Tensors are used all over math and science to reveal hidden geometric truths. What are they?
After Albert Einstein published his special theory of relativity in 1905, he spent the next decade trying to come up with a theory of gravity. But for years, he kept running up against a problem.
He wanted to show that gravity is really a warping of the geometry of space-time caused by the presence of matter. But he also knew that time and distance are counterintuitively relative: They change depending on your frame of reference. Moving quickly makes distances shrink and time slow down. How, then, might you describe gravity objectively, regardless of whether you’re stationary or moving?
Einstein found the solution in a new geometric theory published a few years earlier by the Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita. In this theory lay the mathematical foundation for what would later be dubbed a “tensor.”
Since then, tensors have become instrumental not just in Einstein’s general theory of relativity, but also in machine learning, quantum mechanics and even biology. “Tensors are the most efficient packaging device we have to organize our equations,” said Dionysios Anninos, a theoretical physicist at King’s College London. “They’re the natural language for geometric objects.”