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When 1+1 doesn't equal 2: new book reveals why traditional concepts of equality are holding us back from creating a fairer world [1]
['Ellsworth Toohey']
Date: 2025-09-02
Mathematician Eugenia Cheng once attempted to learn Russian, struggling with a particularly difficult letter. щ. She says. "the session with my teacher went something like this"
Me: sh
Teacher: no
Me: sh
Teacher: no
Me: sh
Teacher: yes!
Me: sh
Teacher: no
Me: sh
Teacher: yes!
Me: sh
Teacher: yes!
Me: sh
Teacher: no
Me: sh
Teacher: no
Me: sh
Teacher: yes!
To Cheng's ears, she was saying exactly the same sound each time, but to the native speaker, crucial differences were audible. This linguistic frustration, Cheng argues in her new book Unequal: The Math of When Things Do and Don't Add Up, captures a mathematical truth: sameness is always a choice about what we decide to notice.
Cheng, a scientist in residence at the School of the Art Institute of Chicago, claims "almost everything can be considered equal and unequal at the same time." Through category theory — her field of mathematical research — she reveals that what we call "equality" is far more flexible and contextual than we imagine. A bagel and a coffee cup are mathematically "the same" (both have exactly one hole), while 1 + 1 can equal 0 ("such as if you turn over a piece of paper and then turn it over again").
This isn't mathematical relativism but rigorous thinking about relationships and contexts. When two students score 85 on an exam, we declare them "equal" while ignoring that one may have overcome far greater obstacles. Cheng argues this oversimplification — reducing complex, multidimensional situations to single numbers — corrupts everything from university rankings to discussions of social equality.
The mathematics grows challenging as Cheng ventures into higher dimensions, but she never loses sight of human implications. Whether analyzing "false equivalence" arguments in politics or explaining why mathematicians spend years classifying abstract shapes, she demonstrates that mathematical rigor enhances rather than eliminates nuanced thinking.
Unequal offers hope that better mathematical thinking can clarify rather than obscure important social questions. As Cheng puts it: "if we all had more practice at careful logical reasoning, we would get there faster" in creating a more just world. For readers willing to follow her intellectual adventure, this book reveals mathematics not as rigid rule-following but as creative, flexible tools for understanding a world where sameness and difference are far more complex — and more important — than they first appear.
Previously:
• Flatland is one of my favorite Math(ish) books
• Weapons of Math Destruction: how Big Data threatens democracy
• Weapons of Math Destruction: invisible, ubiquitous algorithms are ruining millions of lives
[END]
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