Andrew Stacey: I have a confession to make that would probably get me thrown out of every respectable Mathematics Society – were I to belong to one.
I am not a fan of the Fibonacci sequence.
Neither am I keen on the golden ratio. It’s not even transcendental.
It’s not really their fault, it’s just that they get levered in everywhere whether they belong there or not. Particularly in discussions of nature and beauty, and this is exemplified by that ridiculous origin story. We’ve been subjected to a variety of bizarre origin stories over the years (cough radioactive spider cough) but the rabbit story is another level of bizarre.
So I was intrigued, and then delighted, when one of my students, who is a bee enthusiast, told me about a genuinely natural occurrence of the Fibonacci sequence in the ancestry of bees.
In this guest post, Greg Benedis-Grab shares the story of when he discovered Pick’s Theorem, and how he coded an interactive version to play with.
Have you ever been intoxicated by a mathematical theorem? Well that’s what happened to a class of 9th grade geometry students at my school. Their enthusiastic teacher showed them Pick’s theorem.
(Author Positionality: I want to start this post by stating I am writing this from my position and lived experience as a white, male-passing queer, non-binary person who has lived their whole life in the United States of America. I am employed full-time as the mathematics & statistics librarian at a large endowment public doctoral granting university in the USA. I do not have to go up for tenure. I am a highly privileged person. I have not been perfect and I have been a part of the problem. I believe anti-racism is the way to no longer be a part of the problem. I believe Black Lives Matter.)
Note: This post will focus on the mathematical sciences within the USA as that is where my lived experience and knowledge lies. Also, this is an evolving post and resources will be added/changed over time.
Systemic racism, empowered to a great extent by white supremacy, is a part of the society of the USA. The results of this systemic racism can be seen everyday and has most recently made itself crystal clear through the killings of George Floyd, Tony McDade, and Breonna Taylor (among many others), by police and Ahmaud Arbery by a former officer, as well as the differential impact race has on COVID-19 infection rates and outcomes. The mathematical sciences (under whose umbrella I include both Mathematics & Statistics) are a part of this society and not immune to this systemic racism as can be seen day in day out in many ways, including the lack of representation of Black people in the mathematical sciences. A lack of representation that is ongoing and historic with the first Ph.D granted in mathematics in the USA was in 1862 while it was not until 1924 Elbert Frank Cox became the first Black person granted a Ph.D. in mathematics in the USA and intersectionally that Euphemia Lofton Haynes had to wait 19 more years to become the first Black woman granted a Ph.D. in mathematics in the USA. Statistical and Mathematical organizations from around the country have all made statements which are worth reading to understand where the US mathematics and statistics community is collectively at this moment, but I would like to call attention in particular to the one by the National Association of Mathematicians
NAM was founded in 1969, one year after the assassination of Dr. Martin Luther King, Jr. sparked widespread protests throughout the nation, similar to the ones we are seeing today. Indeed, NAM’s founding was a direct result of the marginalization of Black people within the professional mathematics community, which then and now serves as a microcosm of the society in which we live. Over 50 years since NAM’s founding, despite the lessons of the civil rights movement, we still see systemic racial inequities in education, economic prosperity, criminal justice and public health. Today, it should be clear to us all that the consequence of ignoring these racial inequities is dire.
In my own journey toward removing things like false neutrality and color-blind ideology and incorporating anti-racism and social justice into my life and work I have put together a set of lists and resources which may be helpful for those who see a need to take anti-racist steps against this systemic racism. These resources are especially helpful to those with white privilege like I have, especially if you have never interrogated your privilege.
First let us define Anti-Racist:
There is no such thing as a “not-racist” policy, idea or person. Just an old-fashioned racist in a newfound denial. All policies, ideas and people are either being racist or antiracist. Racist policies yield racial inequity; antiracist policies yield racial equity. Racist ideas suggest racial hierarchy, antiracist ideas suggest racial equality. A racist is supporting racist policy or expressing a racist idea. An antiracist is supporting antiracist policy or expressing an antiracist idea. A racist or antiracist is not who we are, but what we are doing in the moment.
There are a lot of learning and actions happening and a lot more which need to happen. I know there is still so much left for me to do and so much left for me to learn. You can reach out to me if you want to discuss these topics more. If you are starting out and struggling with the concepts or you are looking for more ways to learn more about anti-racism and social justice or you are wondering what a next step could be I can not guarantee I will have an answer but I am happy to talk with you. I hope everyone has been able to find and access the support they need, and if there is a way I can provide needed support let me know and I will do what I can.
For International Women’s Day, mathematician Lucy Rycroft-Smith has read a selection of maths books by women authors, and recommended some favourites.
There’s a strange irony about being a woman in mathematics. You spend a huge amount of time and energy answering questions about being a woman in mathematics instead of, you know, using that time and energy to do or write about actual maths. We women are somehow both the problem and the solution.
But behold: 2020 is here, and better and braver women than I have solved this conundrum. Here are a whole host of excellent books about maths by women that you should definitely read, collected for you by another woman in maths.
In the Aperiodical’s Big Internet Math-Off 2019, Becky Warren posted an entry about Geogebra’s ‘reflect object in circle’ tool (it’s the second article in the post). I enjoyed playing with the tool and, after making a few colourful designs, it occurred to me that one of them would make a great cake for the MathsJam bake-off. It would only work if the curves were accurate; sadly this would be beyond my drawing abilities, and definitely beyond my piping abilities. But with some help from 3D printing I thought I might be able to manage it.
Here are the steps I used to transfer the design to a cake.
I’m grateful to Jemma Sherwood and Rob Low for reading an early draft of this and for their comments thereon. All opinions are, of course, my own.
This post is inspired by something that I see crop up now and again in discussions with other Maths teachers. It usually manifests itself as a rallying cry to use ≡ in place of = in identities and reserve = for equations. My standard response is to mutter something about identities being equations and leave it at that. But in the latest round, Jemma Sherwood challenged me, in the nicest possible way, to explain a bit further. This is that explanation.
Although I’m going to state my case here, I’m well aware that there are different opinions. In matters of opinion, such as this, agreement and disagreement is less important than that all sides think. So if what I write seems to you wrong, that’s fine so long as it makes you think about why you think that it is wrong.
