Edward Nelson: My encounter with infinity was when I was 16 and I came across a copy of Bertrand Russell’s book, Introduction to Mathematical Philosophy. This introduced me to Cantor’s theory of the infinite and this was entirely a mental construct that had nothing whatsoever to do with the starry heavens or vast spaces. It was qualitatively different.

In front of the enormous observational potential offered by instruments available today, what is your attitude regarding man’s capacity to know? Would you say it’s the hope to be able to attain complete knowledge, or the discomfort in front of a battle lost at the outset, or something else?
Beckwith: To me, the real miracle of human thought is how productive the scientific method has been in letting us understand things that we never understood before. It is a marriage of pure logical thinking and a need to check these things through some kind of experimentation–because pure logic often yields more things than might be applicable to the particular universe, and so the experiment is necessary to distill which things are really relevant.
When I was in graduate school, I never imagined that in the span of 30 years we would come to where we are now–pinning down natural constants of nature to a very high accuracy, discovering extrasolar planets… I spoke today about the first 10 -32 seconds of the universe, which is almost magic. So, I’m an optimist about the application of science in its ability to explain things and to make our understanding of the deeper universe better, and even to improve human life on earth, if properly applied.
At the moment, I don’t see science as addressing all the important questions of life, or necessarily giving us answers to deeper moral questions or questions of meaning that have also occupied the realm of religion. I do think that where religions attempt to explain the natural world, they do so at some peril. I’m an optimist about science telling us about even the infinite in terms of the physical universe. I think that we have to keep trying and never think that it’s impossible to solve this problem.

Nelson: Isaac Newton very famously said that all he had done was to gather some pretty pebbles on the shore of the vast ocean of truth that lay undiscovered before him. I believe that. This is not a source of pessimism, it’s a source of wonder. The pebbles that we do find are a joy.

How does your work as a researcher contribute to your vision of the meaning of reality?
Beckwith: As an experimental scientist, I tend to be agnostic about everything because new discoveries, either in thought or in experiment, are often overturning old ideas. In almost all productive cases they enrich our views. But even Newton’s laws we still hold as great even though they’re not quite the correct description according to relativity or quantum mechanics, but it doesn’t matter, because in one realm they are sort of the truth and we can build on that.
And I’d say the same thing is true about religious matters. I hold open the possibility that many of these things may be true, it just depends on how human thought and human experience evolves over the next centuries.

Nelson: I’ve worked both in physics and mathematics and it astonishes me that in the early to mid-20th century the interpretation of quantum theory was accepted by physicists even though to a large extent it denied the objective reality of the world. And it’s equally astonishing that most mathematicians do believe in the objective reality of our own creations of mathematical systems. Both of these things are questionable to me.
Now, when I was younger, I would have said that mathematics has nothing to do with my faith. But I no longer say that. I think that if one goes deeply enough into anything, whether it’s mathematics or carpentry or running trains, if one goes deeply enough, one encounters God.

You both certainly have an interest and passion that has sustained you in your pursuit of science. How might education foster this same interest in students?
Nelson: I had a high school teacher who was an excellent teacher of mathematics. I remember we were studying analytic geometry and he had a student go to the board and graph a number of points–x and x2. Then he asked the student, “What is the curve like if you draw all of these points?” The student (correctly) drew a parabola. The teacher went to the blackboard and, leaving the points, erased the parabola. “How do you know it doesn’t look like this?” And he drew a funny line through them. And then, he did not answer the question. That was the important thing. He piqued our interest. That was wonderful teaching!

Beckwith: I, too, think that it is very important to have teachers who can reveal to others the beauty and the satisfaction that comes about from applying your own mind to something creatively and deriving a reward from that. We need teachers who have a calling and can reveal to the students in a very personal way why it’s so rewarding.

Edward Nelson joined the mathematics faculty at Princeton University in 1959, and was named full professor in 1964. Well known for his work on mathematical physics and mathematical logic, Nelson is especially celebrated for his internal set theory. He received his Ph.D. in 1955 from the University of Chicago with a thesis on Markov processes, written under Irving Segal, and then spent three years as a National Science Foundation postdoctoral fellow at the Institute for Advanced Study in Princeton, New Jersey. The author of several books and numerous journal articles, Nelson has been honored internationally via books, articles, and conferences dedicated to his ground-breaking contributions to science and mathematics. A member of the American Academy of Arts and Sciences, Nelson holds an honorary doctorate from the Université Louis Pasteur in Strasbourg. In 1995, he received the American Mathematical Society Steele Prize for Seminal Contribution to Research and in 1997 was elected to the prestigious National Academy of Sciences.