DALL·E is an Artificial Intelligence (AI) system that has been designed to generate new images given a text prompt. It’s very much like doing a Google image search with one very important difference: DALL·E doesn’t try to find existing images to match your query, but creates a handful of new ones that it hopes will fit the bill.
You're reading: Posts Tagged: Mathematics
(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.NAM’s Statement on the Death of George Floyd
(you can join NAM here).
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.This is what an antiracist America would look like. How do we get there? by Ibram X Kendi
This set of Scaffolded Anti-Racist Resources provide activities, books, articles, videos, podcasts, and next steps for everyone, even if they have no prior knowledge of social justice and anti-racist concepts. ShutDownSTEM has put together a group of readings and resources for a wide range of people. They have self-care and healing resources for Black academics and STEM professionals, readings for people who are only now starting to think about race, and information for those who want to examine anti-Black racism in academia. For those looking for a more structured approach, Autumn Gupta and Bryanna Wallace have put together a 30 day Racial Justice challenge (at 10,25, or 45 minutes a day). If you are just starting your journey and looking for definitions of some foundational social justice concepts I was on a team which recently published a column featuring 15 such definitions with examples of each from the sciences. Jasmine Rice was also put together a list of 10 actions white academia can take to support their Black colleagues and students.
There are a number of readings on these topics that are related to the mathematical sciences as well. I will call out some I have personally found helpful in conceptualizing and integrating anti-racist and social justice ideas into my conceptualization of the mathematical sciences: The rehumanizing mathematics work of Rochelle Gutiérrez, the Living Proof: Stories of Resilience Along the Mathematical Journey collection, Inventing the Mathematician: Gender, Race, and Our Cultural Understanding of Mathematics by Sara N. Hottinger, Mathematics for Human Flourishing by Francis Su, Lou Edward Matthew’s on rejecting gentrification within the mathematical sciences, Tukufu Zuberi’s Thicker than Blood: How Racial Statistics Lie, AMS’s Inclusion/Exclusion Blog, the many other readings available at University of Michigan’s Math Learning Community on Inclusive Teaching site, the items on NCTM’s Math and Social Justice book and article list, and Kari Kokka’s list of Social Justice Mathematics and Science Curricular Resources for K-12 Teachers are all good, if incomplete, starting points. For more information about the history of Black mathematicians Mathematicians of the African Diaspora is a great resources, and to better understand the lived experience of Black mathematicians check out the profiles in Mathematically Gifted & Black and for the lived experiences of Latinx mathematicians the profiles in Lathisms. If you are looking for more readings that encompass all of the sciences, the pan-STEM Decolonising Science Reading list by Chanda Prescod-Weinstein provides a wide selection.
Finally, I have put together a list of anti-racist mutual aid projects you can donate to,
- Help support the next generation of Black mathematicians with Mathematically Gifted and Black
- Contribute to the new AMS 2020 Fund which will support and promote the work of Black mathematicians and establish a new fellowship to support the scholarship of Black mathematicians.
- Directly provide #BlackAndSTEM Students with mutual aid (via @jazztronomy)
- Directly aid the member of BlackAfinSTEM, or the group as a whole
organizations and projects focused primarily on the mathematical sciences you can become a member of, or otherwise support and sponsor,
- Become a member (or donate to) National Association of Mathematicians
- Contribute to or Sponsor the EDGE (Enhancing Diversity in Graduate Education) Program
- Support the Benjamin Bannecker Association’s mathematics education advocacy work
- Build a new mathematics community with the Math Alliance
- Donate to support TODOs mission of equity and social justice in math education for all
actions you can take,
- Sign the Petition to rename the American Statistical Association’s Fisher Lecture After David Blackwell
- Add your name to a letter asking the Mathematical Community to boycott collaboration with police (Letter will be sent to AMS Notices Jun 15)
- Send letters to ICERM about the combination of silence and history promoting predictive policing and AWM about their choice of a predictive policing expert as the 2021 AWM-AMS Emmy Noether Lecturer,
- (This link used to include a template to contact MSRI but MSRI has now published a statement (even if it is not that visible <it is the small black square> on their homepage) and indicated they will be amplifying their African Diaspora Joint Mathematics [ADJOINT] Workshop via @mathmoves and their email newsletters.)
and others projects to support which cover the rest of STEM.
- Support #VanguardSTEM and their Conversations with Women of Color in STEM video series
- Build a more diverse STEM with Society for Advancement of Chicanos/Hispanics and Native Americans in Science
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.
Black Lives Matter.
Longtime friend of the Aperiodical, artist, mathematician and #BigMathOff semifinalist Edmund Harriss has come up with a new puzzle/toy/exploration set, developing his Curvahedra system. We asked him to explain the maths behind it in this guest post.
Curvahedra is a flexible system of connectors that can make all sorts of different things, combining puzzles (and self-created puzzles) with art. You can get your own to play with, explore, prepare for Christmas (they make great decorations, wreaths and presents) at our online store, and get 15% off with the discount code APERIODICAL.
As this is the Aperiodical, you might be most interested in how it can be used to explore mathematics. In the big math off I talked about the basic ideas behind the system, Gauss’ famous Theorema Egregium and Gauss-Bonnet theorems. A really simple version of this comes from just considering triangles, that can be built up to make this:
Primo, a board game which puts the ‘fun’ in the fundamental theorem of arithmetic, has now been successfully funded via Kickstarter. In a recent blog post, the creators Katherine Cook and Daniel Finkel boast:
The game plays beautifully in play test after play test. It’s one of the most mathematically rich games we have ever seen, and at the same time avoids that icky “educational game” feel. Primo is a real game and it’s worth playing because it’s fun. Really fun.
Since the start of the year, the Math/Maths Podcast has been on hiatus. I’m very much enjoying the extra thesis-writing time but apparently this has left some missing their regular mathematical listen. Not infrequently I get an email from someone wishing me well with my thesis and asking when we’ll be back podcasting. Well, nature abhors a vacuum and here are three offerings that I’m aware are working to fill the void. (Oh, and “pale imitations” – I’m joking, of course!)
All Squared (RSS, iTunes)
My Aperiodical co-conspirators Katie Steckles and Christian Perfect started All Squared, a maths magazine podcast, in February. The description for the first episode (or “number”, as Katie and Christian have it) overtly points out the “unusual paucity of maths podcasts at the moment” and promises “a half-hour podcast featuring maths, guests, puzzles and links from the internet”. The name is designed to be recognisable to mathematicians, who might find themselves reporting that an expression is “all squared”. As someone who named a podcast as overtly as it is possible to be, “Math/Maths”, this obfuscation amuses me. The three episodes so far have been enjoyable with a guest and main topic in each. As far as I’m concerned, this is far more the Aperiodical podcast that should exist than is The Aperiodcast with that third guy.
TES Maths Podcast (iTunes)
This one started just before Samuel Hansen and I went on our hiatus, but if you enjoyed the teaching aspects of what we did you can get a lot more on the theme from Craig Barton and his guests on the TES Maths Podcast. Craig promises “to share the latest news, resources and ideas that are relevant to secondary/high-school maths teachers and general number enthusiasts”.
Wrong, but Useful (RSS)
Wrong, but Useful is a new podcast featuring “a mathematical conversation” between Colin Beveridge and Dave Gale that sets out its stall as a response to the lack of Math/Maths episodes. The title is another nod to the mathematically minded without being overt, referring to a quote from George Box and Norman Draper who wrote “essentially, all models are wrong, but some are useful” (Empirical Model-Building and Response Surfaces, 1987). Episode 1 sees Colin and Dave finding their feet in a rambling, wide-ranging mathematically-themed discussion. There were a couple of awkward moments that gave me Math/Maths early episode flashbacks but I’m looking forward to Colin and Dave getting into the swing for the next episode.
I have a job. This is not the podcasting update, but it does affect it! If you have listened to the latest Math/Maths Podcast you will know that I will be lecturing mathematics from January while trying to finish my PhD thesis, and that we will be putting that podcast on hiatus while I do so. This means no more talking to Samuel Hansen for at least six months.
There is something you can do to fill this mathematical podcasting gap, however. Samuel is trying to raise money through a Kickstarter to allow him upgrade his equipment and improve the quality, to pay for the travel to conduct face-to-face interviews and to make this his full-time job so he can concentrate on a regular release schedule, for his work in maths (math) and science communication over at ACMEScience.com.
At Kickstarter, Samuel says:
ACMEScience.com has spent the last four years trying to do something that very few others have ever attempted, create entertaining, insightful, and interesting content about mathematics and science. Started by Samuel Hansen in the beginning of 2009, ACMEScience has produced a pop-culture joke filled mathematical panel show, Combinations and Permutations, a show that interviews everyone from the CEO of a stats driven dating site to a stand up mathematician to Neil deGrasse Tyson, Strongly Connected Components, a show that tells the stories of the fights that behind DNA, dinosaurs, and the shape of the universe, Science Sparring Society, a video interview show that has featured predatory bacteria and crowdsourced questions, ACMEScience News Now, and a series of hour long journeys into the world of competitive AI checkers computers and stories of the most interesting 20th C mathematician and much more, Relatively Prime.
You may remember that Samuel raised money through a Kickstarter before, for the extremely well-received documentary series Relatively Prime. So you might judge this as evidence that he is capable of delivering this project. However, you may also remember that if he doesn’t raise the whole amount he needs then he gets nothing.
There are various pledge levels, with various rewards. Some of these are aimed at the individual who wants to own a piece of the project. Others are aimed at people who want to sponsor/advertise via the shows and get their message out there. Looking at the level of pledges so far, Samuel could really do with a few companies or individuals who want to get a message out to a mathematics or science audience coming forward and pledging some money. Relatively Prime was very well listened to, and you could get your message to a large, focused, engaged set of listeners.
There is not long to go (only four days at time of writing) and it doesn’t look good. So please pitch in and also tell everyone you know via your own blog/podcast/social networks/etc. so that others will support his effort.
Here is the video in which Samuel makes his case. It’s six minutes so at least watch that! The Kickstarter page is ACMEScience.com by Samuel Hansen. Donating is easy through Amazon payments.
Last Sunday saw the anniversary of the birth of Martin Gardner, and as a celebration, the Gathering for Gardner people planned a world-wide party ‘G4G Celebration of Mind‘. It happened to be Maths Jam night on Tuesday, so we put the Nottingham Maths Jam on the G4G-COM map. Then on Friday three of us had agreed to take a puzzles stall to the Nottingham STEM Pop Up Shop, so I added this to the map as well.
A Celebration of Mind party is supposed to “celebrate the legacy of Martin Gardner on or around Sunday, October 21, 2012 through the enjoyment of [one or more of] Puzzles, Magic, Recreational Math, Lewis Carroll, Skepticism and Rationality”.
At Maths Jam I printed a bunch of flexagon material from the Flexagon Party page. I also had a plan: having finished two jobs in recent years with piles of business cards outstanding, I brought these to try some business card origami. In fact, we decided to make a business card Menger sponge. So we started folding.
|Business card folding begins|
Meanwhile, John Read had come equipped with some colourful designs to make hexahexaflexagons.
|John Read’s first hexahexaflexagon of the evening. Designs from flexagon.net.|
|John Read’s second hexahexaflexagon. Designs from flexagon.net.|
At the same time, Jon made a trihexagon.
|Trying to make a triflexagon|
Finally, after much business card folding,we had a Menger sponge* (*not a real one, it being a fractal after all!). Here it is, in Maths Jam-style, balanced on a pint of beer.
|The completed business card Menger sponge|
And here’s a shot through the Menger sponge, where a geometry puzzle is being attempted.
|Through the completed business card Menger sponge, some geometry is happening|
Here are a couple of the other puzzles that we tried, some from the #MathsJam tag on Twitter:
You have 100 coins, 10 of which are showing heads and 90 of which are showing tails (though these are indistinguishable by touch). Blindfolded, you must divide the coins into an even number of heads and tails.
Which is bigger, 3^(21!) or 2^(31!)?
Then on Friday we made our way to Broadmarsh shopping centre for our afternoon at Nottingham’s STEM Pop Up Shop.
|Nottingham STEM Pop Up Shop welcome notice|
Here’s a picture of our stall, with Kathryn Taylor presiding, and in the foreground the posters about Martin Gardner, mathematical games and mathematicians that I had printed. Someone did ask me who Martin was and I explained a little; I think I also convinced him to come to Robin Wilson’s talk on Lewis Carroll next month in Derby.
|Martin Gardner posters on our stall|
Here’s the detail of our stall, which we called ‘Solving it like a mathematician’. You can get details of the set of puzzles on my website.
|The STEM Pop Up Shop ‘Solving it like a mathematician’ stall|
Looking around the shop, I requisitioned the Alan Turing postcards from the ‘My Favourite Scientist’ set for our stall!
|Alan Turing postcards|
Here’s a wider view of the stall, with Kathryn entertaining a customer.
|Kathryn Taylor at our stall|
And finally, here’s John Read bewitching a crowd with the loop on a chain trick.
|John Read enthuses a crowd with a ring on a chain|
Thank you for reading!
|Thank you for visiting|