Researchers have discovered that problems solvable in time t only require approximately √t bits of memory, challenging long-held beliefs about computational complexity. This breakthrough, presented by MIT's Ryan Williams, demonstrates that efficient memory usage can significantly reduce the space needed for computation. The findings suggest that optimizing memory is more crucial than merely increasing it.

A recent laser-powered fusion experiment has achieved significant advancements, doubling its power output and marking a pivotal step towards practical fusion energy. This breakthrough demonstrates the potential for more efficient and sustainable energy sources in the future, emphasizing the importance of ongoing research in fusion technology.

Spanish mathematician Javier Gómez Serrano has joined forces with Google DeepMind to tackle the Navier-Stokes equations, a millennium-old mathematical problem with a $1 million prize for its solution. Utilizing artificial intelligence, the team believes they are close to a breakthrough that could revolutionize the understanding of fluid dynamics, impacting fields such as meteorology and medicine. Gómez Serrano emphasizes the rapid progress being made and the potential of AI to transform mathematical research.