Linear A is a writing system from Minoan Crete. About 1,400 inscriptions survive, written between roughly 1800 and 1450 BC. Nobody can read them. The language underneath is a complete isolate with no known relatives. It has been undeciphered for 70 years.
I got interested in it a few months ago and I have not been able to stop thinking about it since.
Why it hasn't been solved
The standard approach is phonetic matching. You take the known sound values from Linear B, the related Mycenaean script, and try to apply them to Linear A signs. The problem is that Linear B is Greek and Minoan is not Greek. Every attempt at phonetic mapping produces results that don't make sense in any known language.
The corpus is also small. 1,400 inscriptions is not a lot to work with, and most of them are short. The longest tablets are administrative records, not literature. There is no bilingual text. There is no Rosetta Stone equivalent.
What I've done so far
Honestly, not much yet. I've been collecting the data. The full Linear A corpus is available through the SigLA database and the lineara.xyz project which has every known inscription digitized with photographs and sign annotations. I have all of that downloaded locally.
I've been reading through the academic literature on Minoan archaeology, the palace economy at Hagia Triada and Knossos, what the tablets actually record at a functional level. Most of them are storage inventories and tribute records. The numbers and logograms are partially readable because they match Linear B conventions.
I have an idea for an approach that I think is worth trying. I'm not ready to write about it yet because I haven't tested any of it. I'll post more when there's something real to show.
Why I think it's worth trying
Most of the people who have worked on this are linguists and archaeologists. That's the right background for a lot of the problem. But there's a computational angle that hasn't really been explored, and the tools available now are different from what existed even five years ago.
Also it's one of the last genuinely unsolved puzzles from the ancient world. The hieroglyphs are solved. Linear B is solved. The Minoan script is still sitting there. That's hard to walk away from.
If you work in this area and want to talk, my email is contact@phnix.dev. Updates here when there's something worth writing about.