Mathematicians Harness Randomness to Crack a 55-Year-Old Conjecture
9 hours ago
- Mathematician and juggler Ronald Graham conjectured in 1971 that any set of nonzero integers modulo a prime can be rearranged so that all partial sums are distinct.
- The conjecture was solved using a combination of randomness and probabilistic methods across four papers by multiple mathematicians.
- Key contributions came from Müyesser and Pokrovskiy (large sets), Kravitz and Bedert (small sets), and finally Sauermann and Pham (medium sets) using anti-concentration and Fourier analysis.
- The proof shows that for sufficiently large primes, a random ordering can be fixed to avoid zero-sum subsequences, confirming the conjecture.
- The solution is theoretically significant but not practical for actual juggling due to the enormous size of numbers involved.