Science
Mathematicians deploy artificial intelligence to solve longstanding inverse Galois problem
Scientific American reports that researchers used AI assistance to find the missing polynomial for sporadic group M23.
The short version
- A team of six mathematicians assembled after a Caltech meeting solved the inverse Galois problem for the M23 sporadic group.[Scientific American]
- The inverse Galois problem requires identifying an equation matching a specific symmetry group, a puzzle unresolved for M23 since the 1980s.[Scientific American]
- Researchers utilized artificial intelligence to approximate surface equations numerically before adjusting coordinates to overcome computational memory limits.[Scientific American]
Key facts
- In the 1980s, mathematicians found corresponding polynomials for 25 of 26 sporadic groups, leaving only M23 unsolved.[Scientific American]
- A newly formed six-person research team utilized AI to evaluate symmetry combinations in M23 and approximate surface equations.[Scientific American]
- The numerical approximations reached 90 digits and exhausted computer memory before a change in coordinate systems allowed progress.[Scientific American]
What remains uncertain
- Prior to the finding, researchers had questioned whether a polynomial generating the M23 group existed at all.[Scientific American]
Sources
Outlet counts describe coverage, not independent confirmation. Reports may share a wire service or original source.
- Mathematicians use AI to find mysterious symmetries, solving decades-old problemScientific American metered