Explore the final chapter of our special series
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Over the past few months, our special series has been exploring the ways that math is constantly reinventing itself. The fourth and final chapter digs into an ambitious project to rewrite the core of topology.
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Two Researchers Are Rebuilding Mathematics From the Ground Up
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By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.
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How Alexander Grothendieck Revolutionized 20th-Century Mathematics
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Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?
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The Man Who Stole Infinity
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In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism.
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How Can Infinity Come in Many Sizes?
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By MARK BELAN & JORDANA CEPELEWICZ
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Intuition breaks down once we’re dealing with the endless. To begin with: Some infinities are bigger than others.
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Chapter 2:
LOGIC VERSUS PROOF
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In Math, Rigor Is Vital. But Are Digitized Proofs Taking It Too Far?
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The quest to make mathematics rigorous has a long and spotty history — one mathematicians can learn from as they push to formalize everything in the computer program Lean.
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How Writing Changes Mathematical Thought
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David E. Dunning explores how mathematical notation is a social, world-building technology.
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Chapter 3:
CUT TO THE CORE
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What Can We Gain by Losing Infinity?
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Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond.
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Why Math’s Final Axiom Proved So Controversial
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Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily.
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