...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.

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"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

Monday, March 17, 2014

John Allen Paulos... Spreading Math Literacy

Math-Frolic Interview #22


"For most nonscientists, what's most important in science education is not the imparting of any particular set of facts... but the development of a scientific habit of mind: How would I test that? What's the evidence for it? How does this relate to other facts and principles? The same, I think, holds true in mathematics education. Remembering this formula or that theorem is less important for most people than is the ability to look at a situation quantitatively, to note logical, probabilistic, and spatial relationships, and to muse mathematically."
                                                                -- John Allen Paulos (from "Beyond Numeracy")


John Allen Paulos was the recipient of the 2013 Joint Policy Board for Mathematics Communications Award, a well-deserved award that puts him in some fine company. I imagine that most readers of this blog have read one or more of Paulos' several books (my own favorite is "Beyond Numeracy"). He's a professor of mathematics at Temple University, with a homepage here: https://math.temple.edu/~paulos/

Enjoy his responses below, and you can follow him on Twitter at: @johnallenpaulos

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1. I'll start with a quirky question: probably most people have middle names, but you actually seem to USE yours all the time (at least I always see you referenced as "John ALLEN Paulos")… can you tell us what, if anything, is the significance of your middle name?

Using my middle name is probably just an inertial continuation of a practice dating from my first writings. I don’t know any deeper reason. Perhaps a soupcon of vanity, narcissism, grandiosity, fear of parakeets? Or maybe it’s related to the fact that I was born on July 4th and when I was a toddler my parents told me the fireworks were for me and thus I grew to believe I needed a grander name. I joked in Innumeracy that I use “Allen” to distinguish myself from the then Pope John Paul. Except in bylines, book blurbs, and public contexts I go by John Paulos, never John Allen Paulos, which in everyday contexts sounds affected.

2) On to my more usual inquiries… Do you recall when you first got interested in mathematics, and at what point you knew you wished to pursue it professionally?

 A few relevant early memories. I was very interested in sports, especially baseball, in grade school and once caught my bully of a math teacher in a mistake. I loved algebra and solved a few problems that no one else in the class did. Also read popular math books. A brash atheist in junior high, I became enamored with Bertrand Russell and learned he was both a philosopher and a mathematician. Despite this attraction to and affinity for math, as an undergraduate at the University of Wisconsin I at one time or another majored or seriously considered majoring in English, classics, philosophy, and physics. Yet I always returned to math.

3) Among the many books you've written do you have a favorite, and are you currently working on a new volume that you can tell us about?

The old saying about loving all your children equally does extend to books. That being said, Innumeracy, A Mathematician Reads the Newspaper, and I Think, Therefore I Laugh are probably the first among equals. Yes, I am working on a new book about the mathematical aspects of biographies.

[hmmm... "mathematical aspects of biographies"... I'm not even quite sure what that means, but sounds interesting!]

4) One of the main focuses of your writing over the years has been mathematical literacy, or "numeracy." It seems to me that math literacy (probably science literacy in general) in this country hasn't changed much over say the last five decades, or has DECLINED! Do you feel the same, and is that discouraging?

 It’s of course hard to generalize about the millions of students in school or college. As with many other domains, there may be a kind of Zipf-like power law in education, some variant of “the rich, get richer (and richer faster).” The tendency can and should be fought, but it’s difficult. Consistent with this idea are the many pockets of pedagogical excellence and mathematical achievement, which are truly stellar. Unfortunately, as you suggest, the mathematical knowledge and understanding of the average person doesn’t seem to have improved much. Most people’s understanding of probability, for example, seem limited to versions of “one in a million,” “50-50,” and “sure thing.”

The internet revolution in digital resources gives me some greater hope for the future… again, would you feel the same, or how do you view the future of math education and literacy in America?

I don’t want to re-enter the math wars. Different approaches work for different people, and whatever approach becomes standard will no doubt be wrong for many. Unfortunately, there is no royal road to mathematics or mathematics education.

5) When you're not reading/doing math, what are some of your other favorite reads, and favorite activities/interests?

 I like to read, of course, unfortunately fewer novels and more blogs and news sites than formerly. We have a summer cabin near Bar Harbor where I like to hike, bike, climb, eat ice cream. Do some of that at home in Philadelphia as well. I also very much enjoy “traveling the world” from Bangkok and India to Peru and Brooklyn.

6) You're a prolific writer, and active on Twitter, so seem a natural candidate for a blog, but I don't think you've ever done one… just not enough time, or some other reason?  But you do write math columns… who are you currently writing for?

 For a decade I wrote the monthly "Who’s Counting" column for ABCNews.com. It dealt with the mathematical aspects, both apparent and implicit, of stories in the news. It was very well-received and I very much enjoyed writing it, but eventually I tired of the monthly regimen. I still write pieces for a variety of publications and am working on the book mentioned above. I do enjoy Twitter, which is consistent with my belief that, with some thought, most ideas can at least be hinted at succinctly. Twitter’s 140 character constraint reduces empty blather and locutions like “at the end of the day.”

7) Probability is a particular interest of yours, and there are so many great counter-intuitive probability problems/paradoxes… do you have some special favorites?
What are your other technical areas of professional interest?


 My Ph.D. was in mathematical logic, model theory in particular, obtained after a futile year spent quixotically trying to come up with a plausible axiom that would show the falsity of the continuum hypothesis. Most, but not all, of my popular writing has centered on probability and adjacent areas, and I think that an understanding of many of the standard probability oddities would be most helpful to people regardless of their primary interests. Among these oddities are real world analogues and illustrations of Simpson’s paradox, prevalence of false positives, ubiquity of coincidences, gambler’s ruin, Banach match book, Buffon needle, conditional probability, coupon-collecting, birthday, Monty Hall, and on and on.

8) People like you, and Drs. Devlin, Strogatz et al. simultaneously teach complex, high-level mathematics at major universities, yet find time to write books at a more general interest level… that's always seemed to me almost like operating in two different worlds -- does it feel that way to you, or is the transition smooth and natural from preparing for an audience of sharp grad students and for the lay public?

 They are different, but in a way writing for a large general audience is more difficult because you can’t assume that your readers possess very much background knowledge. You have to structure your presentation very carefully and sometimes have to choose between clarity and precision. If you can think of a familiar everyday scenario or vignette illustrating a mathematical notion, that is usually preferable to a more formal approach.

 9) I'll end with a broad question if you care to take a stab at it: I think you could be characterized as a political progressive and a scientific skeptic, in addition to being a 'math geek,' and I often find those three traits hanging together. From your own lifetime of experience around mathematicians do you think there is anything about mathematical thinking that tends toward progressivism and skepticism, or is diversity among mathematicians as great as in some other fields?

 I think the three traits do hang together somewhat with, of course, many exceptions. Skepticism and progressivism are natural allies, as are dogmatism and reactionism. Being mathematically savvy or just plain numerate does also tend to make one a skeptic. As for progressivism, reality itself does seem to have a liberal bias.

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Thanks Dr. Paulos for filling in a bit of yourself here. Several of your books are 'classics' in the popular math genre; if any readers aren't already familiar with them, by all means check 'em out, while waiting for his next one!


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