Mathematicians spent 2025 exploring the edge of mathematics
Somewhere at the edge of mathematics lurks a number so large that it breaks the very foundations of our understanding - and in 2025 we came a step closer to finding it
Mathematics
Somewhere at the edge of mathematics lurks a number so large that it breaks the very foundations of our understanding - and in 2025 we came a step closer to finding it
26 December 2025
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When numbers get large, things get weird
Jezper / Alamy
In 2025, the edges of mathematics came a little more sharply into view when members of the online Busy Beaver Challenge community closed in on a huge number that threatens to defy the logical underpinnings of the subject.
This number is the next in the “Busy Beaver” sequence, a series of ever-larger numbers that emerges from a seemingly simple question – how do we know if a computer program will run forever?
To find out, researchers turn to the work of mathematician Alan Turing, who showed that any computer algorithm can be mimicked by imagining a simplified device called a Turing machine. More complex algorithms correspond to Turing machines with larger sets of instructions or, in mathematical parlance, more states.