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.

The UK Space Agency and space startup Vast just signed an agreement to send Paralympic sprinter and below-knee amputee John McFall into orbit as early as 2027. Most coverage framed it as a victory for inclusion. As a space health researcher, I think something far more interesting happened.

For 70 years, spaceflight has assumed a rigid archetype: a healthy white man with a military background. The assumption was that physical uniformity minimised risk. As we prepare for Mars, the evidence increasingly suggests the opposite.

Star Trek understood this decades ago: exploration rewards difference. The further you travel into uncertainty, the more kinds of human experience you need. It debuted in 1966 with a Black female communications officer, a Japanese helmsman, a Russian navigator, a biracial Vulcan, and a captain who made mistakes and felt his humanity down to the last drop.

What strikes me now as a scientist is not how idealistic that vision was, but how practical. Despite decades of spaceflight, we still cannot reliably predict how one person’s health will change in space. Consider Mars 500, a 520-day simulated isolation mission between 2007 and 2011 where six male crew members in identical conditions diverged dramatically in psychological resilience. Two participants remained stable; three developed severe sleep disturbances; and one suffered persistent depression.

Additionally, around 17% of astronauts experience significant physical deterioration in spaceflight despite following identical exercise regimes. Disability does not necessarily introduce uncertainty into spaceflight; uncertainty is already the norm.

Who performs best in space?

Sometimes those excluded perform better. In 1961, several female pilots outperformed the men of Mercury 7 programme, the first US astronauts. Jerrie Cobb scored in the top 2% of all candidates ever assessed by Nasa. Several of the women outperformed the men on cardiovascular endurance. And the late Wally Funk remained in an isolation tank for over ten hours while the male Mercury astronaut record was just over three. But the women never flew. Nasa insisted on military jet pilot experience as an entry requirement, while simultaneously barring women from flying military jets.

About a decade earlier, Nasa recruited eleven deaf men to study motion sickness, a condition affecting 60 to 80% of astronauts in their first days of weightlessness. Motion sickness happens when conflicting inner-ear signals cause nausea and disorientation severe enough to impair performance. Most of the eleven men had lost vestibular function (the inner-ear balance system) following childhood meningitis. In rotating rooms and on rough seas, as experienced test pilots were sick around them, the deaf participants played cards. The trait that excluded them from military careers made them unusually tolerant of the environments that undid everyone else.

Researchers are finally investigating this issue: like asking whether amputees, who carry less mass and respond differently to microgravity, offer advantages in space. People with lower-limb mobility impairments or vascular differences may be naturally adapted to the headward fluid shifts of weightlessness that cause brain swelling and vision changes in around 70% of astronauts.

When a cooling leak filled Italian astronaut Luca Parmitano’s helmet with water during a 2013 spacewalk, it left him nearly blind and deaf to mission control. He survived by navigating back to the airlock using touch alone. On Mars where dust storms reduce vision to near-zero, blind people would have an advantage here as they are dependent on other senses.

There is no perfect astronaut

The myth of the perfect astronaut has always been just that – a myth. Chuck Yeager, celebrated as the gold standard of what an astronaut should be, broke two ribs the night before he broke the sound barrier in 1947. He concealed the injury, improvised a way to seal his cockpit door using a broom handle, and flew anyway. The right stuff was never about physical perfection. It was about adaptation.

In 1985, Soviet cosmonauts Vladimir Dzhanibekov and Viktor Savinykh manually docked with the dead and uncontrolled Salyut 7 station and spent a week manually rewiring it in freezing pitch-black conditions to bring it back to life. For many people in the disability community, navigating broken infrastructure, sensory issues and isolation is an everyday reality. Disabled people spend their lives adapting to environments designed for somebody else. That makes us experts at navigating the unknown.

The real “right stuff” is interdependence: being creative together with your crew when a plan fails. When Apollo 13’s oxygen tank exploded in 1970, the crew came home not because of perfect engineering, but because people depended on each other under pressure. A Mars mission, years from home and communication delays of 20 minutes each way, will demand it. Astronauts will face problems nobody could anticipate, because that is the nature of exploration.

Disability is an extreme environment

Every person who lives long enough will experience disability at some point. It is my normal. In my research career, I have improvised creative solutions to inaccessible equipment, and learned to pace my energy carefully. Even getting into the building or having access to a bathroom could be my engineering problem for the day.

I’ve been told using a mobility aid is unprofessional and for years, even doctors dismissed my symptoms. When they finally had an answer, it came with a caveat: there is no cure and no treatment pathway. The medical system had reached its limit. I had not. These experiences forced me to monitor my own health, adapt and advocate for myself. On a Mars mission, millions of miles from the nearest specialist, every astronaut will need exactly that skill.

Perhaps the most undervalued asset the disability community brings to space is its relationship with joy. Disabled people do not survive extreme environments through stoicism alone. They survive through humour, putting flowers on their wheelchairs (like mine), and deeply loving communities. On a three-year Mars mission, that may be the most critical thing of all.

Design can be better too. Deaf pilot Sheila Xu described in June 2026 at the United Nations how she designed a colour-changing light signal system to use instead of auditory cues during parabolic flights, aircraft that fly a steep arc to produce brief periods of weightlessness, used in astronaut training. It improved safety for everyone on board, deaf or not, when engine roar made verbal commands impossible. This is the “curb cut effect”: solve for the margins, and you make the system better for everyone.

The good news is we are seeing a paradigm shift. In 2021, Hayley Arceneaux spent three days in orbit on SpaceX’s Inspiration4, becoming the first person with a prosthetic bone to reach space. In 2025, ESA engineer Michaela Benthaus became the first wheelchair user on a suborbital commercial flight. McFall’s selection marks the first time a major space agency has cleared a disabled astronaut for long-duration scientific work in orbit.

Progress does not come from excluding each other, but from discovering what becomes possible when the universe’s criteria finally replace our own.

The goal, then, should not be simply to send one disabled astronaut to space and call it progress. It is to involve disabled thinkers, engineers, and designers at every stage of mission planning. The systems they would help build would be demonstrably better for it.

Adaptation, more than perfection, may turn out to be what matters most.

Zoe Elisabeth Swann Baillie, PhD is supported by funding from the Leverhulme Trust via the Leverhulme Centre for Humanity and Space.