Mathematicians have proven the 'sandwich conjecture,' a 2004 hypothesis that any sufficiently large graph can be mathematically sandwiched between two simpler graphs. This breakthrough, completed in 2025 by three mathematicians, shows that random binomial graphs and more complex regular graphs are connected through a unified random process, allowing difficult properties of regular graphs to be derived from simpler binomial graphs.
Mathematicians proved in 2025 that any sufficiently large graph can be sandwiched between two simpler graphs, a conjecture posed in 2004 that connects two different types of random graph structures. This breakthrough demonstrates that random binomial graphs and random regular graphs are related in a deeper way, allowing difficult properties of regular graphs to be proven through their simpler counterparts.
A global survey of physicists revealed surprisingly little consensus on fundamental physics questions, with no majority supporting the standard cosmological model, leading dark matter explanations, or any single quantum gravity theory. However, 68% agreed the Big Bang does not necessarily represent time's beginning. Researchers interpret the divisions as evidence that physics frontiers remain genuinely unsettled and alive.