Science and mathematics work “from opposite sides” to align reality with human conceptions of reality: science (empiricism) by carving away falsehoods from without, mathematics by building partial truths from within. And they do work: electronics, computation, communication, space travel, on and on. All are permitted by the structure of the physical universe. None would have been discovered, much less developed as technologies, without understandings coming from sciences and mathematics.
There is an authoritarian assault on both science and mathematics, leading to political, social, and environmental chaos today; and to unpredictable ruination for ecosystems, for all of us whose lives and well-being depend on them, that will play out over coming decades, centuries, millennia, and longer. The human roots of this ideological war closely resemble effects described and interpreted by Iain McGilchrist in The Master and His Emissary. Particularly, patients whose right hemispheres have been damaged or temporarily suppressed sound eerily like voices of power in 2025: absolutely assured, expediently self-contradictory, in blunt denial of facts and their own senses.
The Project Gutenberg ebook Science and Hypothesis by Henri Poincaré, translated into English by William John Greenstreet in 1905, is particularly pertinent today. In thirteen chapters written for the non-technical public, Poincaré discusses scientific and mathematical concepts and truths, and how they inspire and support each other.
In a related expository spirit, The Foundations of Mathematics: A Contribution to the Philosophy of Geometry by Paul Carus is a philosophical essay on geometry, experience, and concept. Published in 1908, the book predates general relativity.
When concepts ignore or flout reality, there is no contest as to which will prevail: Challenger, Chernobyl, Titan. An urgent tragedy of our era is that large-scale human systems, fueled by concepts and stories, are effectively at war with reality. Ecologically the world is finite, interconnected in ways we do not imagine, indifferent to suffering and survival. Permanent fixed-percentage growth cannot continue forever: not by subtle constraint, but for blunt, simple arithmetic.