...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

Friday, February 28, 2014

A Helping of Friday Potpourri

A compendium of mathy links you might want to check out over the weekend, if you've missed….

1) A "fiendish" set of brain teasers here:


2) If you missed this CBS News clip on math teacher Jim O'Connor, well, stop whatever you're doing and watch it (…and have a kleenex ready):

3) A creative approach to trigonometry here (from the BetterExplained site):


4) Interestingly, just weeks after a Kazakh mathematician claimed a proof (still being studied) of Navier-Stokes equations, none-other than Terry Tao has offered a new approach to the problem:


5) I won't pretend to understand all this digital currency stuff… but that doesn't stop me from finding it fascinating... enter "Riecoin": http://tinyurl.com/kgjg7q4

6) just some fractal fun, Sierpinski style: http://beautyandthemaths.tumblr.com/post/77265096812

...as always, a lot of math education ideas bouncing around the mathosphere, including:

7) another Top 10 issues in math education, this time from Brie Finegold:

8) more on the troubles in math education here, via Slate:  http://tinyurl.com/kfbkedf

9) Meanwhile, Arizona is dumping Common Core; read all about it in these 2 places:

http://www.goodmath.org/blog/?p=2882  (from Mark Chu-Carroll)

http://tinyurl.com/kky7z46  (AZ. newspaper)

10) And Alex Bellos gets schooled on current math education in Britain in this 1/2 hr. podcast:
http://www.bbc.co.uk/programmes/b03szv89 , and I already linked (over at Math-Frolic) to this Conrad Wolfram piece on reforming British math education: http://tinyurl.com/kyp8yto

11) Lastly, not math, but still an interesting post, on who gets hired by Google... where "expertise," even a college degree, is not so important, but here's what is:  http://tinyurl.com/lxny6g9

-- Sunday, or Monday at latest, I should have another interview up here with another cyber math enthusiast, meanwhile enjoy some of the above links… and, your weekend! (and let me know ASAP of any broken links)

Wednesday, February 12, 2014

Cathy O'Neil (mathbabe)... Math Quant Turned Blogger/Activist

 Math-Frolic Interview #20

 "Exploring and venting about quantitative issues." 
   -- "Mathbabe" blog

I've been reading Cathy O'Neil's "Mathbabe" blog off-and-on pretty much since its inception, but either I've changed or her blog has, because for the last several months almost every entry seems like a gem to me.  Cathy is somewhat outside-the-box of the typical math bloggers I follow...  a blogger with a tad more 'attitude' and range of issues.  She is a Harvard (PhD) graduate (also Berkeley and MIT) and a data scientist, who left the finance industry when disillusioned.
Political candidates often talk of having a "fire in the belly," and that's also the sense I've had of Cathy's blog for awhile now. So I was very happy to learn more about the life of the blogosphere's mathbabe, and think you will as well:


1) To start, could you tell readers a little about your diverse background and how you came to be a sort of math "freelancer" and blogger… including when did your interest in mathematics originally arise, and when did you know you wished to pursue it professionally?

I started liking math when I was 4 or 5. I remember thinking about which numbers could be divided into two equal parts and which couldn't, and I also remember understanding about primes versus composites, and for that matter g.c.d., when I played with spirographs and taking note of different kinds of periodicities and when things overlap. Of course I didn't have words for any of this at that point. 

Later on in elementary school I got really into base 2 arithmetics in 3rd grade, and I was fascinated by the representation of the number 1 by 0.9999... in 7th grade. I was actually planning on becoming a pianist until I went to a math camp after 9th grade (HCSSiM), and ever since then I've known. In fact it was in that summer, when I turned 15, that I decided to become a math professor.

Long story short I spent the next 20 years achieving that goal, and then when I got there I realized it wasn't the right speed for me. I went into finance in the Spring of 2007 and was there throughout the crisis. It opened my eyes to a lot of things that I'd been ignoring about the real world, and when I left finance in 2011 I decided to start a blog to expose some of the stuff I'd seen, and to explain it as well. I joined Occupy when it started and I've been an activist since then.

[Because so many carry the stereotyped image of a mathematician as someone standing at a blackboard writing inscrutable, abstract symbols, I think Cathy's "activism" has been one of the most appealing aspects of her blog!]

2) You're involved in quite a number of important activities/issues… what would you list as your most ardent (math-related) goals, for say the next year, and then also longer-term?

My short- or medium- term goal is to write a book called "Weapons of Math Destruction" which I recently sold to Random House. It's for a general audience but I've been giving a kind of mathematical version of it to various math departments. The idea is that the modeling we're seeing proliferate in all kinds of industries has a dark side and could be quite destructive. We need to stop blindly assuming that because it has a mathematical aspect to it that it should be considered objective or benign.

[...Love the title of the book.]

Longer term I want to promote the concept of open models, where the public has meaningful access to any models that are being used on them that are high impact and high stakes. So credit scoring models or Value-Added Teacher models are good examples of that kind of thing. I think it's a crime that these models are opaque and yet have so much power over people's lives. It's like having secret laws.

3) Related to the above, you've been especially outspoken about various financial/banking issues and the "Occupy Wall Street" movement… I have to believe that there are both very rewarding and very frustrating/exasperating aspects to tackling those issues… care to comment?

I'd definitely say more rewarding than frustrating. Of course things don't change overnight, especially when it comes to the public's perception and understanding of complex issues. But I've seen a lot of change in the past 7 years around finance, and I expect to see more skepticism around the kind of modeling I worry about, especially in light of the NSA surveillance programs that people are up in arms over.

4) Your blog covers a wider diversity of topics than most "math" blogs. Sometimes your blogposts seem to be a combination of educating the public while also simultaneously, venting! (indeed your subheading hints at such)… how might you describe your feelings/attitude/mood when writing typical posts? And what are your favorite (math-related) subjects to write about or study?

Honestly blogging has crept into my daily schedule like a cup of coffee in the morning. It would be really hard for me to stop doing it. One way of thinking about it is that I'm naturally a person who gets kind of worked up about how people just don't think about a subject X the right way, and if I don't blog about those vents then they get stuck in my system and I can't move past them. So maybe a better way of saying it is that getting my daily blog on is kind of like having an awesome poop. But then again maybe that's too gross. Sorry if that's too gross.

[Let's just say that I may never think about composing blog posts in quite the same way again! ;-) ]

5) Is "Mathbabe" blog principally "a labor of love" or is it more than that for you (some sort of means to an end)? i.e., You're writing a book and you do speaking engagements, along with other activities… is the blog a mechanism to help promote/sustain those other endeavors, or do you view it as just a recreational side activity?

I've been really happy with a decision to never let mathbabe be anything except fun for me. There's no money involved at all, ever, and there never will be. Nobody pays me for anything, nobody gets paid for anything. I do it because I learn more quickly that way, and it forces me to organize my half-thoughts in a way that people can understand. And although the thinking and learning and discussions have made a bunch of things possible, I never had those goals until they just came to me. 

At the same time I wouldn't call it a side activity either. It's more of a central activity in my life that has no other purpose than being itself.

6)  Go ahead and tell us about the book you have in the works and its timetable...

It's fun to write! I can't believe people are willing to let me interview them! It won't be out for a couple of years. At first I thought that was way too long but now I'm glad I have the time to do the research.

7) How do you select the topic you post about on any given day? And are there certain blogposts you've done that stand out as personal favorites or ones that were the most fun to work on? From the other side, which posts seem to have been most popular or attention-getting with readers?

I send myself emails with ideas. Then I wake up in the morning and look at my notes and decide which issue is exciting me or infuriating me the most. 

I have different audiences that get excited about different things. The math education community is fun, they have a LOT to say on comments. People seem to like Aunt Pythia but nobody comments -- I think it's a guilty pleasure.

[Yes, I was skeptical of Aunt Pythia when you announced it (seemed a bit of a stretch), but it too is a fun read... though I most enjoy the passionate posts about issues tangential to mathematics.]

I guess it's fair to say that people like it when I combine venting with strong political views and argumentation. My most-viewed post ever was when I complained about Nate Silver's book.

8) What are some of the math-related books you've most enjoyed reading and/or ones you would particularly recommend to lay folks?

I don't read very many math books to be honest. I've always enjoyed talking math with people more than reading about it. 

But I have been reading a lot of mathish books in preparation for my writing. For example, I really enjoyed "How to Lie with Statistics" which I read recently and blogged about

Most of the time I kind of hate books written about modeling, to be honest, because usually they are written by people who are big data cheerleaders. I guess the best counterexamples of that would be "The Filter Bubble," by Eli Pariser which is great and is a kind of prequel to my book, and "Super Sad True Love Story" by Gary Shteyngart which is a dystopian sci-fi novel that isn't actually technical but has amazing prescience with respect to the kind of modeling and surveillance -- and for that matter political unrest -- that I think about all the time.

9) Anything else you'd want to say to a captive audience of math-lovers, that you haven't covered above?

Math is awesome!

Thanks so much, Cathy, for filling in a bit about yourself here. Good luck in all your endeavors!
Cathy tweets, BTW, at @mathbabedotorg 
And she did this fascinating interview for PBS's "Frontline" in 2012 (largely on the financial crisis):

Sunday, February 9, 2014

Still More Beauty.... and Appreciation

The previous MathTango posting touched upon the frequent topic of "beauty" in mathematics, and then lo-and-behold just yesterday Nobel physicist Frank Wilczek posted his own brief take on that very topic:


Wilczek links "beauty, prediction and reward" and also "novelty" in a simple and interesting way (though I'm not sure others haven't written similarly before, with different words). Wilczek speculates on why so many people "don't find mathematics beautiful at all, and who in fact fear and hate it," based on his prediction/reward emphasis, and believes his ideas will have "important practical implications for teaching and learning." His piece is very brief but he also mentions having a forthcoming book in-the-works fleshing out the subject more, so something to look forward to!

Slightly relatedly, this weekend I was reading a 1981 essay by R.P. Boas, which included this passage:
"…it was not until I became editor of the [American Mathematical] Monthly that I quite realized how hard it is for mathematicians to write so as to be understood even by other mathematicians (outside of fellow specialists). The number of manuscripts rejected, not for mathematical deficiencies but for general lack of intelligibility, has been shocking. One of my predecessors had much the same experience 35 years earlier.
"To put it another way, why do we speak and write about mathematics in ways that interfere so dramatically with what we ostensibly want to accomplish? I wish I knew."
Knowing and understanding math, has never been a guarantee of ability to effectively communicate mathematical content or beauty to others -- and if it is hard to communicate to one's mathematical peers, how much harder is it to communicate to the wider public. Thus, I think it worthwhile on occasion to salute those who do accomplish that goal, and also acknowledge those who toil away less prominently striving toward such a goal.

So to the Strogatz's and Stewarts, the Devlins and du Sautoys, the Pickovers and Posamentiers, the Hershes and Hofstadters, (and of course to Martin Gardner, who may stand in a class all by himself), and so very many others who do a great job of communicating mathematical material/thinking for a wider audience... and also to those in the blogosphere, and in their personal classrooms, who similarly endeavor to do the same, THANK YOU! Even the titan-likes of Tim Gowers and Terry Tao, when they put their mind to communicating to a broader audience, do so splendidly! It remains astonishing to me, in this culture of such widespread math dread and discomfort, how many wonderful books for a general audience yet appear every year! (thank you also to editors at Princeton University Press and Basic Books, et.al.)  I don't know that there's ever been a better, richer time in history to be a student (or just an interested follower) of mathematics. Enjoy.

Tuesday, February 4, 2014

Should Mathematical Explanation Entail Mathematical Beauty?


Is there any math writer/blogger left who hasn't written about the beauty of mathematics… on multiple occasions? It is an almost overwrought topic that audiences either 'get' by now… or likely will never comprehend. I have an acquaintance who, upon once being told that I was reading a book entitled "Love and Math," responded, "well, THAT'S an oxymoron; those two words should NEVER go together"… I presume she would say the same thing about the phrase 'math and beauty.' :-(

Nonetheless, "Mathbabe" blog has a wonderful new post up (from a guest-poster, not from mathbabe Cathy O'Neil herself) which is a great take on this matter; I recommend it to all even if you've read a plethora of these 'math and beauty' type posts before, not because it necessarily offers something new or profound, but just because it is so well-composed:


Further, the post notes that there will be a conference in Sweden, March 10-12, on this very connection of math and beauty, or as the author puts it, "Specifically, we will look at the question of whether mathematical beauty has anything to do with mathematical explanation. And if so, whether the two might have anything to do with visualization".

By coincidence, this post came along just as I was also reading some old 1960/70's essays on the history and nature of formal/symbolic logic, somewhat dividing that history into the pre- and post-Gödel periods. Anyway, this all got me to thinking how differently (I believe) logic is viewed from mathematics in this "beauty" regard... even though logic is very much at the foundation of mathematics.

Math enthusiasts easily perceive the beauty of their field (and wish everyone beheld it). But I suspect logicians don't perceive their subject in the same way (...but professional logicians please let me know if you do see beauty as an integral, prevalent feature of your field as well).
Formal logic seems to much more aptly fit the cold, dry, analytical (dare I say, boring) stereotype people so often apply to mathematics (not that there isn't any beauty to logic, but that you have to more deliberately look for it to see it, than in math).
The difference between logic and math seems somewhat akin to the difference between machine code (all 1s and 0s) versus the richer, higher level programming languages most people learn, even though the latter are ultimately based, in some sense, on the former. 

I guess I'm wondering if others (especially those more regularly working with academic logic) agree with my impression that logic is less pervaded by "beauty," and more befitting of the common stereotypical view many hold toward mathematics… or, alternatively, if taught and approached correctly, is logic also a matter of under-appreciated beauty?

ADDENDUM: I'll close this out with a concluding quotation from one of the essays I was reading (by Leon Henkin, 1962), which may bear some pertinence: 
"…perhaps of greater significance is the consensus of mathematicians that there is much more to their field than is indicated by such a reduction of mathematics to logic and set theory. The fact that certain concepts are selected for investigation, from among all logically possible notions definable in set theory, is of the essence. A true understanding of mathematics must involve an explanation of which set-theory notions have 'mathematical content,' and this question is manifestly not reducible to a problem of logic, however broadly conceived.
"Logic, rather than being all of mathematics, seems to be but one branch. But it is a vigorous and growing branch, and there is reason to hope that it may in time provide an element of unity to oppose the fragmentation which seems to beset contemporary mathematics -- and indeed every branch of scholarship."