inequality
Eugenia Chen (Profile book (UK, for sale) Basic Books (We, September 2nd)

Are things equal or aren’t they? At least mathematically, that’s a question worth considering. Eugenia Chen argues in her new book, Inequality: With mathematics and tactics when things are done. In maths, as in life, some aspects have more weight than others.

Consider this: the equation 180 = 180 reveals nothing, yet x + y + z = 180°, where x, y, and z are the angles of a triangle, conveys a deeper insight. This statement holds true only under specific circumstances—yes, but not on the surface of a sphere.

Chen aims to investigate how mathematics identifies things as “equal.” Her methodology blends playfulness with the gravity of abstract concepts, linking them to diverse topics such as knitting and creating Battenberg cakes. She isn’t shy about tackling significant political and rights-related questions surrounding equality.

When simplifying through numbers, Chen humorously remarks that their dullness helps clarify potentially overwhelming complexities into a manageable figure. Numbers can be potent tools, focusing on a specific element of a situation.

However, overlooking this simplification can lead to misunderstandings. For instance, assuming two individuals with identical IQ scores are equally intelligent is misleading. As Chen remarks, “It’s alright to disregard the details, but you must remember that you have.”

Fortunately, mathematics encompasses more than mere numbers. Chen delves into the concepts of “local” and “global,” engaging in extensive discussions. Essentially, she explores surfaces formed by stitching together smaller flat areas.

By promoting “diverse thinking,” she proposes a valuable lens through which to view reality. In mathematics, debating whether a sphere and a torus are “the same” is futile. They can be understood as locally distinct but globally different. Similarly, in political discourse, it’s crucial to recognize when one faction utilizes localized arguments (“individual women benefit from the right to choose regarding abortion”) while the opposing side employs global ones (“all abortions constitute murder,” etc.).

Chen ventures deeply into abstract discussions regarding identity within categorical theory, guiding the reader through theoretical territories. Some of the most remarkable creations in art, literature, and music are indeed complex, yet we appreciate them without fully grasping the intricacies of chiaroscuro, counterpoints, or other sophisticated elements. Chen devotes herself to exploring the formal definitions of categories. Like art, we all appreciate certain abstract notions, but discovering their depth is worthwhile.

“If you believe that mathematics is solely about equations, seeing them as rigid black-and-white facts, then you likely perceive mathematics as solely stringent and binary,” states Chen. This book serves as a compelling counterargument to that misapprehension. Delving into the nuances of “equality” in mathematics will enrich your understanding of this field’s complexity and illuminate how the idea of equality is applied (and misapplied).

Sarah Hart is Professor Emelita and Provost of Geometry at the University of Gresham, UK. She authored Once Upon Prime.

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