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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?
New Calculations Show How to Escape Hawking’s Black Hole Paradox
Inside of a black hole, the two theoretical pillars of 20th-century physics appear to clash. Now a group of young physicists think they have resolved the conflict by appealing to the central pillar of the new century — the physics of quantum information.
In New Paradox, Black Holes Appear to Evade Heat Death
The puzzling behavior of black hole interiors has led researchers to propose a new physical law: the second law of quantum complexity.
Are There Reasons to Believe in a Multiverse?
Several areas of physics suggest reasons to think that unobservable universes with different natural laws could lie beyond ours. The theoretical physicist David Kaplan talks with Steven Strogatz about the mysteries that a multiverse would solve.
Is Perpetual Motion Possible at the Quantum Level?
A new phase of matter called a “time crystal” plays with our expectations of thermodynamics. The physicist Vedika Khemani talks with Steven Strogatz about its surprising quantum behavior.
New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’
Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.