I really want to read an essay on this topic by someone I'm more confident actually understands what math is. Or truth, for that matter. The author smears the boundary between what people believe and what is logically entailed, and between mathematical techniques and the way they are applied in modelling the real world. They persist in phrasing their statements about how people conceptualize math in terms of "is" and "are", which I tend to assume is a stylistic choice to speak in the perspective of their subjects, but they're so sloppy about perception and truth and "reason" in the rest of the piece that I can't be sure.
> The Neapolitans did not reject modern analysis simply because they considered it French.
And yet after reading the article, it sounds like that is exactly what happened. They took some minor philosophical dispute in math and blew it up for cultural reasons to stick it to the invader. It doesn't sound like it ever really was about the math for most people in that context.
Hot take: the author sneaks in a premise that synthetic mathematics is per se "reactionary", but this is itself pure reactionary copium for not getting it: https://ncatlab.org/nlab/show/synthetic+mathematicshttps://en.wikipedia.org/wiki/Synthetic_mathematics . There's nothing wrong with wishing to pursue a "coordinate-free" approach to any mathematical field: the old geometers were quite right about this.
The critique of calculus as lacking in rigor goes much further back than that. Bishop Berkeley famously argued calculus was no more dependable than theology. It was only with Cauchy and the formalization of analysis in the 19th century that this issue would be put to bed.
I wonder if the issues that this essay claims came up in Italy persisted in any way. I ask that, because there was later (1885-1935) an infamous breakdown in Italian mathematics (the "Italian School of Algebraic Geometry") due to foundational issues.
If we review the history we can notice that there was always an influence from politics/religion to science, literature, arts, philosophy and the use of them by politics, maybe to justify some decision and state of facts.
It helps to empower control over population and fits perfectly in the social and historical context: the emperor blessed by God, the evolution theory, the epic poems, theory of race, the industrial revolution, and modern times don't escape these patterns too, we just suppose to be neutral.
Since the dawn of electronics, mathematics has entangled with politics indirectly, via technological change. The article describes a de facto technological change (emergence of Real Analysis), a kind of technology with many practical applications with economic implications.
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[ 2.8 ms ] story [ 27.0 ms ] threadAnd yet after reading the article, it sounds like that is exactly what happened. They took some minor philosophical dispute in math and blew it up for cultural reasons to stick it to the invader. It doesn't sound like it ever really was about the math for most people in that context.
https://en.wikipedia.org/wiki/The_Analyst
I wonder if the issues that this essay claims came up in Italy persisted in any way. I ask that, because there was later (1885-1935) an infamous breakdown in Italian mathematics (the "Italian School of Algebraic Geometry") due to foundational issues.
https://en.wikipedia.org/wiki/Italian_school_of_algebraic_ge...
History doesn't repeat but it sometimes rhymes.
It helps to empower control over population and fits perfectly in the social and historical context: the emperor blessed by God, the evolution theory, the epic poems, theory of race, the industrial revolution, and modern times don't escape these patterns too, we just suppose to be neutral.