Instant Genius How the maths of sameness and difference can change the way you view the world
Jul 6, 2025
Eugenia Cheng, a renowned mathematician and author of 'Unequal – The Maths of When Things Do (and Don’t) Add Up', joins the discussion to reveal the hidden depths of the equals sign. She explains how understanding sameness and difference can reshape our world view. The conversation delves into the role of perspective in math and its applications in everyday problem-solving. Cheng illustrates the importance of logical equivalence in reasoning and highlights how mathematics enhances critical thinking and encourages embracing complexity.
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Equations Show Points of View
- Equations represent two different points of view on the same thing being equal in some way.
- We usually focus only on equality and overlook the inherent inequalities in how we decide what counts as equal.
Seeing Math from Different Angles
- Explaining 1 plus 3 equals 3 plus 1 to children involves physical objects and different viewpoints.
- Walking around a table literally changes your perspective on the same equation.
Local and Global Views Matter
- Zooming in reveals details, while zooming out shows how parts form a whole.
- This ability to switch perspectives is key in topology and useful in understanding real-world complexity.