# Binary logic: man and mathematics

- Cambridge Mathematics
- Mathematical Salad
- Binary logic: man and mathematics

## Binary logic: man and mathematics

Look at the title of this blog. Did you read it quickly, not noticing anything in particular? Or did you focus on anything interesting or jarring?

For me, the word ‘man’ there stops me in my tracks. But why? Is this not simply used legitimately as a plural(ish) noun for the human race? What’s all the fuss about?

The origins of ‘man’ here come from Anglo-Saxon. Unlike modern English, Anglo-Saxon had two words that could mean male: *mann*, which could also mean ‘humans’ and *wæpenmann* which meant ‘person with a weapon and/or penis’ and only referred to males. (This means, delightfully, *mann* is an autohyponym, a word that can mean both a member of a particular category and a member of one of its subcategories.) The addition of the prefix *wæpen* helps to add some clarity as to which meaning was being used, although it is likely this was a muddy boundary.

So, in modern English, using ‘man’ or indeed ‘mankind’ in this way is confusing. It could mean ‘men’ or it could mean ‘humans’ and, given that we have plenty of words to denote the latter (e.g. people, humans, humankind, the population…) linguistic accuracy suggests no need for the former. But that is not the only reason for eschewing it, of course. Using ‘man’ in the manner of the title of this blog could feel exclusionary to anyone who isn’t a man – and in a subject that, as we can see below, is associated with being highly masculine, that’s a problem we might want to think about carefully.

There is a clear picture that children often, from a young age, see maths as something that boys do more than girls (and better). Research has shown that for women, the stronger the associations of (a) self with female and (b) maths with male, the weaker the association of self with maths (Nosek, Banaji, & Greenwald, 2002, in Cvencek et al, 2011). This can produce a stereotype threat effect, where performance is adversely affected – and indeed, internationally, national differences in gender–science stereotypes predict national sex differences in science and maths achievement (Nosek et al, 2009).

So, how can we start to break down these implicit associations? We change and we challenge the narrative. If binaries are oversimplifications – and they are continually being constructed – then we can also construct our identities, specifically here as gendered mathematicians, differently. Being a mathematician is something you do; being a man, woman or whatever you identify as is also something you do. They are not fixed and they are not defined as mutually exclusive, either. This idea is neatly encapsulated by Dr Heather Mendick in her work *Masculinities in Mathematics*, who explains that “these discourses socially construct ‘mathematical ability’ as natural, individual, and masculine” and that “agency exists in the possibility for variation in the repetitive performances, the discourses, through which ‘women’, ‘maths’ and other objects, comes to exist. If gender and maths are something that we do then they can be done differently.” Put simply, we construct identity – and we have agency over the construction of gender in mathematics. There are millions of people out there who aren’t men who are doing maths – maybe we just need to see more of them (this video is a great start).

So, perhaps there is need for mathematicians and maths teachers – and society in general – to consider the binary logic on both ‘doing’ gender in mathematics and the absolutist views of our subject – and a consideration of the idea that the two may be married. Are we perhaps unintentionally oversimplifying, perpetuating false dichotomies? Are we extrapolating the rules of mathematical logic to define, categorise and ultimately exclude *people*?

Francis Edward Su, current president of the MAA, in his extraordinary talk ‘Mathematics for Human Flourishing’, states “the importance of having an advocate, a faculty member who says ‘I see you, and I think you have a future in math.’” This can be especially important for women who already have many voices telling them they can’t. He asks “Can you be that advocate?”

And indeed, “[some] studies attributed the girls’ drop in performance to their mathematics feelings that their classrooms were unattractive, uncomfortable and hostile. Factors of importance for girls’ performance in mathematics were teacher and peer support (Samuelson & Samuelson, 2016).”

Su concludes with the beautiful thought:

“we are not mathematical machines. We live, we breathe, we feel, we bleed. If your students are struggling, and you don’t acknowledge it, their education becomes disconnected and irrelevant. Why should anyone care about mathematics if it doesn’t connect deeply to some human desire: to play, seek truth, pursue beauty, fight for justice? You can be that connection.”