In a stunning turn of events, two Caltech mathematicians have finally solved a 175-year-old math problem that has confounded researchers for generations. The proof was posted online in September 2021 by Alex Dunn and Maksym Radziwill, who worked tirelessly for several years to finally crack the code.
This math problem, known as the Gauss sum, was first stumbled upon by German mathematician Ernst Kummer in the early 1800s. At one point, the quirky feature of number theory was thought to be false, but then researchers found hints that it may actually be true.
After years of frustrating dead ends, Dunn and Radziwill finally found the key to solving the mystery. Their proof has been met with acclaim by the math community, and finally puts to rest one of the oldest unsolved problems in mathematics.
This activity uses modular arithmetic, which is a type of math that deals with remainders. An easy way to understand it is by thinking of a clock face divided into 12 hours. For example, when it’s noon or midnight, the numbers go back to 1 instead of continuing to count up forever. This “modulo 12” system makes timekeeping simpler since we don’t have to keep track of every single hour.
Modular arithmetic can be applied to any number, not just 12. In the case of the Gauss sum, the modular arithmetic is done modulo p, where p is a prime number. This means that when we divide the sum by p, we’re only interested in the remainder.
The proof by Dunn and Radziwill is a significant breakthrough in the world of mathematics, and will likely lead to new discoveries in the field for years to come. Who knows what other secrets this 175-year-old math problem has yet to reveal?
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