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The Deep Link Equating Math Proofs and Computer Programs
...1934, the mathematician and logician Haskell Curry noticed a similarity between functions in mathematics and the implication relationship in logic, which takes the form of “if-then” statements between two propositions....
How Simple Math Moves the Needle
...do for you.) There’s a fun math problem here about how much space you need to turn your car around, and mathematicians have been working on an idealized version of...
Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they? “There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said....
Physicists Observe ‘Unobservable’ Quantum Phase Transition
...Einstein and Erwin Schrödinger, two of the most prominent physicists of the day, got into a dispute over the nature of reality. Einstein had done the math and knew that...
The Biggest Smallest Triangle Just Got Smaller
...from there — 100 points define 161,700 different triangles. Each of those triangles, of course, has a particular area. Hans Heilbronn, a German mathematician who fled his country before World...
Why Mathematical Proof Is a Social Compact
...Bulletin of the American Mathematical Society about how machines might change mathematics. Quanta spoke with Granville about the nature of mathematical proof — from how proofs work in practice to...
Complexity Theory’s 50-Year Journey to the Limits of Knowledge
...a research program for grounding mathematics in absolute certainty. He hoped to start from a few simple assumptions, called axioms, and derive a unified mathematical theory that met three key...
Math Proof Draws New Boundaries Around Black Hole Formation
For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help...
Two Students Unravel a Widely Believed Math Conjecture
...in the group of the mathematician Katherine Stange. Stange is a number theorist who describes herself as a mathematical “frog” — someone who delves deep into one problem’s intricacies before...