Quite A Week

First, In Memoriam....:



In honor of Sally Ride, who would've turned 64 a few days ago (born the same year as myself!) and Grant Wiggins, who's sudden death this week at ~65 stunned many educators who he touched and influenced (I didn't know him, but surely admired his passion... and passion for what you do in life is what it's all about isn't it!).

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....now on to this week's diverse assortment of links:

1)  On the 5-year anniversary of Martin Gardner's death, Colm Mulcahy paused to contemplate what he wishes he would've asked Martin, but never did (LOTS of links in this piece also):
http://www.huffingtonpost.com/colm-mulcahy/myles-from-mathematics-ma_b_7383794.html

2)  There were a multitude of tribute articles to John Nash this week; three of my favorites:

http://en.chessbase.com/post/john-forbes-nash-1928-2015 (from "Chess News")
http://tinyurl.com/ncj8axm (from "The Conversation")
http://tinyurl.com/ltmzgu6 (from "Bustle")

3)  Nautilus piece on how math was used to catch research fraud:
http://nautil.us/issue/24/error/how-the-biggest-fabricator-in-science-got-caught

4)  A teacher seeks some middle ground in the education debates:
https://thegeometryteacher.wordpress.com/2015/05/22/the-ongoing-debate-direct-instruction-vs-inquiry/

5)  Another delightful post from Ben Orlin, this time on succinctly describing major branches of mathematics (if you're of a certain age, the Beatles' references will crack you up):
http://mathwithbaddrawings.com/2015/05/27/one-word-math-classes/

6)  Scott Aaronson on the NSA and recently-released speculations:
http://www.scottaaronson.com/blog/?p=2293

7)  Keith Devlin tweeted a link to this movie clip problem (from the film "X + Y"):
https://www.youtube.com/watch?v=mYAahN1G8Y8

8)  Hour+ long Soundcloud podcast with Cedric Villani and Michael Harris:
https://soundcloud.com/shakespeareandcompany/cedric-villani-and-michael-harris

9)  Sort of a fun discussion over at Gelman's blog last week about quantitative comparisons (be sure to read the comments):
http://andrewgelman.com/2015/05/23/kaisers-beef/

10)  A great, short profile here of Davidson's Tim Chartier who seeks "the whimsy in math":
http://www.charlottemagazine.com/Charlotte-Magazine/June-2015/The-Nutty-Professor-Mime-Tim-Chartier/

11) A few book notes:

 a)  Evelyn Lamb reviewed two books I've recently also reviewed as well:
http://blogs.scientificamerican.com/roots-of-unity/proof-pudding-and-pi-math-books-that-will-make-you-hungry/

 b)  Jordan Ellenberg's bestseller from last year (and my favorite book-of-the-year for 2014), "How Not To Be Wrong" is now out in paperback:
http://amzn.to/1FPmvzv
...and Max Tegmark's "Our Mathematical Universe" (more physics than math) is also available in paperback:
http://amzn.to/1AtWljo

c)  not math, but feel compelled to note Maria Popova's ("Brainpickings") wonderful review of Oliver Sacks recent autobiography:
http://www.brainpickings.org/2015/05/18/oliver-sacks-on-the-move/

12)  And if you need more hands-on-math there's always LOTS at Mike Lawler's place:  https://mikesmathpage.wordpress.com/


Potpourri BONUS! (extra NON-mathematical links of interest):

1)  The subject of human longevity doesn't usually much interest me, but did enjoy this segment on the topic from last week's TED Radio Hour:
http://www.npr.org/player/v2/mediaPlayer.html?action=1&t=1&islist=false&id=408023437&m=408562493&live=1

2)  This whole business of echolocation in blind humans is simply astounding (what our bodies/senses are capable of is mind-blowing):
http://motherboard.vice.com/read/what-its-like-for-someone-whos-blind-to-see-by-echolocation


Hope everyone finds some interesting things here you missed, and have a great weekend.

Marianne Freiberger... of Plus Magazine

Math-Frolic Interview #32


"My interest in maths popularisation simply comes from the fact that I love the ideas and think that everyone should know about them. It’s almost a cliche, but it’s true: maths is poorly understood and misunderstood by 'the public'....
"Few subjects are as impenetrable to non-experts as mathematics – half of the time we don’t even understand each other’s work! It takes experts to help translate the jumble of symbols and strange words into something that can be understood by the rest of the world. If academics don’t help, then everyone else loses out."   -- Marianne Freiberger


Marianne Freiberger is one of the editors of a site most of us know and love: plusmaths.org  
(If by any chance you don't know of it, go and play around on it for awhile; you'll get lost in all the great articles and other content, including podcasts ).
Plus Magazine also has a Facebook page here:  https://www.facebook.com/plusmagazine
...and tweets here:  https://twitter.com/plusmathsorg

Dr. Freiberger has done a TEDTalk as well:   https://www.youtube.com/watch?v=GwT9ajo7a5Q

The interview is shorter than usual because I had asked Marianne several questions related to British math education which it turned out she didn't feel qualified to respond to, but you can also learn more about her at this "European Women in Mathematics" page:
http://www.europeanwomeninmaths.org/women-in-math/portrait/marianna-freiberger

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1)  How did you first become interested in mathematics, and when did you know you wished to pursue it professionally?

It was at school when I learnt about the epsilon/delta definition of a limit. I was amazed at how such a subtle concept can be captured using a few symbols! I didn’t immediately decide to do maths professionally, but when I found myself in England a few years later and wanted to do a degree, I thought that (not being a native English speaker) maths was the best option since it doesn’t involve writing essays. It turns out it was a great choice because I haven’t looked back.

[Fascinating, I don't think I've ever heard anyone pinpoint the "epsilon/delta definition of a limit" as the thing that turned them on to math! -- just shows the diversity from which one's interest in math can stem from!]

2)  How do you go about selecting the topics you write about at +Plus Magazine?
Also, my sense is that you maintain a greater focus on the foundations, ideas, philosophy, and history of mathematics, than on mathematical procedures/computation...  Is that a fair statement? (...in one place I saw you quoted as saying you were "fascinated by the ideas, but bored by the details" of math... which I can relate to).

In my experience most mathematicians are more interested in ideas than in computational details — but maybe that’s because my background is in pure maths. But also, my co-editor Rachel Thomas and I see Plus as a place where people come to explore the world of maths, rather than find answers to particular problems or learn about techniques — there are other places for that. We’d like to provide the "big picture" that people often lack when it comes to maths, and that involves looking at applications of maths, which we do quite a lot, but also at history and philosophical and foundational issues.

3)  +Plus is now in part an offshoot of the Millennium Mathematics Project -- can you say a little about that effort, and how well it is going so far, for any unaware of it?`

The Millennium Mathematics Project is an umbrella organisation comprising a number of projects. Plus is one of them. The MMP is physically based at the University of Cambridge, but active nationally and internationally. It's about  increasing mathematical understanding, confidence and enjoyment, enriching everyone's experience of mathematics, and promoting creative and imaginative approaches to maths to all ages. Another of its projects is our sister site NRICH which has thousands of free resources for ages 3 to 19. The MMP also comprises maths-themed road shows that visit schools, as well as local activities. You can see all the projects here: http://mmp.maths.org.

The MMP has been around since 1999 and has quite a wide reach. During 2013/14 the online resources attracted nearly 8 million visits and more than 32.6 million pageviews. We worked face-to-face with more than 26,000 students aged 5 to 18, and over 5,500 teachers.  Over 1,500 people took part in our activities in the Centre for Mathematical Sciences in Cambridge.

[Fantastic!]

4)  What are some of your own favorite popular math books or authors that you'd recommend to a general reader? And tell us about your own recent book, with Rachel Thomas, "Numericon.”

It was Ian Stewart (in particular his book “Does God Play Dice?”) who inspired me to do a PhD in maths, in particular in complex dynamics. So he’s definitely one of my heroes. I also really like the books by John D. Barrow (who happens to be my boss, but honest, they’re good) for his clear and easy style and wide range of topics. Mario Livio is another author I like… and there are many more, too many to list!

"Numericon" was the perfect popular maths book for me and Rachel Thomas (the other editor of Plus) to write. Essentially it’s a journey through the land of maths, visiting some of our favourite places, faces and landmarks. Each chapter is headed by a number, which we use as a jumping-off point into some area of maths: from prime numbers, or  the classification of finite simple groups, to climate science and network theory. It was lots of fun writing Numericon — in our time as Plus editors we have come across so much interesting maths and so many fascinating mathematicians; writing the book felt like downloading our favourite stories onto a page.

5)  There's a lot of emphasis today on encouraging more females in mathematical (and other STEM) careers. What was your own experience like following that path, and do you have any advice for young women contemplating a future in mathematics today?

My own experiences have been mostly very positive and I’d encourage any woman who likes maths to go for it. It can be intimidating to walk into a maths department and see mostly white males, but think of yourself in terms of what you have in common with people (a love for the subject) rather than what sets you apart. Also, mathematics offers such a wide range of career options, so if you like maths, you really can’t go wrong with a maths degree.

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Thanks Dr. Freiberger, and continued success with Plus Magazine, a great resource which any reader of this blog should certainly be following.

Br-r-rimming Potpourri

Another quirky, weekly compilation of math bits that I didn't cover at Math-Frolic:

1)  The latest "Carnival of Mathematics" with all its festivities is ready-and-waiting (it includes the infinite Kolakoski sequence which sort of semi-blew my mind!):
http://solvemymaths.com/2015/05/17/carnival-of-mathematics-122/

2)   Not exactly math, but survey research...a fun, longish read from the 'But-tell-us-how-you-really-feel' Dept. (about student-satisfaction surveys in New Zealand):
http://tinyurl.com/mr376yc

3)  A nice 5-minute discussion from TED Ed of the question, is mathematics discovered or invented (this is a good introduction for young people not familiar with the debate):
http://ed.ted.com/lessons/is-math-discovered-or-invented-jeff-dekofsky

4)  Interesting post from Sue VanHattum on her son's transition from previous "unschooling" and homeschooling, to a forthcoming charter school:
http://mathmamawrites.blogspot.com/2015/05/teaching-my-son-post-one-of-many.html

5)  Evelyn Lamb gets a little 'luney' with this great piece on grapefruit (spherical) geometry:
http://blogs.scientificamerican.com/roots-of-unity/grapefruit-math/

6)  A teacher posts some survey results from students... hmmm:
https://fivetwelvethirteen.wordpress.com/2015/05/19/math-survey-students/

...which he followed up on with this extended post:
https://fivetwelvethirteen.wordpress.com/2015/05/21/reflecting-on-mathematics/

7)  Nassim Taleb on probability, Black Swans, fat tails, social science, journalism vs. statistics...:
http://finance.yahoo.com/video/nassim-taleb-black-swans-war-193040925.html

8)  A quick blurb in the NYTimes by Jordan Ellenberg on childhood talent:
http://tinyurl.com/ktpxdsr

9)  Fun read from Ben Orlin on differences between Americans and those silly British ;-) when it comes to math(s):
http://mathwithbaddrawings.com/2015/05/20/us-vs-uk-mathematical-terminology/

10)  This week, "Social Mathematics" blog related the "coastline paradox" to the city of Boston:
http://socialmathematics.net/2015/05/20/measuring-boston-coastlines-with-increasingly-tiny-measuring-sticks/

11)  And another elementary(?) puzzle hit cyberspace with Alex Bellos reporting it here:
http://tinyurl.com/m8hnj9c
...and Presh Talwalkar quickly posted an analysis of it at "Mind Your Decisions":
http://tinyurl.com/mvdjtsw

12)  Ivan Oransky and "Retraction Watch" covered another widely cited study (including by NPR's "This American Life"), which has now been retracted for fraud:
http://tinyurl.com/luqvdg5

...Another embarrassment for the journal Science, as well as all involved -- there is even greater ease and incentive to fake data these days, in some fields at least, than there was 40 years ago... and, it was easy enough back then. Moreso than acknowledged, science operates on an honor system. oy veyyy...

13)  A podcast interview with the excellent math/science journalist Erica Klarreich (who I interviewed in April), with a lot of info on math journalism:
http://www.acmescience.com/2015/05/episode-59-erica-klarreich/

14)  A thought-puzzle from Futility Closet:
http://www.futilitycloset.com/2015/05/20/ride-sharing/

15)  Mike's Math Page: as always, chockfull of good weekly stuff: https://mikesmathpage.wordpress.com/

16)  And it was a busy week here at MathTango: an interview with philosopher Penelope Maddy last Sunday, a book review ("How To Bake Pi") on Wednesday, and already another interview this coming Sunday!


Potpourri BONUS! (extra non-mathematical links):

1)  A surprisingly touching bit from NPR's Marketplace (it'll bring a smile):
http://www.marketplace.org/topics/your-money/transaction-hawaii-condo

I usually use somewhat lighthearted, newsy, or sciencey items for the potpourri bonuses, but this one, that seemed worth passing along, is a less pleasant topic (children dealing with death/grief):

2)  Episode #3 from last week's "This American Life":
http://www.thisamericanlife.org/radio-archives/episode/557/birds-bees?act=3


["Bonus potpourri" picks often come from podcasts, especially NPR programs I hear in podcast form, but the podcast universe keeps growing and growing. In addition to NPR I'm aware of Panoply, Gimlet, Wiretap, the 7th Avenue Project, Love + Radio, and Stitcher listings, but if you know of other great podcasts touching on science, human behavior, or just society and culture, that are definitely worth-a-listen let me know your favorites (...not that I even have time for any more!)]

ADDENDUM: I've now learned of a nice list of "best podcasts" here:
https://medium.com/thoughts-on-media/a-huge-collection-of-the-best-podcasts-d97a13608bb4

Category Theory, Not Quite Fully Cooked

"How To Bake Pi" by Eugenia Cheng

[In Britain, this book goes under the title, "Cakes, Custard and Category Theory," a title I prefer!] 

An intrinsic hazard of reviewing media, be it movies, TV, plays, music, books etc., is that 'expectations' play a significant role in any judgment.
I like Eugenia Cheng's new book, "How To Bake Pi," and recommend it, and believe it will be on my year-end top 10 list... B-B-BUT I suspect it won't be in the upper tier of that list. It didn't quite live up to the high expectations I had for it, in a year (that isn't even half-over) with many excellent popular math volumes already out.

Very oddly, Cheng's book appeared almost the same week as Jim Henle's "The Proof of the Pudding," which I reviewed HERE -- two books sharing the unusual approach of combining mathematics and kitchen recipes! Other than the analogies to cooking, there is little similarity between the volumes however, and to my surprise, I actually enjoyed the Henle offering more, though Cheng's effort is more substantive, serious, and covers matters I specifically wanted to learn about.

"How To Bake Pi" is divided into two broad parts, 1) on what mathematics is, and 2) on category theory. Structurally, it reminds me of Paul Lockhart's "Measurement," which was also divided in two parts, and in both instances the first part is the easier, faster read, while the second is a heavier slog (for Lockhart it was "size and shape" largely on geometry, versus "time and space" largely on calculus).

"...Bake Pi" begins, simply enough, trying to explain "what math is," and in the process, demolish preconceptions that many hold. Cheng focuses on "abstraction" and "generalization" as key elements of mathematics. The author does a good job of explaining "abstraction," which involves taking away all the "clutter" or non-essential components of an idea or problem, and reducing it to bare necessities.
She further notes that mathematics is "different" from "science," where evidence is key. Instead, in math, "logic" is what drives thinking forward. She goes on to talk about "principles," and "process," leading to "generalization" and eventually "axiomatization." With analogies and examples Cheng does a good job of walking the reader through this garden of mathematical features.
Similar to Jim Henle's book, each chapter here begins with a kitchen recipe of some sort -- I didn't find Cheng's recipes as mouth-watering as Henle's, but their real purpose is to make some point via analogy that readers can relate to.

I enjoyed the whole first half of this book (especially the wrap-up eighth chapter), as Cheng delineates what mathematics is really about, for those who have the misperception of math as just numbers, computations, and memorization. I'm not fully comfortable though, with her conclusion that while "life is hard," "math is easy." I think math (and specifically, abstraction) is genuinely hard for many individuals (and that is regardless of how it is presented). It can make folks feel more frustrated or inferior if they repeatedly hear that 'math is easy' while they continue to struggle with it. I prefer Paul Lockhart's take when he writes in his book "Measurement," that:
[math is] "very hard work... Be prepared to struggle, both intellectually and creatively. The truth is, I don't know of any human activity as demanding of one's imagination, intuition, and ingenuity."

[There is also a greater sense of accomplishment, even exhilaration, for kids succeeding in math when they think it challenging rather than 'easy' -- somewhere there must be a middle-ground between scaring them by saying it's hard, and frustrating them by saying it's easy!]

Chapter 9, the beginning of Part 2 of Cheng's volume, starts off innocently enough, explaining that "category theory," which began as a study of topology, is "the mathematics of mathematics" or what can be called "metamath." The focus is on relationships and structure, but this is where the book begins faltering a bit.  Despite Cheng's earnest efforts, I still did not come away from Part 2 feeling a deep grasp of just what category theory is, how it is used, or what it's main differences/advantages over set theory are, though possibly a second-reading will help clarify what a first reading left fuzzy. I was also hoping to learn more about the connections between category theory and "type theory" or "homotopy type theory (HoTT), but these go unmentioned in the book. Perhaps I hoped for more than is even possible in a volume aimed at a general audience. [In a coincidental stroke of timing, Quanta Magazine just published a fine introductory piece to some of these latter topics:
https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/ ]

Another reviewer of the book (at MAA) writes, "I can't help but feel the target audience for this book is very small (in particular I can't think of a specific person I would give it to as a gift)..." I think that's overly-harsh, but I do understand the sentiment -- actually the "target audience" is quite broad, but I'm less certain how well-illuminated and satisfied readers will be on the central topic of the volume: category theory (...yet, there may be no other introductory books on the subject to compete with it).

In fact while making my way through Part 2 of the volume, I wondered whether a different publisher/editor might have fashioned a better result. Could Princeton University Press (my favorite publisher) have rendered a sharper edition of this volume than did Basic Books, the actual publisher (Basic publishes many good popular math volumes, but I usually feel their presentation is a notch below Princeton).
Or, alternatively, I wondered how an explanation of category theory from two of my favorite math explicators Steven Strogatz or Keith Devlin (if they could even expound on the subject) might have differed from/improved upon Cheng's effort.
But Cheng is clearly passionate about her subject, loves teaching, and I do hope will give us additional popular math offerings in her future (...and for now hers may be the best introduction to category theory available).

So by all means consider this book, and especially so if you've been waiting for a primer on category theory to come along... just don't presume that that murky topic will be made crystal clear by the time you finish the volume.

Natalie Angier's favorable review of the book is here:
https://theamericanscholar.org/a-taste-for-higher-math/#.VPjByIY8LCQ

...also worth noting that Cheng participates in a YouTube channel that further reviews category theory:
https://www.youtube.com/user/TheCatsters/featured

Penelope Maddy... the Continuum Hypothesis Beckons

Math-Frolic Interview #31

"Penelope Maddy is the candy-store kid of metaphilosophical logic and maths. She’s stocked up with groovy thoughts about the axioms of mathematics, about what might count as a good reason to adopt one, about mathematical realism, about Gödel’s intuitions, naturalism, second philosophy, Hume and Quine, world-word connections, about where mathematical objectivity comes from, about the limitations of drawing analogies, about depth, about Wittgenstein and the logical must, about the Kantianism of the Tractatus and about the relationship between science and philosophy."  -- Richard Marshall

After a couple dozen interviews with bloggers, teachers, and popular math authors, I realized one area I'd not heard from yet was "philosophy of math," so that omission is corrected today!
Penelope Maddy is Distinguished Professor of logic and philosophy-of-science at the University of California Irvine, and well known in philosophy circles for her explorations of the foundations of logic and math.

A brief Wikipedia page covers a little more of her background and publications here:

http://en.wikipedia.org/wiki/Penelope_Maddy

Without further adieu, here are her responses to some questions I posed:
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1)  My understanding is that your interest in mathematics was initiated by set theory, at an age when I think most young people are more interested in computations, recreational math, or methods (not theory).
Can you describe what it was about set theory that appealed to you at a young age?

What first caught my attention was the rigorous proofs in high school geometry -- the idea that pure reasoning could squeeze so much information out of such simple assumptions.  Algebra, word problems, had something of the same charm:  you were given some meager bits of information, and by manipulating equations, you could answer questions you wouldn't have thought answerable.  But I really caught the bug in one of those great NSF summer programs for high school kids, where I learned that 2+2=4 could be proved in naive set theory!  I soon read about transfinite numbers (what?! more than one kind of infinity!), but the topper was Cantor's Continuum Hypothesis.  This is Cantor's answer to the first question that arises in the exponentiation table for transfinite numbers, a question that involves the very structures used scientifically to model space and time -- and it turns out not to be provable or disprovable from the accepted axioms that found all the rest of classical mathematics!  What could a solution to that kind of problem even look like?

Well, soon I was off to UC Berkeley to study set theory.

2)  What would you say are a couple of the most significant unresolved problems in the philosophy of mathematics these days?

And what questions/issues (if different from above) do you spend most of your own time working on these days?

Since the Continuum Hypothesis remains unsettled, I'd have to list it as a significant unresolved problem.  What I've been trying to do on the more philosophical end of things is to develop a cogent picture of what would count as a resolution and why.

[...I asked Dr. Maddy to flesh this out a bit more and explain how she approaches such a resolution, given that within Zermelo–Fraenkel set theory (with the axiom of choice, ZFC) mathematicians generally find CH UNdecidable.]:

Everyone pretty much agrees that CH can't be settled from ZFC.  You have to buy that ZFC is consistent (otherwise it proves both CH and not-CH!) and that our formal model of 'proof' captures what mathematicians actually do well enough for these purposes -- but most people accept these things.

So, as you suggest, the obvious way to try to resolve CH is to look for a new axiom to add to ZFC.  Some mathematicians resist this idea, taking ZFC to be somehow sacrosanct, so that independence from ZFC is the end of the story, but when you examine the reasons why the axioms of ZFC are accepted, it doesn't seem so far-fetched to think that there might be others that could pass similar tests.  There are various candidates up for debate, and for a philosopher like me, there's the fascinating problem of understanding what kinds of considerations should count one way or the other.

[...I further inquired if she had her own hunch regarding the truth/falsity of CH?]:

Years ago, when I was a young math major, the consensus among set theorists willing to take the question seriously (that is, among those who didn't take independence from ZFC to be the end of the story) was that CH is not only false, but badly false.  (If you think about the real line, CH says there's no set of points with size in-between that of the set of points corresponding to natural numbers only and that of the set of all points on the line.  For CH to be 'badly false' is for there to be sets of lots of different sizes between these two.)  Since then, it's come to seem more plausible that it's false but not badly so (say only one intermediate size) or even true.  There are potential axioms that settle it various ways, but no clear winner. 

So the truth is that I don't have a hunch.  It could even turn out that two conflicting new axiom candidates might have all the attractions one could ask for, and that set theory would end up bifurcating.  This would require a major rethinking of what set theory is supposed to be, but stranger things have happened.  For what it's worth, on this one I do have a hunch -- I don't think set theory will bifurcate. 

3)  I recently read a quote from a mathematician saying, "There are two kinds of mathematics: applied mathematics and mathematics that is not yet applied."
How do you feel about that? Is there any such thing as "pure mathematics" that will never have any practical application?

In the times of Newton and Euler, mathematics was just the study of the mathematical features of the world; as we might put it, all math was applied.  Over the course of the 19th century, this changed, for a number of reasons:  mathematicians began to pursue questions of purely mathematical interest, the rise of non-Euclidean geometries implied that at least some geometries were independent of the world, the role of atomic theory in physical chemistry and kinetic theory gradually revealed that differential equations, formerly regarded as the language of 'the great book of Nature' (Galileo), are actually 'a smoothed-out imitation of a really much more complicated microscopic world' (Feynman).  The idea that mathematics shouldn't be tied down to physical applications became the orthodoxy of modern pure mathematics.  It's certainly true that a surprising variety of these pure mathematical theories have ended up being useful in natural science after all, but I don't see any reason to assume that this will be true for every pure mathematical theory.

[...Dr. Maddy has a paper, which she cites further down (question #6) and I link to, that addresses this topic in greater detail.]

4)  For many professional mathematicians, Martin Gardner played a significant role in steering them toward math at a young age. Did Gardner (or recreational math more generally) have much influence on you?
(I might note that Gardner's undergraduate degree from U. of Chicago was actually in philosophy, and he was a vocal mathematical Platonist.)

Alternatively, any significant influence from logician Raymond Smullyan?

I guess I was more fascinated by questions about what mathematics is and how it manages to do what it does than by particular mathematical or logical puzzles.

[...I'll just note that Gardner did write philosophical essays as well, and was heavily influenced by his own professor, Rudolf Carnap and logical positivism, though indeed his main influence on other mathematicians was through his "Recreational Games" column for Scientific American.]

5)  As you probably know, physicist Max Tegmark promotes an ultra-Platonist view that mathematics is ultimately ALL there is in the Universe; that fundamentally everything is reducible to mathematical description or relationships... 
How do you view Tegmark's outlook? Do you know of any philosophers who share Max's view?

In ancient times, the Pythagoreans thought that 'all is number', and they were stunned when it turned out that the square root of two isn't even a ratio of numbers.  Nowadays most philosophers think of mathematical things as abstract -- without location in space and time, without causal powers -- and in this way quite different from ordinary objects.  But there are those in the philosophy of science who take the position that 'everything is structure', and I suppose that might be a version of Tegmark's position.

6)  For readers who may be inclined toward mathematics, but are unfamiliar with "philosophy of mathematics" could you recommend a couple of "primer" books that are a good introduction?
And do you have any Web-accessible pieces of your own on math philosophy that you can recommend to non-specialists?

Let's see ...

Gottlob Frege,  Foundations of Arithmetic (1884) is a classic text. 

A couple of nice contemporary introductions:

Stewart Shapiro,  Thinking about Mathematics 
Mark Colyvan,  An Introduction to the Philosophy of Mathematics

People might enjoy a paper of mine called 'How Applied Mathematics Became Pure'.

7)  Finally, David Hilbert famously said that if he ever woke up from a 1000-year nap, the first question he'd immediately ask would be, "Has the Riemann hypothesis been solved?"
1000 years is too far off to even imagine, but if YOU were to come back, say 200 years from now, what mathematical or philosophical question would you most like to find settled?

This will come as no surprise:  I'd want to know what ultimately became of the Continuum Hypothesis!
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Thanks for taking part here Dr. Maddy. Nice hearing from someone with a little different approach to mathematics than folks I usually interact with on this blog (wish I knew enough philosophy of mathematics to ask better/deeper questions!) And good luck with that Continuum Hypothesis!... just don't let it drive you batty like it did a previous fellow! ;-)

Another, longer, more detailed, transcribed interview with Penelope (from earlier this year) is also online:
http://www.3ammagazine.com/3am/the-stuff-of-proof/

Finally, this is the fourth female interviewee in a row that I've had here folks (and I think another is lined up for late June?), so are there any males out there who like math and are any good at it, who'd care to be interviewed? ;-))  Let me know....

This Week's Math-Mix

some maths from the week:

1)  The 2015 topic for the FQXi annual essay contest was "Trick or Truth: the Mysterious Connection Between Physics and Mathematics." Peruse the entries here:
http://fqxi.org/community/forum/category/31424?sort=community

2)  Another interview with Cedric Villani:
http://www.huffingtonpost.com/2015/05/07/cedric-villani-mathematic_n_7223966.html

3)  Just another lesson in Bayesian statistics, the NSA, and terrorists:
http://headinside.blogspot.com/2015/05/simple-math-not-so-simple.html

4)  Perhaps it's just me, but here's an example of the sort of socio-neuro-psycho-biologic study (producing a mathematical formula for "happiness") I don't much enjoy reading :
http://www.pnas.org/content/111/33/12252.full

5)  VERY interesting Numberphile interview with mathematically-inclined billionaire investor James Simons:
18 min. condensed version: https://youtu.be/gjVDqfUhXOY
full length, hour-version:  https://www.youtube.com/watch?v=QNznD9hMEh0&feature=youtu.be

6)  Computer scientist Bill Gasarch tries to use logic on the Republican presidential candidates, and it's not pretty:
http://blog.computationalcomplexity.org/2015/05/the-law-of-excluded-middle-of-road.html

7)  One blogger's response to the b-b-b-bogus notion that "teachers stop improving after three years":
http://tinyurl.com/qybl559

8)   Michael Harris on the recent Breakthrough (mathematics) Prize Laureates panel discussion:
https://mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/

9)  "5 Reasons to Teach Mathematical Modeling" from American Scientist:
http://www.americanscientist.org/blog/pub/5-reasons-to-teach-mathematical-modeling

10)  Peter Cameron offers an overview of "Mathematics, Poetry, and Beauty" by Ron Aharoni:
https://cameroncounts.wordpress.com/2015/05/11/mathematics-poetry-and-beauty/

11)  Interesting video on the 3-D Gömböc object having just one stability point (h/t Steven Strogatz):
https://vimeo.com/51887199

12)  Podcast interview with Jim Henle, author of the wonderful "The Proof and the Pudding":
http://slice.mit.edu/2015/05/12/alum-books-podcast-the-proof-and-the-pudding/

13)  Early in week I wondered here at MathTango how many mathematicians ever experience a sudden loss of passion for their subject? ...a question inspired by an earlier post at Mike's Math Page:  http://tinyurl.com/q355eyo

==> Also, be sure to return here Sunday morning when I'll have Interview #31 posted.


Potpourri BONUS! (extra non-mathematical links):

1)  just a nice tweet from the week:
https://twitter.com/CaseyHayden1/status/598380098409144320

2) ...and important news coverage from the New Yorker:
http://tinyurl.com/ng4yuhj

Mathematics: Momentous or Mundane?

Giving pause...:

Over the weekend Mike Lawler, posted about two items ("two incredible descriptions of what it is like to do math research") he wished he had seen in graduate school in order to maintain his avid prior enthusiasm for math (one is a Numberphile interview with Ken Ribet, and the other is Cedric Villani's current book, "Birth of a Theorem"):

http://tinyurl.com/q355eyo

The post contains these sentences that I find oddly-riveting about Mike's sudden loss of interest in math after a 5th-grade-to-grad-school infatuation with the subject:

"Towards the end of my third year in graduate school, though, I completely lost interest in math. It didn’t happen gradually, either – I just woke up one day and wasn’t interested in math anymore. I’ve never known why."

How bizarre is that??? But then I know that I too sometimes have flashes of wondering if perhaps mathematics is just a boring .00001% smidgen of what there is to know out there, and that real knowledge resides elsewhere in some metaphysical/paranormal/spiritual/mystical/other-worldly realm... the power of mathematics being but an illusion! A bit reminiscent of the 2nd Bertrand Russell quote I employ above:
"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)

That was Russell summing up close to 70 years of philosophical contemplation. ...Frustration, or epiphany?
(Yesterday at Math-Frolic, I used quotes from Richard Feynman to stress that "UNCERTAINTY" is the hallmark of all our knowledge.)

On-the-other-hand, we have current-day physicist Max Tegmark arguing that ALL there is to the Universe is mathematics... ultimately, there is nothing else:



(Max's book "Our Mathematical Universe" HERE.)

Sometimes math seems like a Necker Cube, changing appearances when stared at long enough... penetrating and insightful one moment, trivial and mundane the next.

Anyway, I'm left to wonder, do other mathematicians experience the flashes of doubt and lapses in math-veneration of Lawler and Russell (and me), from time-to-time??? Or are these rare occurrences, from too much beer and pepperoni pizza? ;-)  Anyone...?

Weekly Linkfest

Some mathiness you might've missed:

1)  More and more of these 'traveling salesman'-like algorithm stories are showing up in the popular press:
http://tinyurl.com/oslersw

2)  John McGowan reviews (and recommends) "Statistics Done Wrong: The Woefully Complete Guide" by Alex Reinhart:
http://math-blog.com/2015/05/04/review-of-statistics-done-wrong-the-woefully-complete-guide/

3)  Spurious correlations (I'm shocked, SHOCKED I tell you!) via Deborah Mayo:
http://tinyurl.com/mhhdrrj

4)  Teaching 'mathematical modeling' to improve the experience of middle and high school students:
http://www.americanscientist.org/blog/pub/5-reasons-to-teach-mathematical-modeling

5)  Ben Orlin (and his doodles) on why 'good questions' are the ammo and fuel of mathematics, and thus a precious resource:
http://mathwithbaddrawings.com/2015/05/06/america-will-run-out-of-good-questions-by-2050/

6)  How computers have changed the nature of mistakes in math:
http://nautil.us/issue/24/error/in-mathematics-mistakes-arent-what-they-used-to-be

7)  Interesting piece on number glitches leading to computer malfunctions:
http://www.bbc.com/future/story/20150505-the-numbers-that-lead-to-disaster

8)  Jo Boaler's latest piece trying to debunk commonly-held misconceptions:
http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/

...and, by the way, Keith Devlin writes supporting (again) Jo's work here:
http://devlinsangle.blogspot.com/2015/05/time-to-re-read-or-read-whats-math-got.html

9)  Eugenia Cheng's new book "How To Bake Pi" is getting plenty of well-deserved attention around the Web. Almost certainly the best introduction to 'category theory' around for a general audience. (I'll have a review up at some point.)
...and perhaps my favorite tweet-of-the-week (with a link to xkcd) came from Dr. Cheng :-):
https://twitter.com/DrEugeniaCheng/status/596538673736192000

10)  On Twitter, Edmund Harriss passed along this recent YouTube clip of Philip Wadler explaining a lot about "computability theory" in under 9 minutes of education + laughs:
https://www.youtube.com/watch?v=GnpcMCW0RUA

11)  Lest I forget, someone named Mike usually has some interesting lessons going on at his domicile:
https://mikesmathpage.wordpress.com/


Potpourri BONUS! (extra non-mathematical links):

  Last week, TEDRadio Hour replayed this 12-minute episode with the incredible Diana Nyad:
http://www.npr.org/2014/07/18/331332721/what-does-it-take-to-dive-into-dangerous-waters

Weekly Math Grab-bag

Another grand week in math cyberspace:

1)  Some star geometry from Futility Closet:
http://www.futilitycloset.com/2015/04/25/star-power-2/

2)  Evelyn Lamb interviewed two math communicators, Katie Steckles and Laura Taalman, last week:
http://tinyurl.com/kuyhjcb

Will quickly mention too that Evelyn has chosen one of my very favorite 2014 books, Matt Parker's, "Things To Make and Do in the Fourth Dimension" as an adjunct text for one of her math classes.

3)  Patrick Honner posted about the $25,000 Rosenthal Prize for innovation in math teaching, for those who may wish to apply for it:
http://mrhonner.com/archives/14799

4)  A nice problem from Stephen Cavadino:
https://cavmaths.wordpress.com/2015/04/23/equal-products/

5)  Alex Bellos on "The Travelling Politician Problem":
http://tinyurl.com/lgw6e7e

6)  The ills of bar graphs:
http://www.nature.com/news/bar-graphs-criticized-for-misrepresenting-data-1.17383?WT.mc_id=FBK_NatureNews

7)  Anniversary of Ramanujan's death:
http://www.huffingtonpost.com/amir-aczel/homage-to-a-mysterious-ge_b_7113474.html

8)  A conversation transcript with Cedric Villani about his Fields Medal-winning work and recent book, "Birth of a Theorem":
http://tinyurl.com/nx7y6x9
also, Nassim Taleb loves Villani's new book:
http://www.amazon.com/gp/customer-reviews/R21UUMQ8KAGPT9/ref=cm_cr_pr_rvw_ttl?ie=UTF8&ASIN=0865477671

9)  New Rubik's Cube solution record set last weekend, now down to 5.25 seconds!
http://boingboing.net/2015/04/28/watch-solving-a-rubiks-cube.html
Now, I want to know how long it takes to RE-SET a Rubik's Cube back to a 'random' starting position... and what does all this have to say about P vs. NP ;-)))

10)  A little bit from the creator of Ken-Ken puzzles:
http://www.deseretnews.com/article/865627475/Have-fun-and-do-basic-math-with-KenKen-puzzles.html

11)  Science/physics writer Margaret Wertheim interviewed last weeked on NPR's "On Being" (including some math):
http://onbeing.org/program/margaretwertheim-the-grandeur-and-limits-of-science/7472/audio?embed=1

12)  Seems like P-andora's Box has been opened with p-values... Good, bad, and mediocre p-values from Gelman:
http://andrewgelman.com/2015/04/30/good-mediocre-bad-p-values/ 

13)  Deborah Mayo on "junk science" at the FBI:
http://tinyurl.com/kfkeqd2
(which links in turn to this Wash. Post piece on suspended testing at the D.C. DNA crime lab:
http://tinyurl.com/qzdecz9 ) 

14)  David Bressoud warns of a "perfect storm" brewing in higher math education:
http://launchings.blogspot.com/2015/05/calculus-at-crisis-i-pressures.html

15)  Last weekend, I reviewed Jim Henle's wonderful new book, "The Proof and the Pudding":
http://mathtango.blogspot.com/2015/04/jim-henle-serves-up-math-piping-fresh.html 

16)  Am passing along so many links already this week I won't even bother to mention "Mike's Math Page," with its plethora of weekly content here ;-):
https://mikesmathpage.wordpress.com/



Potpourri BONUS! (extra non-mathematical links):

1)  As a Freeman Dyson fan, will just note that he has a new volume out, "Dreams of Earth and Sky," a compendium of book reviews he did for The New York Review of Books. I especially enjoyed the second half of the book (though no math content):
http://www.amazon.com/Dreams-Earth-Sky-Freeman-Dyson-ebook/dp/B00N6PBDPC

2)  Will close out with this posting (that contains no math) from the "Delta Scape" math blogger/teacher, because I suspect most of us can never be reminded too many times of "What Matters":
http://deltascape.blogspot.com/2015/04/what-matters.html