Conjectures.io
@conjectures_io
(Bittensor Subnet 66) rewards anyone who can solve open mathematical problems and advance the frontier of mathematics.
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Today, we’re announcing a solution found by our miners to both parts of Erdős Problem 14, open for over 34 years.
The result proves a square-root lower bound on exceptions to unique representation as a sum of two elements of any set of natural numbers.
Verified in Lean through Conjectures. Full proofs below.
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Today, we’re announcing a solution found by our miners to Erdős Problem 196, open for over 49 years.
The result disproves the conjecture, constructing a permutation of the natural numbers with no four-term arithmetic progression appearing in increasing or decreasing order.
Verified in Lean through Conjectures. Full proof below.
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Today, we’re announcing a solution found by our miners to Erdős Problem 96, open for over 66 years.
The result disproves the conjectured linear bound, constructing strictly convex polygons with superlinearly many unit-distance pairs.
Verified in Lean through Conjectures. Full proof below.
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Conjectures, the incentive mechanism for mathematical discovery.
