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Humanist Discussion Group, Vol. 33, No. 661. Department of Digital Humanities, King's College London Hosted by King's Digital Lab www.dhhumanist.org Submit to: humanist@dhhumanist.org Date: 2020-03-06 11:43:00+00:00 From: Merisa MartinezSubject: Re: [Humanist] 33.656: mathematics --> ? addendum Dear Willard, Excellent questions that I hope will stimulate some discussion. I consider mathematics under two basic trees, one being pure mathematics, the other being applied mathematics. The roots of both are intertwined, but above ground, people can point at them and say "those are two separate trees." However, from far away, when they are just out of view, people looking at them might point and say "that's a tree." This seems to be the case in humanities disciplines looking at (or talking/writing about) mathematics from afar. To extend the metaphor hypothetically, it is not clear at this point which tree's seeds flew off the branch and spawned the second, but they are interconnected and each serves to stimulate the growth of the other. Off the top of my head I can think of three branches of mathematics wherein developments are immediately interconnected above ground to both trees: topology, graph theory, set theory (though of course there are bound to be more and my brain is working at 50% due to the never-ending presence of thesis thoughts). Now, if we consider computer science, I am in no doubt based on my own limited experience studying pure and applied mathematics that the discipline is closely-aligned with applied mathematics (as well as information science), but has relatively little to do (from day to day) with pure mathematics *as a whole,* though is certainly immediately relevant to specific theoretical fields within pure mathematics. There is some unfortunate snobbery among some pure mathematicians about their work being conflated with applied mathematics (though as seen above with the example of topology, graph theory and set theory this changes from branch to branch), and this indeed might be similar to that long-standing debate in literary studies regarding the value of higher versus lower criticism (i.e., the unfortunate notion that one is trivial and leading to the 'real work' of the other.') Hence, the name 'pure'- it is mathematics for the sake of mathematics, not for the sake of solving trivial, immediate human problems, though the solving of those problems by 'lesser' applied mathematicians is helpful to the 'real work' of pure mathematicians. (Let it be clear here that this is an attitude I have seen espoused but to which I do not subscribe).[1] At its root, pure mathematics is simply the ability to think abstractly about hypothetical spaces and concepts that do not yet exist, but if they did exist, would have to exist with internal logic, and it is the internal logic that pure mathematicians attempt to ascertain. With that proviso, I think we are already engaging in this type of abstract thinking in the humanities as a group of disciplines and in the digital humanities and computational humanities, specifically. I also think that we are going to see more computational humanities projects that utilize continued advances in super and quantum computing as they become more readily available, and this may be one way to attract more funding to DH/CH projects.[2] The questions you raise seem to me relevant to the philosophy of mathematics, and indeed there may be current ongoing discourse about your questions in that field. I would argue from my own experience of a study conducted in the US about why mathematics is developed at a young age in some and not in others (mostly young men) that this is due in part to socio-political factors such as 1) encouragement and 2) access to resources, such as the camp and the personal attention from professors that you describe in your email. A study (to which I cannot now find the citation, though I will keep searching) conducted in the 2010s found that until age 13/14, young women in the US outperformed young men in mathematics and then steadily declined in their performance throughout high school. Another recent study (https://www.nature.com/articles/s41539-019-0057-x) found that there would be no neural reason for this decline in performance, as both young men and young women use the same neural processes to perform mathematical thinking. From widespread, countless examples of anecdotal evidence, it can be argued that this decline in performance is due to young women not being adequately encouraged to participate in or develop their skills in higher mathematics. Indeed, in 84 years there has only been one female Field's Medal winner (mathematics' highest prize, given to 1-4 mathematicians under 40 every four years), out of 60 recipients, and that was Maryam Mirzhakani in 2014. I would also contend that for all young people, encouragement and access to resources are key indicators of success and development in any subject. Early pedagogical failings can cast a long shadow. Having been in classes with very young people learning basic arithmetic, I cannot advise telling young people 'this is going to be difficult/tricky/hard' before they even begin! Yet time and again, this scary phrase is used and can simply put young people off, which may account for quite a lot. This answer is of course tangential, and does not address your main concern, but will, I hope, provide some context for how your questions might be addressed? Yours sincerely, Merisa Martinez Swedish School of Library and Information Science Digital Humanities Commons, KU Leuven Libraries [1] I would be remiss if I did not note the more complex factors for this derision on the side of (some) pure mathematicians: one is the attempt during the twentieth/twenty-first centuries to use pure mathematicians' proofs as the basis for some of the most catastrophic human failings the world has ever seen, including the nuclear bomb. So disgusted was Alexander Grothendiek, one of the most gifted and prolific mathematicians (algebraic geometry) of the 20th century, with the unintended and unapproved use of his proofs by the French Ministry of Defence that he quit a lucrative project, and ultimately mathematics as a field, completely. The Department of Defence in the US routinely sends out employees to make the rounds in mathematics conferences, seeking out proofs and potential employees who can help them build yet more destructive nonsense. And today, this is indeed one major gripe that (some) pure mathematicians have with applied mathematicians who take lucrative contracts to work with the NSA, or for private companies that use applied mathematical principles and theorems to spy on/steal information from people. [2] One very real aspect of the advances in applied and pure mathematics is that it can be (though is not always) performed slowly (indeed that is what Maryam Mirzakhani called her practice - slow mathematics) and deliberately, thanks to the implicit value of mathematics to the wider world. In my experience, no one is ever worried that a mathematics department is going to completely lose its funding, or have to cut staff. We must take this attitude, and the effect it has on people's ability to conduct good work, into account when we consider how we can import some of the attitudes and theoretical and practical applications of mathematics into our work - it takes time, and often more time than our short grants in the humanities will allow. Further, the ideal mathematical proof is simple and succinct (one to two pages being ideal) - thus the product of mathematical knowledge is in inverse proportion to our own typical products. On Fri, Mar 6, 2020 at 9:38 AM Humanist wrote: > Humanist Discussion Group, Vol. 33, No. 656. > Department of Digital Humanities, King's College London > Hosted by King's Digital Lab > www.dhhumanist.org > Submit to: humanist@dhhumanist.org > > > > > Date: 2020-03-06 08:34:47+00:00 > From: Willard McCarty > Subject: mathematics --> ? addendum > > Apologies for omitting the references. Here they are: > > Hacking, Ian. 2011. "The Mathematical Animal". Toronto: Woodsworth > College, University of Toronto. > https://www.youtube.com/watch?v=E8f-5Ipdy5U > > Mahoney, Michael Sean. 2011/1997. "Computer Science: The Search for a > Mathematical Theory". Histories of Computing. Ed. Thomas Haigh. 128-46. > Cambridge MA: Harvard University Press. > > Yours, > WM > -- > Willard McCarty (www.mccarty.org.uk/), > Professor emeritus, Department of Digital Humanities, King's College > London; Editor, Interdisciplinary Science Reviews > (www.tandfonline.com/loi/yisr20) and Humanist (www.dhhumanist.org) _______________________________________________ Unsubscribe at: http://dhhumanist.org/Restricted List posts to: humanist@dhhumanist.org List info and archives at at: http://dhhumanist.org Listmember interface at: http://dhhumanist.org/Restricted/ Subscribe at: http://dhhumanist.org/membership_form.php

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