In the spirit of Hortense's Faceoffs, here goes:

Danica McKellar played Winnie Cooper on The Wonder Years, then went on to study math at UCLA, help prove the Chayes-McKellar-Winn theorem, become the only undergraduate to speak at a statistics conference, and write two books, Math Doesn't Suck and Kiss My Math. She also continues to act.

Danica Patrick started racing go-karts at age 10, was the first woman to win an IndyCar race, and this year placed third in the Indy 500.

Advantage: McKellar, for renaissance-womanness.

Danica McKellar posed in lingerie for Stuff, and a swimsuit for Details.

Danica Patrick posed in a bikini for Sports Illustrated (twice) and in a minidress for Playboy.

Advantage: Tough to call, but Stuff folded, so you can only find McKellar's underwear photos at places like Guns, Girls, and Other Things and, um, GolfHos.com. So, advantage goes to Patrick, I guess.

Danica McKellar did a Volkswagen commercial once, but she also did public service announcements for a Math-A-Thon to fight childhood cancer
and spoke before Congress about getting more women and minorities involved in math.

Danica Patrick played out several frat boy fantasies in her GoDaddy commercials: showering with another woman, and watching a hot female cop strip and pole-dance (this always happens when you speed).

Advantage: Hmm, taking a shower vs. doing math while fighting cancer. McKellar wins.

On girliness, Danica McKellar says,

I think that being girly, and playing with glamorous make-up and fashion is fun. I don't see anything wrong with it, as long as you don't think that it's the most important thing. [...] To all those who'd say or argue are you dumbing down math for girls?' I'd say, 'only if you think there's something inherently dumb about being girly.'

And Danica Patrick says,

There's nothing I can't do in a race car because I'm a girl. These days I love being a girl.

Advantage: Both seem comfortable with both their sexuality and their chosen career. Draw.

On intelligence, Danica McKellar says,

I certainly want to do my part to show girls that the more you develop your intelligence, the better equipped you're going to be able to handle the decisions you'll be making in your life. And hopefully you'll make better decisions, and not think that you need to be reckless and irresponsible in order to be glamorous.

And,

To all those who'd say or argue are you dumbing down math for girls?' I'd say, 'only if you think there's something inherently dumb about being girly.'

But Danica Patrick says,

I've never claimed to be a handy person. [...] I used to be able to do a lot of stuff. I'm sure I still could, but I play dumb and say I don't know how. It's easier when you don't have to do it.

Advantage: McKellar.

The verdict: While McKellar's Stuff spread crosses the line between being comfortable with your body and using it to further your brand, her brand still has a lot more substance than Patrick's. Both women inhabit sort of uncomfortable territory — by being sexy and successful, are they showing girls merely that it's possible to be both, or that they must be both? McKellar is more firmly in the former camp, spending a lot more time telling girls they can achieve — and achieving herself — than she does posing, showering on television, or talking to Sports Illustrated about not wearing underwear. And while Patrick's image may have something to do with the sexist nature of sports culture (Sports Illustrated asked her about underwear, after all), she seems to be buying into this culture wholeheartedly. McKellar's not perfect, but of the two Danicas, we'd still rather see her on a teen girl's wall.

What Danica Patrick Could Do for Nascar, Sponsors [AdAge]
Danica McKellar [Official Site]
Danica Patrick's Q&A [Sports Illustrated]
Danica Patrick 20Q Interview [Playboy]
Danica McKellar [Wikipedia]
Danica McKellar Interview [UGO.com]
Danica Patrick Shower Commercial For The SuperBowl 2009 [YouTube]
Speeding - Internet Only [Commercial, GoDaddy.com]

Inspired in part by Larry Summers's comment that "issues of intrinsic aptitude" were behind the gender gap in math performance, Professors Janet Hyde and Janet Mertz of the University of Wisconsin-Madison decided to review the available evidence and see if boys consistently outperformed girls at the highest levels. Summers's claim — and one accepted by many others — was that while girls might perform as well as boys on average, boys had a greater variability of mathematical aptitude and thus might always dominate in the upper echelons of mathematics. No woman, some note, has ever won the Fields Medal, math's most prestigious honor. But Hyde and Mertz found that the gap between boys and girls at the top levels of achievement did not persist throughout the world, and was smaller in countries with greater gender equality.

In Iceland, Thailand, and the UK, 15-year-old girls outnumbered boys at the top levels of math achievement. In most countries studied, girls' math skills were just as variable as boys', and in the Netherlands they were actually more variable. In general, countries where girls matched or outperformed boys were also countries with high gender equality — like Denmark, Iceland, in the UK. All of these are in the top twelve — the US is 31, right before Kazakhstan. This suggests that culture, not biology, is holding girls back in countries where boys still outperform them.

Hyde and Mertz found that the gender gap in math doesn't even hold across all ethnic groups in the US. For Asian-Americans, more girls than boys scored in the top 1% in one battery of tests. Essentially, Summers's claim of greater variability seemed only to apply to white American kids. Mertz says, "U.S. culture instills in students the belief that math talent is innate; if one is not naturally good at math, there is little one can do to become good at it. In some other countries, people more highly value mathematics and view math performance as being largely related to effort."

It's no surprise that in a country where math skill is assumed to be innate, and where prominent people tell girls they have less innate skill, that girls might not always measure up to boys. We know that negative stereotypes can affect performance, but even in the face of people like Summers, girls in the US are catching up to boys. Girls now take high school calculus at the same rate as boys, and 30% of math doctorates go to women now, as opposed to 5% in the 1950s. American girls may have a ways to go before they reach total equality, but it's going to take more than Larry Summers to keep them down.

Girls Worse At Math? No Way, New Analysis Shows [Reuters]
Culture, Not Biology, Underpins Math Gender Gap [EurekAlert]
Girls Get Math: It's Culture That's Skewed [LiveScience]
Gender Gap In Maths Driven By Social Factors, Not Biological Differences [ScienceBlogs]
Gender Stereotypes Can Affect Men's And Women's Test Performance in Math, Study Shows [NYU]
The Global Gender Gap Report 2007 [World Economic Forum]

Danica was promoting her new book, Kiss My Math, and she was telling girls that "Attacking something that's challenging will make you stronger," so they shouldn't get too bummed out if they do poorly on a test. Her message was really getting across until Al Roker ended the segment by saying he might have been better at algebra "If my math teacher had looked like you…" Blerg. Clip above.

Earlier: The Wonder Years' Danica McKellar Tells Brooklyn To "Kiss My Math"

"I'm a middle-school teacher," said one young woman, "and I really want to get girls more involved."

"I just think she's hot," said a creepy nerd in his mid-thirties.

McKellar, when she stepped up, looked exactly like Winnie Cooper. Attired in a fitted purple jersey dress and gold hoop earrings, it was hard to believe she was 33 — which is, I guess, the point. She had a bubbly, girlish speaking style and a SoCal intonation and peppered her speech with "hecks" and "goshes." "I was scared of math," she began frankly, explaining she didn't see herself as fitting the stereotype of the math nerd and doubting her early successes. "When a girl fails at math, it's like confirmation of what she already believes about herself." McKellar explained that she wants to show that math is for everyone, "that you can be that girly girl who wears four-inch heels and is good at math" - and that "being smart doesn't make you a nerd, whatever that even means!" Math, she said, "is like exercise for your mind," and useful in more contexts than most girls understand. "If you want to open a cute little boutique? You're going to need math! I even have a section on unexpected careers that require math, like designing," she said.

Despite McKellar's enthusiasm, the audience — with the exception of one elderly man with a none-too-clean iron-gray ponytail who guffawed indiscriminately throughout — remained stony-faced. ("Do you remember math tests?" she asked confidentially at one point. Silence. "Well, I sure do!" she continued pluckily.) The reading portion, because it's a math text, was necessarily brief. Then, of course, questions.

"I'm a teacher," said the first speaker. "Are you going to continue with the series and do pre-calc, calculus and trig, too?"

McKellar said she might.

"I'm also a teacher," said the next. "And I'm already seeing girls feeling really discouraged by seventh grade. "
"I'm a middle-school teacher, too," said a third. "are you going to be doing any speaking at schools?"

A guy asked if she was encouraged by the recent reports that girls were as good at math as boys.

"Those statistics are nothing new," said McKellar heatedly. "It's not a question of ability; girls just don't see themselves as able to compete at a high level."

Someone asked about her speech before Congress for funding for scholarships for women.

"The truth is, scholarships aren't the problem, really," said McKellar. "By college, it's too late - women don't think of themselves as mathematicians, end of story. They're not applying for those scholarships."

"Don't you think it's unfair to be focusing on girls when kids across the board are struggling with math?" asked one guy aggressively.

"Well, lots of boys read the book," said McKellar defensively. She went on to say that textbooks had always been geared towards a male sensiblity, so this was more about redressing a balance.

"When is The Wonder Years coming out on DVD?" demanded an old man with a mustache and a Nascar cap.

McKellar very graciously replied that she didn't know but that "I've heard there are bootlegs out there, but they're illegal."

As the customers lined up, marshaled strictly by the B&N employees, to have their books signed, I heard an 11-year-old girl say, shyly, "I like your book. It made math fun." McKellar beamed with pleasure. At that same moment, I noticed a group of young guys pass by the picture window in front of which the actress and math genius was standing and give her rear end a thorough and unabashed once-over. The two things, combined, seemed like a pretty good window into the one-time Maxim model's life. Kiss My Math, indeed.