Mansplaining mathematics

Well, mathematics and teaching.

First, let me clarify what I mean by mansplaining. It is not, as some people misinterpret it to mean, any time a man explains something to a woman. Mansplaining is what happens when a man knows that a woman has considerable knowledge in a field, and still decided he needs to explain some basic principle of the field to her. It is more broadly a sign of men (not all men!) disrespecting and devaluing women’s knowledge and expertise.

Mandatory XKCD

For example, when I meet with my advisor and he explains some mistake I’ve made in a proof, or a concept I’ve misunderstood, that is not mansplaining. He has more knowledge than me, and I’ve clearly demonstrated that I need the explanation.

On the other hand, when my brother  decides he needs to explain to me (working on my PhD in probabilistic combinatorics) how lottery tickets  work, that is mansplaining. I made a joke about how it said that every fourth ticket was a win, and I’d not won anything on my six tickets and thus should ask for my money back. He decided that clearly it was serious and I needed to be educated on what “one in four” means, and why it was in fact probably to not win anything on six tickets. Clearly my several semesters of advanced probability theory are useless next to his high school degree.

When I have a booth at a science fair aimed at the general public, and two men respond to hearing that I’m working on my PhD in mathematics by telling me condescendingly that I should watch “The Code” on Netflix to further my education, that is mansplaining. Both of these charming gentlemen were engineers, so had some limited knowledge in mathematics. They still decided that they were qualified to recommend a TV series as a good way to further my graduate studies in the subject area. Not as entertainment for me, but as education. One of them even proceeded to act hurt when I didn’t express my gratitude for the recommendation, and ask me why I wasn’t writing down the name of the series. I don’t know, maybe something about the 10 people sitting in the booth waiting for me to show them how to play Nim?

When I’m having a discussion with a fellow PhD student at a party about university admissions, and an undergrad with zero teaching experience, zero knowledge about public policy, and zero knowledge about pedagogics butts in to tell me that I’m wrong, high school grades are a better predictor for success than motivation, that is mansplaining. The other grad student and I were both backing up our arguments with research studies from our mathematics teaching seminar: the undergrad was just convinced that his ideas were just as valid as our research studies, if not more. He then proceeded to inform us that since he had once explained Lagrange multipliers to his 12-year old brother, high school is pointless and all university instructors are incompetent.

All these three are examples of men assuming without any cause that they could educate me on something they knew I am knowledgeable about. They knew about my graduate studies, the undergrad heard me quote studies to support my view, and still they persisted, thinking that their ignorance is valuable to me.

Please, stop. Before you explain something to a woman, think about it. Did she ask for an explanation? Did you make sure you actually know more about the area than her before starting? Is the explanation even necessary at this point in time? Before you offer advice on say a study plan for a PhD student, think about it. Were you asked for advice? Do you actually know anything about the area?

Almost all women have these experiences, and they are terrible. We come out of them either feeling like men don’t even acknowledge our education and experiences, or ready to laugh at how pathetic you are. Usually it’s some mix of both. For some more examples of truly egregious mansplaining, check out this Tumblr: Academic Men Explain Things To Me

Do you know what’s really sad?

My examples are all from the past three weeks.

Inappropriate Mathematics

Warning – inappropriate language ahead! Proceed with caution!

I’m sure anyone who studies mathematics has at some point come across some theorem or algorithm with an inappropriate name. Here I’m going to summarise some of my favourites, as well as give a basic intuition about what they are. Feel free to add your own in the comments.

Wiener’s Small D attack: This is a proposed attack on the RSA cryptosystem. We came across this attack in class, and our very foreign lecturer had no idea why the entire class was giggling through that entire lecture. If you don’t know how the RSA cryptosystem works, you should read up a little on it before continuing. One issue when implementing RSA is the time it takes to encrypt and decrypt a ciphertext. Since the moduli have to be very large to ensure security, the exponents are also very large. However, we can choose to speed up decryption by choosing a small decryption exponent. If this exponent (D) is chosen to be too small, then the message can easily be decoded with the help of the Euclidean algorithm and some continued fractions.

Hairy Ball Theorem: This has to do with some rather interesting topology. The formal statement if the theorem is that “there is no non-vanishing continuous tangent vector field on even-dimensional n-spheres”. The more understandable version states that one cannot comb a hairy ball smooth. However much you try, there will always be a cowlick somewhere. There is a really neat application to meteorology. If we think of wind around the Earth as a continuous tangent vector field on a 3-sphere, then there will always be a point with no wind. Since the only way we can have no wind (if there is wind elsewhere on Earth), is if the wind moves in a circle around this point, we can conclude that there is always a cyclone somewhere on Earth.

Pumping lemma: This requires some background in computability theory to understand. It states that for a language to be a member of a language class, and sufficiently long string can be removed, or repeated any finite number of times (hence ‘pumping’), with the resulting string still in the language.

Killing-Hopf Theorem: I’m not going to explain this one in a very detailed way, since it requires a lot of topology to just understand the formal statement of the theorem. I’ll just tell you that it has been stated as: “there exists a method to kill a Hopf and get away with it”.

Sexy primes: Sexy primes are primes that differ by six, for example 5 and 11. There are also sexy prime triplets (5, 11, 17), quadruplets (5, 11, 17, 23) and a single sexy prime quintuplet (5, 11, 17, 23, 29). The reason there is only a single quintuplet is that in an arithmetic progression with common difference 6 and length 5, there must be a term divisible by 5 (as 6 and 5 are relatively prime). The same argument can be extended to explain why there are no longer sequences of sexual primes.

Cox-Zucker Machine: This is an algorithm which determines if a given set provides a basis for the Mordell-Weil group of an elliptic curve. This algorithm wasn’t named by accident. Most of the work was done by David Cox, who the heard that another member of his department was called Steven Zucker and asked Zucker to co-author the paper for the funny name.

Sexual functions: These are simply functions of six variables. Just as with sexy primes, the name comes from the Latin word for 6, ‘sex’.