When can a sum of reciprocals of natural numbers sum to a rational number? There are many unsolved problems in this area, by Erdős and others. With Vjeko Kovac, we have been able to resolve some open questions and make progress on others: https://terrytao.wordpress.com/2024/11/27/on-several-irrationality-problems-for-ahmes-series/
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and I happen to have just completed a decade of research into number theory from 3.000 BC to 300 BC,
Two pages of my paper for arXiv (I am an unaffiliated amature so can’t auto publish)
The Sumerians chose base sixty because sexagesimal reveals complete order in the prime numbers and total predictability of the sequence.
Happy to email you the whole paper (if you’re not like Knuth).