those itching for their Good Will Hunting moment, the Guinness Book of Records puts Goldbach's Conjecture as the current longest-standing maths problem, which has been around for 257 years. It states that every even number is the

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Today's mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It's one of the seven Millennium Prize Problems, with $1 million reward for its solution. It has implications deep into various branches of math, but it's also simple enough that we can explain the basic idea right here.