# Combinatorics and Pampers

I’m a mom of a toddler and a newborn, so my house goes through a lot of diapers. We’ve been using Pampers almost exclusively since my son was born in 2010. Pampers offers a program called “Pampers Rewards” where you can enter codes found on Pampers products to their website, and redeem for cool stuff. (Let’s agree to ignore all issues about the effects of disposable diapers on the world ecology, or on family size and the exponentially growing population of humans on our planet, or the obvious questions about why Pampers is trading me stuff for lots of data about how often my kids pee.)

The coding scheme that Pampers uses has bothered me for a while. Each Pampers item comes with an alphanumeric 15-digit code, something like “T9PDXPKKGA3M4GK”. Given that for each character we have 36 possibilities, and the codes are 15 characters long, there are a whopping 3615 such codes. This is about 2.2×1023. That’s a lot of possible codes! How many? If every single one of the seven billion people (7×109)  on the planet used Pampers, there would be enough possible codes for each person to have one billion codes just for themselves — and then there would still be some left over. While my kids use a lot of diapers, I surely hope we don’t end up needing a billion boxes of Pampers for each of them.

Why does Pampers do this? I am not sure. Instead of an alphanumeric code, why not just use an alphabetical sequence of length 15? This would mean “only” 2615, or a little shy of 1.7×1021. In this case, there would still be more than a billion codes available for each one of the seven billion of us.

It’s in Pampers’s interest to make sure only a small percentage of all possible codes are actually connected with a particular product; this prevents fraud on their Rewards program. If I were going to design codes, I’d want to make sure that of all possible codes, maybe only one in a million actually worked. I’ll even be very cautious and allow only one in ten billion (1 in 1010) to actually appear on a product. What is one ten-billionth of 3615? It’s about 2.2×1013. This would still leave Pampers with over ten trillion (1013) usable codes. Surely they could find a more efficient coding scheme.

Apart from efficiency, I’d really love it if Pampers would just print the associated QR code along with the actual 15-digits. Having to type in multiple 15-digit codes on my Pampers iPhone app, while chasing a toddler, nursing a newborn, and typing a blog post, is really quite taxing!

# Mathematics in Fiction Class Visit

Today I attended a colleague‘s “Mathematics in Fiction” course. This course is designed as a First-Year Seminar course, not necessarily for math majors, and has a large writing component. I was invited to attend the class as a “guest participant” so I could be part of a dialogue on the broader issues about gender & mathematics, and how women are portrayed as mathematicians in works of fiction.

Overall, I really enjoyed the discussion we had. I’m hoping the students continue to ponder the issues and questions that were raised. In our conversation, I realized I wanted to make two distinctions that the students perhaps didn’t see.

Mathematician, Math Professor, and Math Teacher
Several students said they were unsure that there are still problems about gender in mathematics, citing that they had mostly female math teachers in high school. There seems to be a cultural conflation of mathematician, math professor, and math teacher. When I tell people I have had very few female math professors, a common response is, “Well all of my high school math teachers were female.” In my mind, these three titles have different connotations. I don’t consider high school math teachers to be “mathematicians” necessarily. To me, a mathematician is someone with advanced training and who has engaged in mathematical research (and, in most cases, who is continuing to do so). The research component separates math professor from math teacher.

As far as the distinction between “mathematician” and “math professor,” I used to think the overlap between these groups was so large that we might as well call these terms synonyms. But “math professor” is an academic job title — one cannot be a math professor if one isn’t employed. Meanwhile, “mathematician” has something more to do with educational background, training, and hobbies and isn’t job related.

One Question Becomes Two
One student brought up that perhaps the gender imbalance in mathematics has more to do with interest than anything else: Could it be that girls are just less interested in math, and that’s why there are fewer female mathematicians? (I don’t believe this to be true.) Our conversation made me want to point out the following distinction, which I think is important: There is a question of whether women like math less than men like math, and then there is a question of whether women like mathematical careers less than men like mathematical careers. In my mind, these are two very different questions.

My experiences & my gut instinct make me think that the bigger issue is that women are less interested in becoming math professors, not that women are less interested in mathematics. Indeed, there has been a lot of discussion about the so-called “leaky pipeline”: While more and more women are finishing both undergraduate and graduate degrees in mathematics, there seems to be a slow-down when it comes to who is being hired into academic mathematics.