#hyperdimensionality

#hyperdimensionality

For more than two millennia, mathematicians have produced a growing heap of pi equations in their ongoing search for methods to calculate pi faster and faster. The pile of equations has now grown into the thousands, and algorithms now can generate an infinitude. Each discovery has arrived alone, as a fragment, with no obvious connection to the others. But now, for the first time, centuries of pi formulas have been shown to be part of a unified, formerly hidden structure.

According to Einstein's General Relativity, for every black hole that exists within the Universe, there are only three properties that go into it that matter in any way: the black hole's total mass, the black hole's net electric charge, and the black hole's intrinsic angular momentum, and that's it. It doesn't matter what type of matter went into the black hole in order to form it; all that matters is its mass, charge, and angular momentum.

In the weeks leading up to September 1891, mathematician Georg Cantor prepared an ambush. For years he had sparred - philosophically, mathematically and emotionally - with his formidable rival Leopold Kronecker, one of Germany's most influential mathematicians. Kronecker thought that mathematics should deal only with whole numbers and proofs built from them and therefore rejected Cantor's study of infinity. "God made the integers," Kronecker once said. "All else is the work of man."

Analogue quantum simulations are a useful tool for investigating these systems, particularly in regimes in which the applicability of numerical techniques is limited. For different simulator platforms, figures of merit include the electron bandwidth and interaction strength, temperature and the number of simulated lattice sites. Their use is further underscored by the ability to realize distinct lattice geometries, on-site degrees of freedom and by the physical observables that are accessible to experimental measurement.

Y.W. designed the experimental protocols, performed experiments, analysed the data and wrote the manuscript. Y.H., X.K., D.C., J.X.X. and W.Z. performed experiments and edited the manuscript. Y.C. and S.P. edited the manuscript. M.J., X.P. and J.D. proposed the experimental concept, designed experimental protocols and proofread and edited the manuscript. All authors contributed with discussions and checking the manuscript. Corresponding authors Correspondence to Min Jiang or Xinhua Peng.