A PhD in Math takes a closer look at LLMs, Paul Erdős and AI’s role in maths and science

Can AI further science? How are hugely well funded AI labs like OpenAI trying to prove this? Today’s article explores the fascinating case of the frontiers of Mathematics. I geek out also about AI’s impact on science as evidenced by a new breed of AI startups generally understood as Neo Labs. To me these are moonshots that are typically highly funded AI research labs, often founded by elite ex-researchers from giants like Anthropic, OpenAI, DeepMind, and Google Brain.

• The pace of “Neo Lab” (a new category of AI startup) creation, AI labs designed to focus on pushing AI faster have received considerable recently funding like Mirendil, Engram, General Intuition, Prometheus, Trajectory and more.
• Mirendil is building “self-accelerating” AI that can do the actual work of an AI researcher. For instance, they train frontier models that are expert at AI R&D and build the product around it.
• Engram (eight months old) is an AI infrastructure startup building a persistent, learned memory layer for artificial intelligence in a bid to improve model efficiency and curb skyrocketing costs. The company says its technology can dramatically reduce the cost of running AI at enterprise scale. The B2B company trains models to study an organization’s documents, workflows, and institutional knowledge in advance, compressing that material into what it calls a “learned memory” layer that can be reused across queries. Read their introductory article here.
• General Intuition AI is a high-profile frontier AI research lab focused on building Large Action Models (LAMs) and “world models” designed to perceive, predict, and act in real time across virtual and physical spaces. Also that AI can learn from video games. Confusing to me in a nutshell, an agentic model that can generalize from gameplay to simulation to embodiment is General Intuition’s raison d’être. The Series A had some heavy hitters like Khosla Ventures, with participation from Jeff Bezos, Eric Schmidt, and researchers from Google DeepMind and MIT.
• Prometheus is a prominent AI startup founded in November 2025 by Jeff Bezos and Vik Bajaj (co-CEOs). I wrote about it here. In an era where physical AI and recursive self-learning AI are hot topics, this unique startup Prometheus, is focused on building AI models for physical tasks.It’s a massive bet to rearchitect how physical things are made. The prototypical definition of what a Neo Lab is post Anthropic, reimagining what’s possible not just with LLMs, but world models, RSI and training physics based datasets.
• Trajectory is building the platform for continual learning. Trajectory is betting the rapid iteration cycle that supercharged vibe-coding can help all kinds of companies build AI products that learn continuously. Their core thesis is that software products shouldn’t rely on static, frozen AI models; instead, they should act as “living systems” that continuously learn, steer, and improve from real-world user interactions.

Protein-folding models are the success story in AI for science.

In the late 2010s, researchers from Google DeepMind used machine learning to predict the three-dimensional shape of proteins. AlphaFold 2, announced in 2020, was so good that its creators shared the 2024 Nobel Prize in chemistry with an outside academic.

Yet many academics have had mixed feelings about DeepMind’s advances. In 2018, Mohammed AlQuraishi, then a research fellow at Harvard, wrote a widely read blog post reporting on a “broad sense of existential angst” among protein-folding researchers.

The first version of AlphaFold had just won CASP13, a prominent protein-folding competition. AlQuraishi wrote that he and his fellow academics worried about “whether protein structure prediction as an academic field has a future, or whether like many parts of machine learning, the best research will from here on out get done in industrial labs, with mere breadcrumbs left for academic groups.”

Industrial labs are less likely to share their findings fully or investigate questions without immediate commercial applications. Without academic work, the next generation of insights might end up siloed in a handful of companies, which could slow down progress for the entire field.

Physicist Mario Krenn sees artificial intelligence as a muse — a source of inspiration and ideas for scientists. It’s a description born from his past research and his current work at the Max Planck Institute for the Science of Light, where he and his colleagues develop AI algorithms that can help them learn new ideas and concepts in physics.

His efforts began years ago, when a research team Krenn was part of struggled to come up with an experiment that would let them observe a specific type of quantum entanglement. Krenn, suspecting that their intuition was getting in the way, developed a computer algorithm that can design quantum experiments.

“I let the algorithm run, and within a few hours it found exactly the solution that we as human scientists couldn’t find for many weeks,” he said. Using the blueprint created by the computer, his colleagues were able to build the setup in the laboratory and use it to observe the phenomenon for the first time.

In a subsequent case, the algorithm overcame a barrier by reviving a long-forgotten technique and applying it in a new context. The scientists were immediately able to generalize this idea to other situations, and they wrote about it in a paper for Physical Review Letters.