The wonderful, beautiful thing about math in my mind is that we work on things and then suddenly somewhere decades down the road someone says, that could be useful. And it becomes useful.

Picture scaffolding as it goes up: There are open spaces connected to platforms by stairs. There are sections around the building that aren't attached to each other, but are contributing to the entire project. They are separate but essential to the whole. This is the type of work that Professor Nathan Ryan does in computational mathematics as he builds foundations in his research as well as in his teaching and outreach.

Much of Professor Ryan's research goes back to old questions about prime numbers (an integer that has exactly two divisors). "Euclid's method gives you a way to compute an infinite list of primes," he says. "That's the first direction of computation." Later, mathematician Carl Friedrich Gauss approached primes with mental calculations and looked at how they are distributed and grow. He proposed approximating and looking at how close his approximation was to the actual data. "It turns out that proving the sharpest bound on the error between those two things is equivalent to proving the Riemann hypothesis," he says, "which is a million-dollar problem and was discovered by computation. So, what I do is that I look at generalizations of that. Distributions of arithmetic data, how well they can be approximated, and then I describe the error."

This process and type of thinking is part of what motivates Professor Ryan's passion for the work of mathematics, but also for what it can bring to students. "To me what's exciting about math is learning how to be creative in your thinking, careful in your thinking, analytical in your thinking, and finding some balance between those things," he says. "You're faced with a problem. How do you solve it? I believe that mathematical modes of thought are very conducive to solving a very large class of problem. If it's quantitative, obviously we can approach that. If it's about a decision, we have the logic to analyze something like that. If it's about writing, well, we write a lot. I think mathematicians are among the more careful and efficient writers that you might find. If students want to be able to think carefully and creatively about these things, they should study math."

Currently, he is working with three other collaborators to write a book that connects the various aspects of number theory together, something that has not been written before. In addition, he is a mentor to students who came to Bucknell through the Posse program and runs a math circle for local kids. He is also planning a conference in collaboration with Professor Jodi Black, mathematics, that will bring faculty, staff and students across the region together to address improving the experience of STEM students from historically underrepresented groups.

His passion for the study of mathematics as well as making math accessible shines through as he talks about the many aspects of his work. "The wonderful, beautiful thing about math in my mind is that we work on things and then suddenly somewhere decades down the road someone says, that could be useful. And it becomes useful."

Posted October 3, 2013

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