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Why the Sum of Three Cubes Is a Hard Math Problem
Looking for answers in infinite space is hard. High school math can help narrow your search. Given that humans have been studying numbers for thousands of years, you might think...
Cosmic Triangles Open a Window to the Origin of Time
...have a different menu of cosmological correlations.” Those are additional calculations to pursue with the new mathematical tools. But the researchers are also continuing to explore the math itself. Arkani-Hamed...
With Category Theory, Mathematics Escapes From Equality
...20th century, mathematicians increasingly began to do math in terms of weaker notions of equivalence such as homotopy. “As math gets more subtle, it’s inevitable that we have this progression...
On Your Mark, Get Set, Multiply
The way you learned to multiply works, but computers employ a faster algorithm. This summer, battle lines were drawn over a simple math problem: 8 ÷ 2(2 + 2) =...
Math Reveals the Secrets of Cells’ Feedback Circuitry
...is backed by a mathematical proof that no simpler answer exists — a good indication that natural feedback systems probably work the same way. Long before biologists figured out how...
His Artificial Intelligence Sees Inside Living Cells
...that doesn’t look like a cell at all.” It was very frustrating for me because the math and probability were all correct. But when we looked at the first images...
How (Relatively) Simple Symmetries Underlie Our Expanding Universe
...before. It is in the language of these symmetries that relativity simplified our mathematical description of the universe. In fact, the math becomes even nicer when the expansion of space-time...
How Randomness Can Make Math Easier
...mathematics were easier, mathematicians might not need to resort to randomness. But most important mathematical questions are too hard for mathematicians to answer directly. “It’s something that may be obvious,...
Philosophers Debate New ‘Sonic Black Hole’ Discovery
...in it. This implies that an evaporating black hole destroys information — something quantum mechanics doesn’t allow. Quantum math relies on the premise that information is never lost. As particles...