad situation at the moment. It's enough to look at the results our students get in international tests. I will be completely honest with you: Part of the reason I write these pop-science books is that I keep hoping that in some small way it acts to encourage more people to get into math and the sciences. With the Hubble, we try to use astronomy to get students interested.

**Gelf Magazine:** It's almost too late when they're that age. We got to get them when they're, like, five.

**Mario Livio:** Exactly! So we're doing K-12. You're absolutely right. You have to start from kindergarten and on. Certainly there is hope. Come on—this is a great country, there are smart students out there. It's just that you need to have the right teachers, you need to give the teachers the right tools and you need to excite the students to get into this. With the new administration you hear this need mentioned, so I can only hope that resources will be put into that.

**Gelf Magazine:** In America, our national character is so based on reality and tangible objects that there's almost a paucity of appreciation for thinking abstractly. I wonder if it's in our national character to be good at math.

**Mario Livio:** America is a great nation. There are 300 million people here. It's not as if we need everybody to be a working mathematician. God forbid. This would be a disaster. What we need is students who have the aptitude who will go into these types of fields, and even those who don't go into these types of field should know a little bit about what's going on there and have some appreciation.

**Gelf Magazine:** It seems like people are missing out on the fabric of our existence.

**Mario Livio:** In the same way you appreciate a play by Shakespeare, you should be able to appreciate a great mathematical theory.

**Gelf Magazine:** I just wish someone would've laid it out like you do, when I was in high school. I would've taken a deeper interest in non-Euclidean geometry. We spend so much time looking at the trees in school, sometimes you can't see the forest.

**Mario Livio:** Non-Euclidean geometry is something almost nobody studies, right? I mean, other than pure mathematicians. And yet it is not only extraordinarily useful—it has changed our entire world view on what geometry is.

**Gelf Magazine:** The book brought to life how much math is contested ground. As a student you feel like it's all been decided. You leave the book with this thrilling sense that it's still up in the air and anything can happen.

**Mario Livio:** Especially in the foundations of mathematics, there are many unanswered questions.

**Gelf Magazine:**I was reading your book at airports. And I thought about how many people in the terminal had any idea the role that non-Euclidean geometry, and hence relativity, played in their lives, whether it be the GPS guiding the plane, or the non-linear equations underpinning the turbulence models of the aircraft. Does it ever bum you out about how little people know of the exciting world they're living in?

**Mario Livio:** I think some people are just not very aware of this. Somewhere in the back of their minds they know there are all kinds of math that go into engineering models and so on, but they just don't pay attention to that.

**Gelf Magazine:** You mentioned Einstein's walking partner, Kurt Gödel. Do you think regular humans bummed him out?

**Mario Livio:** Einstein to a large extent was very much a humanist as well as a scientist. He expressed his views about the war. He was always very strongly opposed to war. And even the greatest scientists, if they live long enough, they see things that they couldn't have dreamt of. Einstein saw quantum mechanics, which he wasn't particularly fond of. He saw the appearance of nuclear forces, which did not exist when he was a student. There is a certain humility that you get with the advancement of science, no matter how smart you think you are.

**Gelf Magazine:** Speaking of advances, Galileo changed everything with a little telescope. What has the Hubble changed about math and physics, if anything?

**Mario Livio:** Hubble at some level has literally shown us Einstein's universe. We've seen things that we've never seen before. We've seen things that for many years were just theories or in our imagination only. By now we've seen galaxies that were born when the universe was five percent its present age. Hubble has taken all these wonders—we just talked about people not being aware of what math has done for them—by now almost everyone is aware of the Hubble Space Telescope. There are very few people who have not seen the pictures. Even if they don't understand the science, they are still in awe when they stand in front of these images. In a speck of the sky, they show you ten thousand galaxies.

**Gelf Magazine:** So the Hubble didn't tear things down, it confirmed things. It "showed us the money," and it was great marketing?

**Mario Livio:** It established what we thought we knew. But it also confirmed, along with other telescopes, the presence of dark energy. So in some cases we did discover things that were completely unexpected.

**Gelf Magazine:** Dark matter and dark energy—are these just the 21st-century versions of epicycles? Are they things that we just use to hold in place until we get a better theory?

**Mario Livio:** It could be that. But I would say that my money right now is on it not being that. I believe that dark matter in the not-too-distant future—perhaps with the help of the Large Hadron Collider—we will know what we think it is, maybe some form of elementary particles we haven't discovered yet. Dark energy—it may take us a little bit longer but we'll know soon enough whether it's another epicycle. Do we just need to change the theory of gravity? Or is it something that's there and we need to find its properties?

**Gelf Magazine:** Is the current recession a failure of math? There were so many different models running during this last big bubble that really failed.

**Mario Livio:** I think it's not failure of mathematics, it's a failure of humans. Economics is not the best place for precise mathematical models. Not because there are so many variables. In physics we solve problems with an infinite number of variables. The problem is there are variables that do not lend themselves to an immediate mathematical interpretation, things like the psychology of the masses. Also, reproducibility is very hard to do in economics at the moment. There are no such fixed relations that allow you to construct such very detailed predictive models. We're pretty good at retrodiction. They tell you why there was a crash yesterday, but somehow they couldn't tell you a day in advance.

**Gelf Magazine:** Do you have any sense of where math will go? It used to be intertwined with the humanities and now it's siloed in deep specializations like knot theory. Is that super-specialization going to just increase?

**Mario Livio:** It's not exactly black or white. I think it's actually going in both of the directions you indicated. On one hand, math is going to become very, very specialized; it is already but it'll get more so. You will have very esoteric branches of mathematics appearing. At the same time, you will have a penetration of more and more math into more and more disciplines. The area that traditionally did not use math will start using it—and of course computers—more and more. The other things that is going to continue to happen is even branches of mathematics that were or will be developed as purely abstract branches will suddenly find unexpected applications.

**Gelf Magazine:** What do you feel the book brings to the meta-analysis of mathematics?

**Mario Livio:** The book contains a lot of the history of mathematics, but I would like to think that it does something that's a little bit different than just telling the history of mathematics because I do actually start with these two very basic questions. One is this question of "invention or discovery?" and the other is this question of effectiveness—"how come it's as powerful as it is?" Unlike a normal book on mathematics, it goes through the thinkers who have contributed very significantly to these particular two questions.

**Gelf Magazine:** Tell me about the reception of *Is God a Mathematician?* Do people "get it"?

**Mario Livio:** For the most part, yes, but one thing I do find a few people misunderstand: We have become very used to things being black and white. So when I say, "Was mathematics discovered or invented?", some people expect that the answer should be, "It was invented" or "It was discovered." And what I actually say is, "Look, it was partially invented and partially discovered" and I explain very precisely why I say it's partially invented and partially discovered. Namely, we invent the concept and then discover the relations among those concepts. Some people see that as my dodging the question. But the correct answer is both and there's no escape from that, so some people are a little bit confused by that, but this is the answer. I explained very clearly why I say that, but still some people expect a yes-or-no type of answer and there just is no yes-or-no answer.

**Gelf Magazine:** I got the sense that if God isn't a mathematician, He's at least very fond of math.

**Mario Livio:** I suppose, yes.

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