Blue badges were for government employees (like I was), and green badges were for private contractors. And yes they have a lot of math and physics guys; my own physics lecturer was in my orientation class, actually. He was there for quantum computing, which reinforces my point. The government can be good at pioneering unproven / uncommercialized technologies, but in general they are like a blunt weapon; the profit motive and lack of bureaucracy eventually makes the private sector far better for improving the technology later. In the case of LLMs, they didn't even originate in government, and I don't think there's any chance they are being developed there at a more advanced level.