Solving Millennium Problems

A solution to the Navier-Stokes equations, which describe fluid motion, is considered "imminent." Several research teams are currently in a competitive race to achieve this breakthrough.

Driven by the use of AI (Google DeepMind) to find new strategies, with a general consensus that a solution is near.

Cryptography & Quantum Computing

RSA-2048 encryption could be broken by a cryptographically relevant quantum computer (CRQC), an event known as "Q-Day."

Accelerated by algorithmic improvements and hardware roadmaps, with predictions pointing to ~2030 (± 2 years).

AI-Driven Mathematical Discovery

AI systems like AlphaEvolve are now solving complex problems, matching or surpassing human performance.

AI acts as a research accelerator, capable of exploring vast problem spaces and identifying patterns beyond human scope.

The Changing Landscape of Mathematical Research

The potential breakthroughs highlighted above are not happening in isolation. They are part of a broader evolution in how mathematics is conducted:

The Rise of AI Collaboration: The partnership between mathematician Javier Gómez Serrano and Google DeepMind exemplifies a new paradigm. AI is no longer just a computational tool but a collaborative partner that can "greatly accelerate research" and "change the way we do mathematics."

Focus on Foundational Impacts: The potential breaking of RSA-2048 encryption underscores how abstract mathematical advances can have immediate, real-world consequences, forcing a global shift to new cryptographic systems.

Global and Collaborative Efforts: Major challenges are increasingly tackled by teams of researchers from around the world, often combining expertise from different fields such as geophysics and computer science, as seen in the Navier-Stokes project.