The Cache

If the lunar prospecting startups hadn't been scanning the moon at ever greater resolution, perhaps it would have never been found on the far side, but nothing that shiny was going to go undetected. Multiple companies found it around the same time, and while they tried to stay quiet the news soon leaked out. A hastily assembled robotic mission succeeded in capturing high resolution images, which made it clear this was no natural meteor.  The lack of an impact crater would have been astonishing, but here was a metallic object that had clearly been crafted. 

Retrieving the object soon became an obsession of the Americans and Chinese space agencies, along with several techno-billionaires with rocket companies. Ordinary concerns around safety melted away, along with several prototypes. Still, NASA got to the device first.

Any remaining suspicions of terrestrial provenance were erased by close inspection; the architecture resembled nothing even dreamed by humans. Whatever propulsion scheme had braked this craft would require years of investigation.  Nor were there obvious observing instruments. The construction had no exotic elements, but certainly unusual alloy compositions and microstructure. But perhaps the most strange was the apparent payload compartment, which showed no sign of being a pressure vessel.

Indeed, when the obvious yet alien latches were opened, the compartment revealed only eight thin metal plates, all but one polished yet mottled in a nearly imperceptible chaotic pattern. The exceptional plate had a golden edge and on one side a pattern of rows of dots, with large golden dots at the top and then at regular intervals the dots halved in diameter.  Microscopic analysis revealed the dots were indeed gold, but alloyed to the metal rather than being inlaid.  The same close inspection made clear the similarly imbued dots of platinum.  The obvious hypothesis proved to be true, testified by the sequence of integers which could be read in the top rows if gold was one and platinum zero.

The early rows had blank patches of metal to first make clear these were 64-bit words.  The same series repeating first with blanks and then with yet another word revealed the first delimiter - no blank metal was found after that.  

Next came sets of Pythagorean triples, first with delimiters and then new symbols, revealing summation and equality symbols.  Rearrangements and refactorings and restatements of these revealed more mathematical symbols and the system of specifying variables.  Additional familiar equations revealed the language of trigonometry. The AI experts and cryptographers now had more than enough to compare all of the data to known theorems, with regular victories exposing more of the alien mathematical lexicography, each discovery priming the revelation of scores of additional symbols and conventions. Even the formats for geometrical diagrams and images fell to the computational onslaught.

The first tablet's pattern of progressive reduction prevented overlooking of the final density, with bits comprising only tens of heavy atoms on the surface.  Every tablet, as well as the back of the alien Rosetta Stone, was covered at this density.  It was soon obvious that the tablets had a solitary purpose: they were entirely devoted to storing mathematical proofs and their foundations. And without exception, every one verified with with computational tools for that purpose. 

The academic mathematical community, already buffeted by the incursion of AI, struggled to even react.  It wasn't just that nearly every theorem known to humanity was here, or that a large fraction of the open problems under active study were also represented. It seemed as though entire tablets were devoted to entirely unknown domains.  

A few academics declared they would abandon their field.  One announced an intention to enter one of the most cloistered monasteries on the planet.  Others vowed to forge on without peeking at the cosmic cheat sheet, as they called it.  Some grabbed fat sinecures from tech companies, delving into whether modern cryptography was now an illusion or if there were other commercial advantages to be gained. Still others switched full time to trying to explain it all, to elucidate for their fellow mathematicians or to the masses the relevance of the corpus from above.

Still others pondered the open questions that weren't covered; it seemed impossible these were oversights.  Had the mysterious authors simply excluded all that could not be proven? And what of the handful of missing theorems?  Was there a pattern to the omissions? Others cared not for the pattern; they declared only these spaces worthy of further human endeavor, untouched by alien influence.

Those of a philosophical bent, whether mathematicians or not, were left to ponder: Why?  Why had a civilization sent so singular an intellectual package?  How many had they sent out into the universe?  When humans had first launched into the void, we had sent images of ourselves, of our home.  We later sent music and voices.  Did these aliens not have art and music?  Or did they believe only math was worthy, requiring no cultural context to understand.  Or had it simply been their religion, the equation the most sacred expression?