...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Sunday, March 24, 2013

Clifford Pickover... One-Man Carnival

Math-Frolic Interview #13

"I do feel that there are facets of the universe we can never understand, just as a monkey can never understand calculus, black holes, symbolic logic, and poetry. There are thoughts we can never think, visions we can only glimpse. It is at this filmy, veiled interface between human reality and a reality beyond, that we may find the numinous, which some may liken to God." -- CP

Cliff Pickover, computer scientist/mathematician/prolific-writer/creative-thinker/curiosity-seeker with a wide-and-wild-ranging array of interests... hopefully needs no introduction here (because I wouldn't even know where to start!).
Dr. Pickover answered a few questions I sent him recently (hope he doesn't mind being interview #13...):


1) Most (but not all) of the folks I interview are active math bloggers; you are quite active on the internet with webpages and on Twitter (which some people call "microblogging"), but you don't have a conventional blog. Have you ever considered doing one, or does that not fit your interests or time constraints?

Shecky, wonderful to hear from you. Your math blogs are great. [hmmm... I should interview this guy more often! ;-)] You raise an excellent question about blogging. I regularly tweet here, and I update my Reality Carnival blog every day. Also, Pickover.com and its various sublinks receive millions of visits. However, I don’t regularly post essays at any web page. Perhaps most of my creative writing is redirected to the various books I write.

2) With your recent Math, Physics, and Medicine books you've developed an almost formulaic presentation mode that has wide appeal… I assume you have another such volume in the works, just can't guess what the next topic might be! (several possibilities). Can you say what you have in store for readers and fans in the near future? And do you work on multiple books at once, or one-at-a-time?

I believe that The Math Book, The Physics Book, and The Medical Book trilogy of books -- which cover key milestones, breakthroughs, and curiosities -- are among my most popular books.  I really enjoyed trying to condense a vast amount of information into page-sized nuggets, each accompanied by a photo or artwork.  I am currently working on the next book in this series.  Perhaps I can tell you more about the project in a few months.  It follows the same kind of colorful format, but the book is more eclectic in terms of science, history, art, and culture.
To answer your other question, whenever possible, I try to work on only one book at a time.

[Okay, I'll take a wild stab-in-the-dark and guess that Cliff's next book is on "Music" ...maybe we'll hear in a few months.]

3) How many hours a day do you spend writing or doing writing-related work/research? And seriously, how many hours a day/night do you sleep!? (And, how much coffee do you drink... no, just kidding on that one).

I started drinking coffee about three years ago. Writing is not too difficult if one is willing to give up other activities. Some people play golf on the weekends. I would prefer to write.

["three years ago"... you got a LOTTA coffee-drinkin'-catching-up to do fella! How many more books would you have written by now, if only...]

4) What were some of your main interests as a child growing up that led to the career you now have?

My childhood fascination with science was partly due to my parents' emphasis of science as a topic of study, as well as my budding interest in science fiction.  I fondly recall watching the old black-and-white Outer Limits and Chiller Theater shows on Saturday-night TV, which featured such notables as Attack of the Fifty Foot Woman and Attack of the Crab Monsters. Wow!  I can still remember the scenes in which scientists discover a pair of giant crabs mutated by atomic tests on a remote island. Many scientists and science popularizers got kick-started in life by reading science fiction.

5) What is the most interesting aspect of mathematics for you?

At first glance, some math classes may appear to involve a long catalogue of isolated concepts.  But as we learn more, we begin to see many linkages.  Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought. For me, mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos.

6) Out of all the books you've written do you have a personal favorite? Also, so far as I'm aware all your writing has been nonfiction… have you ever thought of writing a piece of fiction (…or correct me if you already have)?

In addition to The Math Book, The Physics Book, and The Medical Book trilogy, I really enjoyed writing Sex, Drugs Einstein and Elves.  In this nontraditional book, I explore the borderlands of science. Part memoir and part surrealistic perspective on culture, I attempt to give readers a glimpse of new ways of thinking and of other worlds as we reach across cultures and peers beyond our ordinary reality.
I have written a few novels. Your readers can always visit my page that lists most of my 45+ books to learn more.  The titles of the novels include: Liquid Earth, The Lobotomy Club, Sushi Never Sleeps, Egg Drop Soup, The Heaven Virus, Spider Legs, and Jews in Hyperspace.

[I'm embarrassed that I wasn't aware of all this fiction... I don't read novels so it's somewhat understandable, but still surprised (and impressed)!]

7) Who are some of today's math authors/popularizers that you most enjoy reading? Other than math & science, what is some of your other favorite reading?

I enjoy all of the famous math popularizes, including, and not limited to, Ian Stewart, Ivars Peterson, Steven Strogatz, Rudy Rucker, Keith Devlin, and so many more.  Of course, Martin Gardner’s books still provide a goldmine of joy and information.  For other favorite reading beyond science, I enjoy reading and rereading the multivolume graphic-novel treatments of Proust's Remembrance of Things Past by Stephane Heuet, and some of the later novels of Robert Heinlein, including The Number of the Beast. In this novel, the protagonists can access 10,314,424,798,490,535,546,171,949,056 universes.

8) You're often referred to as a "polymath" because of your wide interests, and in fact I once said that "poly-polymath" was perhaps a more apt description! I can't help but think there's a strong genetic component to your far-flung talents/interests. Going back again to childhood, do you have a sense of where those mind-stretching proclivities stem from -- were your parents so inclined, and do you have any similarly-predisposed siblings?

While growing up in New Jersey, my bedroom featured plastic anatomical models of the heart, brain, and eye; posters of the human circulatory system; and trilobite fossils, science-fiction books, and Ugly Stickers displaying wild-eyed, grinning creatures with names like “Bob, “Sandy,” and “Iris.”  My childhood interest in science also was stimulated by my desire to learn how the world works and from my passion for science fiction. Today, my books are motivated by my interest in bringing science, mathematics and creativity to the broader public.
To answer your other question, I have one brother.  He’s a medical doctor.  He doesn’t write books, but we have similar interests.

9) I think it's accurate(?) to say you have very strong interests in both science and religion. Of course, a lot of scientists (vociferously) feel the two topics are mutually exclusive of one another. Can you say a little about how you hold both of them together in your own thinking and reflection? Do they mix together in some interactive way, or are they more like separate compartments?

Sometimes readers of my books ask me why I have also written on God, strange realities, and religious subjects. I tend to be skeptical about many claims of the paranormal. However, I do feel that there are facets of the universe we can never understand, just as a monkey can never understand calculus, black holes, symbolic logic, and poetry. There are thoughts we can never think, visions we can only glimpse. It is at this filmy, veiled interface between human reality and a reality beyond, that we may find the numinous, which some may liken to God.

10) You have several interviews and/or videos on the Web… If folks want to get to know you still better is there a specific one you would point people to, to learn more about you?

Visit Pickover.com and RealityCarnival.com.  Also, your readers can easily read my latest tweets, for free, here.

[There was a lengthy, wide-ranging audio interview with Cliff I heard on the Web not too long ago, which was what prompted me to ask this question, but unfortunately I can't re-locate it now.] 

11) Any parting words, not covered above, you'd care to pass along to a math-oriented audience?

Yes, the following spooky-looking number is a prime number.  Enjoy: 1000000000000066600000000000001
Belphegor's Prime


Thanks for taking time to participate here, Dr. Pickover, and may you keep exploring that 'filmy, veiled interface between human reality and a reality beyond,' and reporting back to us! (Ohh, and I'll recommend this coffee for you.)
You can check out all Dr. Pickover's books at Amazon here:

Wednesday, March 13, 2013

Taking Math To Court

A book blurb today...:

"Math On Trial" by Leila Schneps and Coralie Colmez, is a recent volume out from a mother/daughter mathematics team. It piggybacks on the current trendy interest in statistical-and-probability analyses of human affairs. Anyone with a penchant both for the 'true crime' genre of reporting, and for math, will likely enjoy this volume, which combines a look at various famous true crimes with the mathematical evidentiary material brought to bear in such cases...

Unfortunately, I'm not one of those people who takes much interest in crime reporting, so for me the volume did not hold undue interest. It covers ten notorious diverse cases (from murder to gender discrimination), but most of them are decades old, or even from over a century ago. A volume of more modern cases, say from the last dozen years, would have made for a more interesting and powerful read to me (...the Amanda Knox murder and Bernie Madoff swindle cases are among the more recent ones addressed in the volume). My own interests run more toward current events than history, and so the reaching back in time wasn't particularly effective, but other readers may find these historical accounts more keenly interesting. Each chapter focuses on a different kind of mathematical error (rather than the same sort of probability error occurring over and over) which is probably one reason for the somewhat odd selection of cases employed here.
At times the focus on math seems to oversimplify the multitude of legal issues and details involved in a given case, while at other times the mathematical material seems a bit buried under the legalities and details of a case. Still, the basic underlying point that math is often misused/misinterpreted in the courtroom can't be denied, and certainly anyone who doesn't already know that should read a book like this, because it is clearly a message worth spreading.

The book ends on the question of whether mathematical evidence should even be allowed in the courtroom, given how easily it is manipulated before a naive jury or judge. The final "Conclusion" chapter discusses Laurence Tribe's 40-year-old "beautifully argued, passionate" article on the subject, before noting that a lot has changed in the four decades hence, especially with the routine use of DNA forensics. Of course DNA evidence can bear problems as well, if not carefully administered, but is also a boon to those falsely-accused who may be exonerated through its use. Lastly, the authors acknowledge the more recent emphasis on Bayesian analysis and the attempt to set standards for its inclusion in the courtroom as well.

This volume didn't happen to grab me, but those of you more enamored of true-crime fare, may find it an interesting and worthwhile read, and its ultimate message that the public needs to be better educated as to the uses and abuses of statistics in legal matters is an important one.

Tuesday, March 5, 2013

Ian Stewart Delivers...

Overview of Ian Stewart's "Visions of Infinity"

"Mathematics is newer, and more diverse, than most of us imagine. At a rough estimate, the world's research mathematicians number about a hundred thousand, and they produce more than two million pages of new mathematics every year...
"When we think of mathematics, what springs to mind is endless pages of dense symbols and formulas. However, those two million pages generally contain more words than symbols... As the great Carl Friedrich Gauss remarked around 1800, the essence of mathematics is 'notions, not notations'. Ideas, not symbols."
                                   -- from Ian Stewart's Preface

Ian Stewart (or one of his clones… because I refuse to be duped into believing that one person can write all these books!) has a new volume out, "Visions of Infinity." There are several popular math books available that review a variety of the most famous, intriguing often-unsolved problems in mathematics (the exact selection can vary slightly from volume to volume, though certain standards almost always show up). Anyway, this is Stewart's contribution to the genre… and… as one might expect, it is excellent. If only it had been written first, some of the other attempts might even have been unnecessary.

To be clear though, while this volume covers some of the most interesting problems in all of mathematics it is NOT a book to draw your non-mathematical friends into the math arena. Even the non-math person who wishes they could like math, and who may have enjoyed Steven Strogatz's "Joy of X,"  I think will find this particular book too heavy-going.  But for the individual already enamored of the subject, and having some familiarity with math's deepest problems, this is a fantastic read. In fact, it's probably my favorite Stewart volume of all the ones I've read.

Stewart gives enough background and depth to each discussion to hold the attention, and exercise the brain, of most math buffs, without getting so technical as to lose them in the dust (though parts, toward the end especially, are definitely tough-going). I have no idea if he was able to produce this work largely based on his past writing and knowledge, or whether it required lots of research on his part to fill in all the detail, history, and richness that are on display here... either way the book is a great accomplishment.

Fermat's Last Theorem, the Riemann Hypothesis, the four-color theorem, the Goldbach conjecture, the Poincare' conjecture, and P vs. NP, are among the classics Stewart rolls out for scrutiny (the title may be a bit misleading in so much as "infinity" is not really the central topic). He does a great job of not only explaining these mathematical conundrums in an accessible way, but also of detailing their histories, context, and relevance (when it exists) to other matters.  The first few chapters tend to warm the reader up. From there the book moves on to more complex and difficult problems as it goes along. The last couple of conjectures dealt with, the Birch--Swinnerton-Dyer conjecture and the Hodge conjecture, are the densest to follow (...but Stewart notes of the Hodge conjecture that it "is arguably more representative of real mathematics, as done by mathematicians of the twentieth and twenty-first centuries, than any other topic in this book"). Soon after those chapters Stewart follows up with a lighter chapter titled "Twelve For the Future," briefly outlining 12 more unsolved problems, some fairly well-known. This section ends with the ABC conjecture, and was apparently written before last year's announcement from Shinichi Mochizuki that he had proven the conjecture, as there is no mention of the claimed proof (which has yet to be confirmed, and indeed some say may not be comprehensible to anyone except Mochizuki!).

I suppose my favorite chapter (pardon the bias) is on the Riemann Hypothesis, where Stewart seems to capture in a chapter what others have written whole books about. Another chapter that I found especially good was on the Mass Gap Hypothesis, and more generally on particle physics, but your own interests will determine which chapters you most enjoy. They are all good. This will likely be the initial 'go-to' volume on my shelf whenever I wish to check on something regarding one of these classic problems.

The book ends with a handy 11-page glossary, an interesting set of succinct "notes," and a brief bibliography for "further reading" -- on a side note, I was pleased to see that the brief bibliography cites Matthew Watkins' "The Mystery of the Prime Numbers," a book I've been touting for quite awhile, but which I'd not yet seen referenced by any prominent author (Watkins gets a very brief mention in the body of the book as well).
This is simply a fabulous book for most mathematics enthusiasts... no matter which clone of Stewart's wrote it!

Friday, March 1, 2013

Evelyn Lamb... of Scientific American

Math-Frolic Interview #12

"If you already love math, welcome. If you were traumatized by a math class years ago, welcome. If your relationship with math is complicated, welcome. I hope there will be something here for everyone."
-- Evelyn Lamb, from her first blog post for "Roots of Unity"

Evelyn Lamb is a mathematics writer and post-doc who was a relatively recent addition to the stable of bloggers at Scientific American. Her blog "Roots of Unity" is fittingly subheaded, "Mathematics: learning it, doing it, celebrating it" and her SA profile is here.
If you're not familiar with her, you'll soon feel much more familiar after reading the wonderful, extensive answers she gave to questions I posed for her (and as usual, I've highlighted, in bold, parts of the responses). Enjoy:


1) You mention in your blog bio that you didn't really get interested in math until your junior year of college… that is so contrary to what I usually hear from mathematicians (who often grow up with an unusual and inherent interest in math and numbers from early on). Can you describe a little further what that was like coming to math relatively late in your academic life (did it feel odd? did other math majors look a bit askance at you? was it a smooth or difficult transition?…)?

As a child, there were times that I learned about mathematical concepts that I found really fun and interesting, but I didn't realize they were real mathematics. My dad taught me about bases when I was in elementary school. I learned to count in binary on my fingers, and I loved figuring out how to represent numbers in different bases and the fact that decimal notation is a choice, not something intrinsic to numbers. But I didn't connect this concept to math. Math was where you learned the routine process of multiplying, not the fun process of representing your age in base eight. (And figuring out that no matter what your age, if you represented your age in base (your age), the answer was 10. Whoa!)

In general, I grew up thinking of math as just formulas: you look at a problem, there's one way to do it, you do it, and then you get the one and only answer. I was good at this, but it didn't excite me. I went to the Texas Academy of Math and Science for my last two years of high school. That is a program at the University of North Texas where high school students who are good at math and science take UNT classes during their last two years of high school. There, I went through the calculus sequence to multivariable calculus, so when I got to college, it made sense to me to work on a minor in math because I had so many math credits already going in. My junior year, I took a class that really changed the way I looked at math.

Coming to math so late in the game has been a challenge, and I still sometimes feel "behind." I was one of the top math students at my university, but at the time their math program was not what it is now. My first semester of grad school, I got a big dose of reality when I saw how difficult the qualifying exams were and how much better prepared everyone else seemed to be. My grad program was very small, and faculty and other grad students were very supportive of me. I felt out of my league a lot of the time, but it was internal. No one there tried to push me out or make me feel like I didn't belong.

2) You also mention that an "inquiry-based learning" class is what really turned you on to the beauty/creativity of math. Again, can you say a little more about what were some of the problems/examples that most moved you?

The class, basically "intro to proofs," was taught using the Moore method, or inquiry-based learning, meaning that our professor prepared sheets of definitions, examples, and theorems for us to work on outside of class. During class periods, students would present material for the whole class, and those who weren't presenting would ask questions or point out errors in the proofs. The professor worked very hard to make it a "safe space" for people so they wouldn't feel bad about being wrong. We pointed out errors in each other's work, but it was always done in a constructive, kind manner. That class, more than anything else, showed me that math is a creative discipline.

There were two mathematical concepts that stuck with me the most from this class. The first was proof by induction. Not only did we use this technique, but we also came up with a proof that the technique worked. That was the first time I had really thought about math as theorems and not formulas. I was used to learning a technique and trusting that it worked, not actually understanding why it worked. (My professors had presented proofs of theorems in calculus, differential equations, linear algebra, and so on, but I had always thought of those theorems as times to "tune out" until we got to the part where we used them to solve a problem.)

The second concept was proving that the rationals are countable and the real numbers aren't. I had worked for about a week on a proof that the irrationals were of a different cardinality than the rationals—my intuition said that n^2 just had to be fundamentally "bigger" than n, and there was some kind of "limit" argument that the irrationals had to be more numerous than the rationals because of this. Obviously, my proofs were not correct, and when another student presented a (basically) correct proof, I was very resistant to it. It took a while for me to learn to accept it, but that process of wrestling with the idea for so long was formative for me as a mathematician.

I'm not saying that inquiry-based learning is necessarily the best way to teach all topics, or the best way to teach all students, but I can say that there is a 99% chance I would not be in math today if I hadn't taken that inquiry-based learning class.

3)  How did the idea for your blog, "Roots of Unity," for Scientific American come about?

I had a fellowship at Scientific American during the summer of 2012, which is how I started writing about math and science. Through that, I met Bora Zivkovic, the blogs editor for Scientific American. Both he and my immediate supervisor Robin Lloyd recognize that Scientific American's audience would like to read more math stories, so they were very supportive of my coming on board with my own blog. I'm really grateful to both of them and my other colleagues at Scientific American for encouraging me and helping me find an audience by giving me the Scientific American platform.

[Bora has a knack for finding and promoting blogging talent! and you certainly seem a great fit for SA.]

4)  I would guess that anyone writing ongoing math pieces for Scientific American might feel the long shadow of Martin Gardner over their shoulder… is there some sense of that for you, or are your pieces different enough (and not restricted to recreational math) so that you don't feel that sort of connection?

I definitely feel the shadow of Martin Gardner! I do want to entertain people and help them engage with math, two things that he did very effectively. I do not know very much about recreational math, so I haven't ventured into that world very much yet. And there are already so many places where that is done so well! I will never be Martin Gardner, but I try to see myself as an entertainer at least as much as an educator. For the most part, I want my pieces to make people happy. If they learn something as well, that's a nice bonus. Sometimes I write about things that aren't happy, but I prefer the happy stuff.

5) What are your favorite aspects of mathematics to study or read about? And what is your math post-doc work related to?

My field of study is hyperbolic geometry and Teichm├╝ller theory, which is the study of spaces of hyperbolic surfaces. I use analytic techniques to attack geometric problems. I am a very visual person, and I love the visual aspect of hyperbolic geometry. I love reading (or looking at) books of mathematical art, particularly when it has to do with hyperbolic geometry. I have recently gotten more interested in math history, which I am actually woefully ignorant of. In my work for Scientific American, I have come across some biographies of famous mathematicians and books of ancient Chinese math, for example, that fascinate me. I do love to read popular books about math, in part as professional "research": how do more experienced math writers approach the subject, and what are their personal styles? I am still working on finding my voice and tone, so hearing the masters do it is very useful to me.

6) Who are some of your favorite mathematicians (living or deceased) to read?

I am an academic descendant of Bill Thurston, and his approach to geometry and mathematical thinking in general. He has a famous essay in a 1994 copy of the Bulletin of the American Mathematical society called "On Proof and Progress in Mathematics," which is an interesting read about the way mathematicians should approach mathematics. It has been circulating in my corner of the math research community a lot since Thurston's death in August. (My corner of the research community is probably at least half mathematical descendants of Thurston.)

I've also read two popular math books in the past few months that I really enjoyed: "Measurement" by Paul Lockhart and "The Joy of X" by Steven Strogatz. They are very different from each other, but both are worth a read. I read Measurement twice because I wrote two different book reviews of it, several months apart, and the second time through, I found it even more delightful. Lockhart reminds me of Thurston in some ways: both talk about math as a human activity in ways that speak to me.

One of my uncles gave me Strogatz's book "Sync" back when it was published, and I've tried to keep up with his writing since then. I was very excited that I got to meet him this past summer when I was in Ithaca for my brother's wedding. It turns out he was on my sister-in-law's oral exam committee. She is a grad student in physics at Cornell.

-- I thoroughly enjoyed and reviewed the Lockhart and Strogatz volumes as well, and Bill Thurston was certainly one of the most loved and respected members of the math community.

7) In an earlier piece you wrote that working at Scientific American made you feel like "two different people" --  being a reporter of sorts (educating the public) for SA, but also still wanting to be a discoverer, as an academic mathematician… Now that you're a regular blogger for SA I imagine that writing for the public becomes increasingly smooth and enjoyable over time. How strongly do you still feel pulled in two directions, or are they more integrated by now?

I very much feel pulled in two or more directions, but that is pretty normal for me. I have always had many divergent (sometimes competing) interests, and I feel like I've spent most of my life fighting to keep as many options open as possible. I am just the kind of person who wants to have lots of different mental stimuli over the course of a day or week. I have the luxury this year of establishing myself as a writer/blogger before starting my postdoc. Once I get there, I will have a whole new challenge of balancing my new professional responsibilities with my desire to write about math for a broad audience, but I know a change of scenery will also give me new inspiration.

My writing has given me a lot to think about when it comes to teaching, and I expect and hope that my work on my blog will help me become a more effective teacher.

8) How do you select the topics you post about on your blog?

My Valentine's Day post about continued fractions literally came to me in a dream, but that doesn't seem to be a consistent source of ideas. I don't have a magic formula. I do get some ideas from press releases and arxiv papers, but I also just notice math in my daily life and in popular culture. When you dig far enough, everything in the world is made of math, so it's just a matter of choosing where to dig and how deep. Right now I'm trying to formulate a blog post about why Project Runway is my favorite  math show on TV, for example, mostly because I want to be able to say I'm watching Project Runway for professional reasons. (Nobody steal my idea, OK?)  -- [just a guess, but I don't think you have to worry about that ;-) ]

So far this year, I've been to three large conferences, and I've gotten lots of ideas from them. But I don't have one tried and true way of finding stories yet, which means a lot of the time I put into my writing is "invisible" and just consists in figuring out story ideas and rolling them around in my head until they work. I am naturally attracted to stories that involve math and the arts because I find it easier to draw people into those stories and because I love the intersection, so I like to have an excuse to spend a lot of time thinking about them.

9) To round yourself out a bit, when you're not doing mathy things, what are some of your main interests/hobbies/activities?

I have way too many hobbies! My mom is a musician, and I have been involved in music since I was a toddler. Currently, I play viola with some amateur chamber music groups and sing shape-note music, a kind of early American folk hymn singing. I also sew, which I actually think of as applied mathematics, and I have been trying to learn to crochet. My husband and I live about a mile from Lake Michigan, and when the weather is nice, we like to walk down to the lake and collect beach glass. We also collect it on trips if we're near a shore. We have a few vases and bowls filled with it, and I've used it for some art projects. We also like riding bikes, doing yoga, and playing ultimate frisbee, although we haven't done a whole lot of that recently. We both do a lot of cooking, and we love traveling. Recently, most of our traveling has been to math conferences and to visit family, but we try to work in some personal vacations as well.

10) Any parting words, not covered above, you'd care to pass along to a math-oriented audience?

When you don't know what to do, do something. I think that's important both in mathematics and in life. When I am teaching or tutoring, I find that students get stuck the worst when they are afraid to write anything down before they're absolutely sure they have the right answer. People sometimes think mathematics happens when a smart loner has a sudden bolt of inspiration, but I think much more progress happens when people, often in collaboration, try lots of different approaches to the same problem until something works. At all levels of study, much of mathematics consists of getting used to techniques that you can get an instinctive feel for what technique might work for a new problem. In life, I try to use the same approach. I don't know what I'm doing with my writing exactly, but I'm doing something, and I'm getting a feel for what works and what doesn't, and what kind of math stories people want to read.


THANKS so much, Evelyn, for these great responses and best of luck both with the blogging and your academic future.
Be sure to check out Evelyn's blog HERE, if you haven't already.