On 18–19 November 2026 the UK Knowledge Exchange Hub for Mathematical Sciences (KE Hub) and Innovate UK Business Connect will hold a two-day Green AI sandpit at STFC's Rutherford Appleton Laboratory, Harwell. The question it asks is how the mathematical sciences can reduce the energy and resource requirements of AI as demand and deployment keep growing. I am on the leadership consortium, and this piece sets out why I think the question is the right one. The sandpit is listed on our events page and described on our future page.
The pressure is real and now formally recognised. The International Energy Agency expects data centre electricity use to more than double to around 945 TWh by 2030, with AI the most important driver. In December 2025 the UN Environment Assembly adopted its first resolution on the environmental sustainability of AI systems, encouraging states and stakeholders to minimise AI's environmental impacts. In the UK, the evidence annex to the UK Compute Roadmap estimates that emissions from AI compute between 2025 and 2035 could range from 34 to 123 MtCO₂, around 0.9–3.4% of projected UK emissions over the period.
Faster, more efficient chips help, but much of the recent progress has come from mathematics: better algorithms, sharper approximations and smaller number formats. Google reports that the energy of a median Gemini text prompt fell 33-fold in a year, and credits software efficiency work alongside clean energy procurement. The Green AI argument made in 2020 still stands: efficiency should be reported and rewarded alongside accuracy, not treated as an afterthought, especially after Strubell and colleagues showed how much energy model development can consume.
The Academy for the Mathematical Sciences' recent primer, Mathematics in the age of artificial intelligence, surveys the fields that underpin AI. The sandpit draws on it for a working list: control theory, complexity theory, complex systems theory, algebraic geometry, dynamical systems, graph theory, information theory, machine learning, mathematical analysis and numerical analysis. Here is what a few of them already contribute.
Large models are heavily over-parameterised, and the changes needed to adapt them to a task often have low rank. LoRA exploits this by freezing the pre-trained weights and training only small low-rank matrices; on GPT-3 175B it cut trainable parameters by 10,000 times and GPU memory by three times, with quality on par with full fine-tuning. The primer notes that the space of low-rank objects is an algebraic variety, which is why algebraic geometry has something to say about when and why this works. QLoRA combined it with 4-bit weights to fine-tune a 65-billion-parameter model on a single GPU.
Every multiplication at lower precision moves fewer bits and uses less energy. The question is when accuracy survives. Mixed precision training showed that half-precision arithmetic, with a single-precision master copy and loss scaling, roughly halves memory. LLM.int8() ran 175-billion-parameter models in 8-bit without degradation by isolating the few outlier features that need 16 bits. These are applications of rounding-error analysis that numerical linear algebra has long studied; Higham and Mary's survey of mixed precision algorithms shows how much theory is there to be used.
Deep Compression pruned connections, quantised weights and applied Huffman coding to shrink networks 35 to 49 times without loss of accuracy, small enough to fit in on-chip memory, and measured layer by layer at three to seven times better energy efficiency. Speculative decoding uses a small model to draft tokens that a large one checks in parallel, giving two to three times faster generation with identical outputs. Both rest on measuring how much information a weight or a token actually carries.
Much AI work, such as training, batch inference and evaluation, can wait. Grid carbon intensity varies by hour and region, and studies of temporal workload shifting and of carbon-aware scheduling in the cloud show that choosing when and where jobs run changes their emissions. Deciding this under uncertain forecasts and deadlines is a problem in optimal control and scheduling.
Complexity theory tells us which problems no amount of hardware will make cheap, and where structure in a problem makes a tractable method possible. As the primer puts it, AI systems are bound by the same laws of computational complexity as any other computation. Knowing that bound prevents spending energy on brute force where a better formulation exists.
The algorithms are only half of it. The software that serves a model, the inference engine, its kernels and the code around it, also draws energy on every prompt, and it can be optimised like any other code. Researchers on GreenCode at Aalborg University have shown this with the GreenCode Constitution (Antheas Kapenekakis, Esther Kim, Dragos Ionescu, Bent Thomsen and Michele Albano, accepted for the GreenAI workshop at ECML PKDD 2026). Instead of ad hoc prompting, an AI agent works to a written hierarchy: five inviolable meta-principles, correctness first, then 37 energy anti-patterns in four severity tiers. It profiles the code, plans ranked fixes, critiques each change against the principles, measures the energy again and keeps only the changes that save.
On llama.cpp, a widely used and already highly tuned inference engine, the agent cut GPU energy by 4.7% (3.7% in total). The same approach saved 28.4% on 4K video transcoding in FFmpeg, 9.4% on a data synthesis pipeline and 25.1% across 45 algorithmic problems in six languages. Two findings matter for green AI in particular. The models that drive AI's energy demand can reduce the energy of the software they run on. And faster is not always greener: on llama.cpp the energy saving exceeded the 3% gain in speed, which is why the loop measures energy directly instead of treating speed as a proxy. The constitution is published as an open skill that any agent can use, with its tooling on GitHub.
GreenCode's pipeline measures, optimises and certifies the energy use of software, and it has to keep its own AI lean. That means small, fine-tuned models instead of the largest available, retrieval so that models look things up rather than memorise, routing each request to the smallest model that can answer it, scheduling heavy work against grid carbon, and measuring inference energy rather than assuming it. Each of these draws on the mathematics above. Our green AI benefit page and the green-optimised generative AI feature describe the approach.
Efficiency alone does not guarantee lower emissions. Cheaper computation tends to invite more of it. Widdicks, Berners-Lee and colleagues argue that addressing rebound effects in digital technology needs systems thinking, treating efficiency as one solution among others that requires constraints on emissions if the savings are to be realised. Our climate case discusses this in more detail. Mathematics can make AI cheaper to run; policy and practice decide whether that becomes lower emissions.
The sandpit brings mathematical scientists together with people from business, industry and government who build and run AI. Over two days they will agree a common language, identify the challenges and barriers where mathematics could make the biggest difference, and test which are feasible and urgent. The formal output is a position paper and roadmap towards a substantial UK research investment in green AI with the mathematical sciences at its centre. Our further resources page collects related tools and standards.
If you work on the mathematics of efficient computation, or on running AI at scale, and would like to contribute, please get in touch.
