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Mathematicians Eliminate Long-Standing Threat to Knot Conjecture
A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.
Special Surfaces Remain Distinct in Four Dimensions
For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.
How Complex Is a Knot? New Proof Reveals Ranking System That Works.
“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.
Machine Learning Becomes a Mathematical Collaborator
Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.
In a Single Measure, Invariants Capture the Essence of Math Objects
To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.