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A new rare high-rank elliptic curve, and an orchard of Diophantine equations
I got an email the other day from mathematician Bogdan Grechuk, whose book Polynomial Diophantine Equations: A Systematic Approach ( was recently released. This is to my mind a rather remarkable bo…
The start of the book solves extremely easy examples, but pays close attention to the process, so that it can identify classes of equations that this method will apply to. This blog post led to a chain of papers using the phrase “fruit equations” by authors wholly unconnected with me, with the first solving what was at the time an open problem on Grechuk’s list. Moreover, trying to optimise to find a small ZFC-undecidable equation, rather than an algorithmically unsolvable one, is another whole kettle of fish; compare how the value BB(745) of the Busy Beaver function is not possible to calculate in ZFC, through a line of work whose current endpoint is by Johannes Riebel’s 2023 Bachelor thesis.
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