Russian mathematician Yurii Nesterov was recently awarded the Gauss Prize for outstanding mathematical contributions for his “groundbreaking work” on optimisation. The award cited his work on gradient descent methods – and in particular, the “efficiency gains [they] provide to AI technologies”.

Everyone using large language model (LLM) chatbots such as ChatGPT, Claude and Gemini – for any purpose – depends on Nesterov’s methods. They may speak like humans and be personified with names, but under the bonnet, LLMs are computer programs that work via optimisation of billions of parameters known as neural networks for their similarity to how brains function.

These pure mathematical systems are powered in part by gradient descent algorithms, or variants of them. Their development represents one of the biggest technological breakthroughs of the 21st century.

But where does the knowledge that underpins this technology come from – and who should be allowed to own it?

Why gradient descent is key to AI systems

If you were standing in a mountain range and wanted to get to the bottom of a valley as fast as possible, you’d take steps downhill until you got there. Fundamentally, this is how gradient descent methods work.

For a given task with a set of parameters – such as how well an LLM can predict the next word in a sentence – the idea is that gradient descent provides a way to get to the best prediction, the point of minimum error, taking as few steps as possible. In our example, this point represents the most likely next word in the sentence.

Nesterov’s contribution has been finding optimal ways to achieve this. One of his key insights is using momentum to help you get to the bottom of the valley faster – known as the Nesterov Accelerated Gradient method (here’s a deeper explanation of the mathematics involved).

This work has made huge-scale optimisation feasible at workable speeds – thus underpinning the rapid development of LLMs, and AI systems more generally, over the last few years.

This technology is affecting more and more aspects of life. At home, AI agents are being touted as ways to manage busy households. In medicine, the first AI-assisted brain surgery was recently performed in a London hospital. In mathematics, AI-generated proofs claim to have solved a number of longstanding problems, with some referring to the AI agents as “collaborators” in this work.

All of this leads to big business. The race for AI dominance is built on massive capital and research and development expenditure, to develop the technology and supporting infrastructure required to support this global industrial revolution.

While in the west, private AI companies are bearing a sizeable part of this burden (without, in most cases, seeing any profits), the role of publicly funded research is and will remain critical to their business models.

In the US, obligated federal government spending on AI increased from US$675 million to US$7.2 billion (£5.3bn) between 2024 and 2026 – an increase of almost 1,000%.

There has already been considerable debate – and some high-profile legal cases – regarding the ethics of AI companies training their models on the back catalogue of human creativity, only to rent the results back to us. Far less scrutinised is the question of AI companies developing technology using knowledge that only exists due to sustained public investment over many decades, via academics such as Nesterov.

The fact that big tech companies use complex international tax strategies to limit their tax liabilities adds to the sense that their aggressive defence of intellectual property rights is out of kilter with the publicly funded research that plays a key role in its development.

Technology built on public knowledge

In most cases, academics work in publicly funded institutions on research grants that are largely funded by governments, whether through the Horizon Europe programme, the US National Science Foundation, or UK Research and Innovation. All of these bodies are ultimately funded by the taxpayer.

None of the rapid development in AI exists in a vacuum. It is built on decades of pioneering, blue-skies work on optimisation and neural networks, done by academics and largely funded by taxpayers at a time when the real-world application was still a distant dream.

Legal arguments around COVID vaccine patents are one example of how the private sector has tried to deny this public sector involvement – and a related share in any profits. So where is the public sector in this debate?

The EU is taking steps to secure control of its digital infrastructure, with a renewed focus on sovereignty in digital services. In the UK and elsewhere, a growing number of open-access mandates should mean that knowledge created by public funding stays public. While it can be used freely for commercial purposes, successful businesses would then theoretically pay back into the system via general taxation.

However, such knowledge flows beyond national borders. Efforts to capture value for reinvestment into the AI research landscape will be made harder by the fact that the tech companies’ business models depend on lobbying governments hard to avoid regulation. Any efforts to make them pay more for upstream public research and development are likely to be strongly resisted.

In the case of Nesterov and his fast gradient methods, this foundational work has been done in European institutions – yet the AI companies dominating the market are overwhelmingly based in the US or China. It rankles when access to these models is then restricted by foreign companies and governments.

James David Pickering does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

Harnessing renewable resources such as wind and solar energy is vital for the green transition. But these renewables are intermittent and unpredictable. It’s impossible to control when the wind blows and when the sun shines.

Currently, we don’t have to rely on the weather to boil a kettle. That’s largely thanks to our use of fossil fuels. To break our reliance on this finite and polluting source of power, we need to be able to store vast amounts of renewable energy cheaply and safely, but unfortunately, no technologies yet tick all the boxes.

Lithium-ion batteries are used in our phones, laptops, and electric vehicles. But lithium-ion technology depends on costly, geographically concentrated materials such as lithium and cobalt.

Cobalt mining can be a dangerous and polluting process. The organic lithium-ion-containing electrolyte (the liquid chemical between the positive and negative terminals inside a battery) is flammable. Because it poses a fire hazard, it’s risky to deploy these batteries at a large enough scale to power our homes, cities, and industries.

But there is an alternative solution: flow batteries.

In a flow battery, energy is stored in liquid electrolytes which are held in large external tanks. To charge or discharge the liquid, it is pumped through a stack of cells where electrochemical reactions generate or consume electrons. This has several advantages.

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Read more: What will batteries of the future be made of? Four scientists discuss the options – podcast

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In most batteries, two properties (energy and power) are intrinsically linked. Energy refers to how much electricity is actually stored by the battery and therefore how long that supply can run at a given rate. Power is the rate at which the energy is delivered and how much can be supplied within a given time.

Usually, it’s impossible to change one without changing the other. To store more, you add cells, and that adds power you may not need (and cost you don’t want).

However in flow batteries, this is not the case. Need to store more energy? Simply use larger tanks with more liquid. Need more power? Simply use a bigger cell stack. This ability to independently control power and energy makes the technology cheaper to scale up. Additionally, unlike lithium-ion batteries, flow batteries can’t catch fire (as they are mostly water) and are extremely durable. Some flow batteries have been in operation for more than 20 years.

Several large-scale flow battery systems have already been deployed. In China, the largest systems that connect to the grid reach gigawatt-hour scale (equivalent to powering 100,000 homes for a full day). In Switzerland, what will be the world’s largest flow battery, at 2.1 gigawatt-hours (equivalent to powering over 200,000 homes for a full day) is being constructed to power an AI data centre. Nevertheless, flow batteries are still an emerging technology, with several challenges still to solve.

Test cells

Worldwide, researchers like us are developing new electrolyte chemistries and materials to reduce the cost of flow battery systems and drive wider adoption. But getting started in flow battery research can be quite daunting. Test cells can often cost thousands of pounds and testing a new cell requires lots of ancillary equipment.

Through our research, we have developed a low-cost 3D-printed test cell. This makes flow battery research much easier and has enabled our research group to test dozens of these cells. But our team struggled to get repeatable test results. It was also difficult to replicate results from previous flow battery studies by other groups in our own labs at Queen’s University Belfast. This resulted in several months of frustration as we scrutinised every aspect of our testing protocols.

As it turned out, our research group was not alone. At a conference in early 2024, we attended a talk by Fikile Brushett, a chemical engineering professor from the Massachusetts Institute of Technology in the US. He described the lack of protocols in this field. Together, we have led a series of studies to investigate and work out how to tackle the issue of reliably replicating data from reported scientific studies.

In one study, published in April 2026, we sent our low-cost 3D-printed test cell to several leading research groups around the world. We were struck by the extent of performance variability between different groups all nominally testing the same battery. Since then, we have identified several potential causes for this variability and have suggested improvements to testing protocols.

Our latest study has involved more than 30 research groups assessing our test cells. Our testing data is now publicly available online. We are using this to pin down why performance varies across the cohort. Our findings will help the community to develop testing protocols that all researchers can use.

Eventually, this work could make it easier for newcomers to make a start in flow battery research. It could also give established groups a reliable foundation to compare results and accelerate their work. This all helps chemical engineers innovate more quickly towards storing renewable energy cheaply, safely and at scale.

Joshua James Bailey receives funding from UKRI's EPSRC.

Hugh O'Connor received funding from UKRI's EPSRC and PSDI.

Society depends on chemistry far more than we consciously realise, from medicines to energy to electronics. However, chemistry is viewed with as much apprehension as gratitude, because of the pollution and health problems that some chemicals cause.

There is a strong desire to have all the benefits of chemistry, but none of the downsides. This has led to terms like “chemical free product” coming into popular usage.

Of course it’s impossible to have a chemical free product – the ingredients in these products are still chemicals. But they employ a different approach, using benign ingredients from nature. These innovative products are examples of “green chemistry”.

Green chemistry takes a holistic – all encompassing – approach to the production of chemicals. This approach brings chemistry into balance with nature and avoids harm. Green chemistry protects the environment and considers the future by design.

Examples of green chemistry include using compounds derived from seaweed to replace man-made plastics. Another is capturing CO₂ from power plants and transforming it into more sustainable fuels for jets and ships. The principles of green chemistry are also being applied to developing smart materials that can change their properties, such as their colour.

Fresh approaches

Instead of merely making older approaches to chemistry a little bit “less bad”, green chemistry is about finding new functions for the materials we use in our daily lives and getting better levels of performance out of them.

This approach reflects the fact that using resources wastefully can be eliminated through smarter chemistry. This involves rethinking everything, including the supply chains.

An example of finding new functions for existing chemicals includes the use of natural polymers derived from seaweed, called alginates, that are already used in cosmetics and foods, to also replace plastics in packaging so that packaging biodegrades in soil.

The Green Chemistry in America 2026 report published by the Gordon and Betty Moore Foundation surveyed 300 US executives and other leaders from the worlds of research and development and technology. Over 90% of those leaders who were familiar with green chemistry agreed that it delivers a competitive advantage. Some 76% of these leaders said that green chemistry will fuel innovation and long term economic growth.

Waste as raw material

Countless tonnes of waste are often generated during manufacturing. This can be produced in far greater quantities than the product itself and can turn into pollution. Instead, green chemistry uses waste as a raw material, making chemical use more circular and sustainable.

Instead of changing our climate with gigatonnes of CO₂ emitted from smokestacks, green chemistry is capturing CO₂ and transforming it into products like more sustainable fuels for jets and ships. These synthetic fuels are created by combining green hydrogen (produced from water using renewable electricity) with the captured carbon dioxide.

Near-term investments are advancing the development of dynamic – and sustainable – materials that will change in ways that we want them to on command; such as their colour, or ability to conduct electricity.

These are but a few of the near-term visions of how green chemistry could foster a revolution in innovation. However, these advances need to take place on a timeframe and scale that can benefit humanity in the near future.

Some of the world’s top scientists met in Stockholm in May 2025 to wrestle with the question of how to make this possible. The result was The Stockholm Declaration on Chemistry for the Future.

This declaration contains two particularly important sentences that reflect its purpose. The first of these is that “the chemistry of sustainability recognises that sustainability without innovation is impossible and innovation without sustainability would be ruinous”. The second key sentence is: “While scientific discovery and invention is crucial, it is also not sufficient by itself.”

The Stockholm document goes on to list all the sectors of society that are needed to implement its vision. These include business, investment, education, communication, policy and public support.

All consumers are affected by “bad” chemistry, so they should take decisions accordingly – demanding green chemistry in all products.

The resources available to improve the ways that chemicals are made include sunlight, wind, agricultural and food waste, geothermal energy and – most importantly – human ingenuity. There is an immense potential for innovation.

Paul T Anastas has equity in several carbon dioxide utilisation companies.

Andrew C Marr does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.