Problems in mathematics often have a simple “yes or no” structure: Is this statement true or false? But the most enduring and interesting problems

Mathematicians Find Long-Sought Building Blocks for Special Polynomials

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2021-05-26 00:00:03

Problems in mathematics often have a simple “yes or no” structure: Is this statement true or false? But the most enduring and interesting problems propagate through generations, the products of decades of work, like the medieval cathedrals that took centuries to build. The answers to these questions open new doors and provide novel structures on which to continue building.

In the year 1900, the mathematician David Hilbert announced a list of 23 significant unsolved problems that he hoped would endure and inspire. Over a century later, many of his questions continue to push the cutting edge of mathematics research because they are intentionally vague.

“Hilbert had a kind of genius when he formulated his problems, which is that the questions were a bit open-ended,” said Henri Darmon of McGill University. “These really hard open questions are great for mathematics, because they sort of guide us.”

Shortly before Hilbert announced his list of problems, mathematicians discovered the building blocks for a specific collection of numbers associated with the rational numbers, those which can be expressed as a ratio of whole numbers. This discovery was the basis for the 12th problem on the list, which asks for the building blocks associated with number systems beyond the rational numbers.