The world has changed immensely over the past several hundred years. Mathematics has too. Are these changes all related?
Plato’s Ghost looks like a good place to start.
Plato’s Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.
Building on Gray’s work is this presentation by Susumu Hayashi, which introduces (to me at least) the notion of “mathematical secularization.”
I also came across The Great Rift.
In their search for truth, contemporary religious believers and modern scientific investigators hold many values in common. But in their approaches, they express two fundamentally different conceptions of how to understand and represent the world. Michael E. Hobart looks for the origin of this difference in the work of Renaissance thinkers who invented a revolutionary mathematical system—relational numeracy. By creating meaning through numbers and abstract symbols rather than words, relational numeracy allowed inquisitive minds to vault beyond the constraints of language and explore the natural world with a fresh interpretive vision.
The focus is on early modernity and the shift to algebra, which is an earlier phenomenon than modernism. But maybe it’s part of the same story?
Also in the category of “is this related? maybe??,” there is a working group of philosophers that call themselves the Mathematics, Mysticism and Secularization working group.
There are all these -isms that I learned about in philosophy of math: empiricism, logicism, formalism, fictionalism (wiki). That’s part of this story too.
What I’m attracted to is the idea that math is as much a part of culture as anything else. Over the last few centuries Western society has gotten less and less comfortable with the abstract, invisible realm of religion and spirits. Wouldn’t that have an impact on how that culture thinks about that other invisible, abstract realm of mathematics?
People used to think of as referring just to a square’s area, but then it was emptied of that meaning. Is the break of algebra from geometry something like the break of philosophy from theology?
People used to think that mathematics was a search for ultimate truths, not just conditional ones. Are we living in a mathematically relativistic world?
Mathematicians sometimes talk — with pride! — of the uselessness of their work. Is that the end result of the sorts of processes described by these authors?
I have no clue, and I have no idea when I’ll be able to read those books. But the questions seem interesting and confusing.