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Humanist Archives: March 8, 2020, 8:31 a.m. Humanist 33.661 - mathematics --> ?

                  Humanist Discussion Group, Vol. 33, No. 661.
            Department of Digital Humanities, King's College London
                   Hosted by King's Digital Lab
                Submit to: humanist@dhhumanist.org

        Date: 2020-03-06 11:43:00+00:00
        From: Merisa Martinez 
        Subject: 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)

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