**Math-frolic Interview #3...**

*" ...mathematics is one of the most remarkable things we do. Its content is full of complex structure, defined fully with respect to itself, and yet it shapes so many of the things that support human life. It is driven by wholly introspective experiments, by imagination, and by symbol."*--Joselle K.

Joselle Kehoe has an interesting combination of interests (psychology, biology, philosophy, art, in addition to mathematics) which makes her blog a tad different from most math blogs. As I'm especially interested in cognition myself I find her frequent efforts to seek links between mathematics and neuroscience or cognitive psychology especially appealing. She has been blogging for over 3 years now at "Mathematics Rising," where she says, "Mathematics Rising is about the emergence of mathematics, which grows out of the body’s contact with the world, and is as much a part of nature as we are." Here's more from her:

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**1) To start, please tell readers a little about your background or anything else pertinent to your being a math blogger…**

I have an MS in mathematics and I was fortunate to be able to do this work at the Courant Institute at NYU in New York City (which is where I'm from). My experience at Courant has impacted almost everything I have done since then. While there, I had the opportunity to meet some really talented students from all over the world; I had some wonderful teachers and, for the first time, became acquainted with the worlds that mathematicians live in. Sylvain Cappel and Peter Sarnak in particular had a big impact on me. I began writing some personal stories soon after that - stories within which I like to weave larger philosophical questions. One of my more recent pieces, called The Pleasure of Knowing Mathematics, was published in the journal Isotope at Utah State University. Sadly, the journal didn't survive the recent economic crisis. In the end, all of my stories, whether about mathematics or not, circle around the same passion - my wanting to get a better look at what we are actually doing as we construct (in largely symbolic ways) the narratives of our lives.

**2) How did your interest in mathematics originally come about, and when did you first know you wanted to pursue it professionally?**

When I finished my undergraduate degree (in 1976!) I had a BA in psychology. But I wasn't convinced that a career in psychology would fully address my need to explore meaning in my experience or even find new ways to understand truth. I decided to return to school and take some undergraduate classes in physics. But by then, I was working full time and so the first class I could fit into my schedule was calculus. My teacher was a PhD student at the time. He was young, enthusiastic and unusually informal. I was completely captivated by a discipline that I felt like I was seeing for the first time. It was alive and (at the level of calculus I) it wasn't about numbers. It was about beautiful, productive, abstract ideas that could be described with numbers. I fell in love with mathematics and never did any physics.

**3) What are your favorite aspects of mathematics (that you yourself most like studying/reading about)?**

There are many, but I find that I am consistently attracted to the steady evolution of math ideas occurring in 18th and 19th centuries. Resolving questions about the meaning of complex numbers, disputes over the definition of a function, the meaning of infinities, questions about the real number continuum and the meaning of geometry... these were all happening alongside really interesting developments in science and provocative proposals in philosophy. I've been particularly captivated by Riemann's influence, on geometry and complex analysis and even the extent to which he helped nurture topological ideas. There was a tremendous amount of self-reflection going on in the math community at the time, with fundamental questions being raised about what mathematics is, what it can do, and how.

**4) Your blog, "Mathematics Rising," often crosses boundaries and covers somewhat different topics (especially in neuroscience/cognitive psychology) than are found at other traditional math blogs. Is that partly a deliberate effort on your part to be different, or just the natural consequence of where your interests take you? And how do you go about selecting the topics you post about?**

It is certainly the natural consequence of where my interests take me.

Since graduate school, a perspective on mathematics has consistently grown in my experience. I'm sure if we had the time to speak about it, it would become clear that it is a perspective that invades most other aspects of my life. But, even beginning with that first calculus class, I became convinced that mathematics is one of the most remarkable things we do. Its content is full of complex structure, defined fully with respect to itself, and yet it shapes so many of the things that support human life. It is driven by wholly introspective experiments, by imagination, and by symbol. It seems inevitable to me that it will eventually show us, by its very existence, new relationships between ideas and material, between what we ordinarily distinguish as internal and external experiences, and so something new about ourselves.

I think of mathematics as something that 'happened,' like language or even the evolutionary changes in vision. It became the way the body was able to look past its fragmented sensations in order to see more. I would say that language, art, music, science and mathematics, are all living human inquiries. One of my favorite quotes is from Anam Cara, where John O’Donohue says, “Essentially, we belong beautifully to nature. The body knows this belonging and desires it.”

Exploring this idea requires looking at the range of topics found on my blog. And so I spend a lot of time reading about work in cognitive science, neuroscience, biology, art, physics, computer science and, of course, mathematics.

**5) Very roughly, how much time per week do you spend working on your blog? And is it principally "a labor of love" or more than that for you? Any likelihood of a book arising from the material you write about on the blog?**

It may amount to 8 or 9 hours. And I did, in fact, begin Mathematics Rising to support a book project. I'm working on the book, and I have an agent, but no publisher yet.

**6) Would you place yourself in any of the philosophical categories that mathematicians often divide themselves into (Platonist, formalist, intuitionist, constructivist, etc.)? And can you elaborate on why?**

One of the things I have always enjoyed about mathematics is how a new insight will be a surprise, even to the mathematician. And also, how relationships among ideas will grow, almost independently, into new, complex structures. Like, for example, how the trigonometric relationships that have their source in an ancient Greek examination of the circle are eventually employed to describe the wave functions of particle physics (not to mention that this requires the use of the 'impossible' complex number). It doesn't seem like we've ever really known what door we may have opened or how ideas might evolve.

With the proviso that I'm not being very precise when I say this, I probably think of myself as being some cross between a Platonist and an intuitionist. I think that mathematics grows out of the body, perhaps initially through the senses. But the body cannot be understood separately from its world and so I think it is also true that mathematics reflects some fundamental, universal structure within which we live.

**7) Are there certain blogposts you've done that stand out for you as personal favorites or ones that were the most enjoyable to work on? And from the other side, which posts seem to have been most popular or attention-getting from your readers?**

I'm not sure about this, but there are some that seem to stick out in my memory, which must mean something:

Ants, instincts and vectors

A little protein and a big bang

Leibniz's Insight? Looking forward and back

Bees, ants, space and algorithm

Pollack, fractal expressionism and a mathematical thought

I don't know that any of these were more or less popular with readers.

**8) What are some favorite math books that you like reading for your own enjoyment, and how about math books that you'd especially recommend to lay people with some math interest?**

These are some of the books that I have enjoyed and that have contributed to the things I have written.

**Number**and

**The Lightness of Being**are particularly suited to a non-scientific audience.

**Number**by Tobias Dantzig

This is just a beautiful book that looks at history and concept in a very thoughtful way.

**Mind and Nature Selected Writings of Hermann Weyl**edited by Peter Pesic

Weyl's pieces provide an interesting glimpse into an earlier time when mathematics and physics were inspiring provocative questions.

**Conversations on Mind, Matter and Mathematics**by Jean-Pierre Changeux and Alain Connes

This is a really nice modern discussion between a Platonist and a neuroscientist

**18 Unconventional Essays on the Nature of Mathematics**Edited by Reuben Hersh

I like this one because it is what it says!

**The Lightness of Being**by Frank Wilczek

The language of this book provides some really nice insights into how mathematics is working in physics.

**What is Mathematics**by Richard Courant

I love this book as a clarification of concepts as well as history.

**9) From your experience in blogging, do you have any words of advice to offer other math bloggers/communicators?**

I don't think I have enough experience to give someone a lot of advice. What I have enjoyed most about it is that Mathematics Rising provides a place where I can follow my impulses, put something together that reflects a perspective I think is important to explore and, with the added gift that individuals from all over the world will find it and read it! It's a great way to begin a conversation.

**10) As a female in a male-dominated field do you have any thoughts or interesting experiences, positive or negative, to pass along to other females on a path toward a mathematics career?**

My own experience has been great. I've never been discouraged, or made to feel like an outsider. But I went to an all girls high school. I was good in math in high school, but there wasn't anyone there who could direct my attention to a future in mathematics. I don't know if it was a gender thing because, looking back, I would say that they probably didn't know enough about mathematics to direct me. But this is true of a lot of educators. I do find it most discouraging that teachers and advisers are often in the habit of letting girls off the hook if they have trouble.

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-- Thanks, Joselle! a lot of food-for-thought in your responses and in you're whole eclectic approach to mathematics... and looking forward to the book, if it happens.

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