Lord Craig of Radley:

Moved by Lord Craig of Radley

12: Clause 11, page 5, line 2, after “social” insert “and mathematical”

My Lords, I speak to Amendments 12 and 14 in the names of the noble Lords, Lord Browne of Ladyton and Lord Clement-Jones, the noble Viscount, Lord Stansgate, and myself. Noble Lords will be aware that a number of fields of modern technology and research are coming to rely more and more on mathematical sciences. When I gained my degree in pure maths at Oxford over 70 years ago, and for many years since, maths was seen largely as an adjunct to other fields of science and technology, but the world of digital—particularly of AI, machine learning, 5G and quantum computing—is now becoming mainstream. These diverse technologies rely very greatly on mathematics for help to find solutions and answers.

Mathematical sciences today are employed in many ways: from risk analysis of the use of driverless cars to the likelihood of collisions and how best to avoid them in space; from sifting with AI through large quantities of medical data to spot treatments for illness, to the best ways of introducing superfast broadband nationwide; contributing to security risk analyses, or delving into the more esoteric problems of known and unknown unknowns. Mathematical sciences feature in improvements that will benefit the lifestyle and health of wide cohorts of citizens and the esoteric work of astronomers unlocking the secrets of the cosmos. Analysing and predicting trends in the Covid-19 epidemic is another active field in which mathematical sciences play an important part.

The marginalisation and exclusion of mathematical sciences in government legislation prompts this Amendment. For example, the 2004 guidelines on research and development limit the definition of mathematical contributions in research and development to the “physical and material universe”. Far from sticking to current definitions in this new legislation, is it not time to recognise the unique and growing contributions of mathematical sciences in the new digital age of AI, quantum computing and much, much more? The ARIA Bill is an ideal opportunity to do so and move on. The focus and capacity of the Bill’s provisions should explicitly embrace the mathematical sciences. These now include “blue skies” maths, which is sometimes referred to as a new form of “pure” maths.

My amendment is thus not a probing amendment; it is a simple and straightforward proposal to reflect the advances being made by mathematical sciences in the digital age. I challenge anyone to assert that this new agency will not be making use of mathematical sciences in its work. This Bill is an excellent opportunity to give the rightful recognition in statute to the key role of mathematical sciences in advanced research and inventions. I beg to move.

My Lords, I support the noble and gallant Lord’s amendments and have added my name to them. More broadly, I support the work of the London Mathematical Society and the Protect Pure Maths Campaign to emphasise the importance of mathematics alongside science and technology, not only to the whole STEM ecosystem but to the UK economy overall. The briefing that I have received from them estimates—I am sure this is correct—that mathematics adds more than £200 billion to the UK economy, which is nearly 10% of our GDP; and it is one of the top three subjects for graduate earnings. As the noble and gallant Lord explained, mathematics enables most of today’s exciting and urgent technological developments, including artificial intelligence, driverless cars, and the development of quantum computers and superfast broadband, as well as the modelling of the Covid-19 outbreak, underpinning national security, the finance sector and the rollout of vaccinations.

Mathematics is a British success story. If it gets recognition at this level from Parliament, I am certain that it will send a powerful and supportive message to young people across the country to consider mathematics as a career or for further study—and that can only be a good thing.

My Lords, my Amendment 13 does not differ greatly from the previous amendment. Indeed, it differs in only one word: “pure”. In proposing my amendment, I have been mindful that mathematics is in danger in universities from an attempt by administrators to reduce its presence. At the University of Leicester, where I am an emeritus professor, a considerable number of staff described either as “pure mathematicians” or “managerial sociologists” have been sacked. The so-called pure mathematicians have been sacked on account of the unpopularity of maths, as revealed in perennial student surveys. Mathematical subjects tend to be unpopular with students because they are challenging. Nevertheless, they are the backbone of degrees in science, engineering and other subjects. I suspect that the managerial sociologists have been sacked because administrators are loath to recognise the expertise of others in a subject in which they believe they have significant experience. Be that as it may, my present concern is with mathematics.

Very few mathematicians would call themselves “pure” mathematicians. They describe themselves as mathematicians without qualification. Pure maths is concerned with giving order and clarity to the subject of mathematics, of which the exposition stands in constant need of reform. Applied mathematics, as the name suggests, is concerned with applying mathematics to substantive issues. We cannot have the one without the other. Legislation that declares that mathematical advances are not science unless they are advances in representing the nature and behaviour of the physical and material universe speaks of a wrong-headed attitude on the part of administrators who may have little understanding of the nature of science. In derogating the role of mathematics, this attitude could have dire consequences. I hope that the acknowledgement of the importance of mathematics to science will serve to counteract the wave of intellectual vandalism occasioned by the insurgency of administrators that is sweeping through British universities. I beg to move the amendment standing in my name, but I propose that it should stand or fall with the other amendments in this group.

I think it may be helpful to your Lordships if I explain that only the first Amendment in a group is moved. The noble Lord is speaking to his amendment, but it is moved or not moved only according to its place on the Marshalled List.

My Lords, I rise to speak in support of Amendments 12 and 14, to which I have added my name, and the other Amendment in this group. I hope the House will appreciate that this is not a subject that was touched on in Committee—so it is fresh for consideration by the House today. It is nevertheless very important. The noble and gallant Lord, Lord Craig, and my noble friends Lord Browne and Lord Hanworth have set out the case in some detail, and I do not want to repeat some of the examples they gave, very good though they are. However, I emphasise that mathematical sciences are vital not just to the future of science but to the work of ARIA.

Amendments 12 and 14 are very simple. They would insert the words “and mathematical” in the definition of scientific knowledge and scientific research in Clause 11. These amendments arise because the mathematical community is unsure about whether mathematical sciences are sufficiently included in the definition in the Bill—and it is because the mathematics community is unsure that this debate is taking place. Sometimes people think of sciences as only, or mainly, the core sciences of biology, physics and chemistry, but this is not the case. Mathematics underpins all the other sciences —hence we now use the term STEM as a routine acronym.

Perhaps I could just briefly introduce into this debate the definition of mathematical sciences that is accepted in the community: it is a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered as sub-fields of mathematics proper, such as statistics, computer science, computational science, data science, quantitative biology, operations research, control theory, cryptology, econometrics, theoretical physics, continuum mechanics, mathematical chemistry and actuarial science.

Noble Lords will note that in the Bill as it stands, the wording reads

“any of the sciences (including the social sciences)”.

Noble Lords might be wondering why in this Bill the social sciences have been specifically included. I think it reflects something of a mistaken belief for many years that social sciences are somehow not proper science, but attitudes have changed over the years. Noble Lords might cast their minds back to how we dealt with the Ebola crisis: social sciences had a very big part to play in that, and they are also playing a part in how we deal with Covid. My point is that I fully support the reference to social sciences, but I am arguing that the Bill needs specifically to add the phrase “and mathematical sciences”, because the work that ARIA does will be bound to involve maths in one way or another.

As I said, the maths community itself is unsure about its position. I want to quote from something that appears today on the government website—the BEIS website—about the definition of science, to which the noble and gallant Lord, Lord Craig, referred. I shall quote it in more detail. It says:

“Mathematical advances in and of themselves are not science unless they are advances in representing the nature and behaviour of the physical and material universe.”

That is what is causing unease, because this is too narrow a definition of the mathematical sciences when applied to ARIA and its work. These mathematical sciences will contribute hugely across a broad spectrum, including security, computing, astronomy and economics, all of which will be impacted by ARIA. Mathematics is visibly at the core of a great deal of what is at stake here.

I have many more examples but, in view of the late hour, I shall not refer to them—but they all illustrate in one way or another the importance of mathematics. However, I shall just point out that the Heilbronn Institute for Mathematical Research, which is a strategic partnership between GCHQ and universities, within which academic mathematicians contribute to problems of national security, is going to be a very important part of the work that ARIA does. That is another reason for adding the words in the amendments that I mentioned.

I look forward to the Minister’s reply, because what she could do very quickly and easily is reassure the mathematical community that it is included in the definition under Clause 11 and that, to some extent, this whole debate may have been unnecessary, as long as it is made clear from the Dispatch Box that mathematics is valued and included.

My Lords, I have signed and I support Amendments 12, 13 and 14. As someone immersed in issues relating to AI, machine learning and the application of algorithms to decision-making over the years, I, too, support Protect Pure Maths in its campaign to protect pure maths and advance the mathematical sciences in the UK—and these amendments, tabled by the noble and gallant Lord, Lord Craig, reflect that.

The campaign points out that pure maths has been a great British success story, with Alan Turing, Andrew Wiles and Roger Penrose, the Nobel Prize winner—and, of course, more recently Hannah Fry has popularised mathematics. Stephen Hawking was a great exemplar, too. However, despite its value to society, maths does not always receive the funding and support that it warrants. Giving new funding to AI, for instance, risks overlooking the fundamental importance of maths to technology.

As Protect Pure Maths says, the 2004 BEIS guidelines on research and development, updated in 2010, currently limit the definition of science and research and development for tax purposes to the systematic study of the nature and behaviour of the physical and material universe. We should ensure that the ARIA Bill does not make the same mistake, and that the focus and capacity of the Bill’s provisions also explicitly include the mathematical sciences, including pure maths. Maths needs to be explicitly included as a part of scientific knowledge and research, and I very much hope that the Government accept these amendments.

I thank the noble and gallant Lord, Lord Craig of Radley, and the noble Viscount, Lord Hanworth, for tabling Amendments 12 to 14, and those who contributed to the debate. We recognise the fundamental importance of pure and applied maths to other sciences, and as the focus of scientific inquiry in its own right. It is right that we take the opportunity to note that importance here.

The noble and gallant Lord gave a number of potent examples of the importance of mathematical contributions to scientific innovation. Much like, we hope, the projects and advances that will be supported by ARIA, breakthroughs in mathematics can lead to unexpected leaps of progress in separate fields or find application in solving intractable and seemingly unrelated problems in other areas of science. As we just heard from the noble Lord, Lord Clement-Jones, who rightly reminded us, the UK has been home to many outstanding mathematicians of global significance, from Isaac Newton to Andrew Wiles.

However, I emphasise to the noble and gallant Lord, Lord Craig of Radley, and the noble Viscount, Lord Hanworth, that the drafting of the Clause that they have sought to amend follows existing powers in the Science and Technology Act 1965, and the Higher Education and Research Act 2017. It is important that it does so. Research into mathematics, including pure mathematics, has been funded in the UK using those powers for over five decades. Maths research is funded by the Engineering and Physical Sciences Research Council—one of the research councils that make up UKRI. The EPSRC spends more than £200 million on this theme, which includes research into maths in areas from number theory to topology and artificial intelligence. It is clear that maths is included in the definition of sciences as currently included in the Bill.

The 2004 guidance referenced by the noble Viscount, Lord Stansgate, predates the Higher Education and Research Act, which makes it clear that maths is included in the definition of science as drafted in the Bill. There is no need to particularise the interpretation through these amendments. Indeed, it would clearly be undesirable to seek to list exhaustively every possible field of scientific inquiry within the Bill. Departing from the existing embedded way these powers to fund research, including in mathematics, are drawn would be unhelpful.

ARIA’s programme managers will set ambitious programme-level goals. Although we do not often expect programme-level goals to lie within pure mathematics, it is right to highlight that ARIA might need to draw on pure and applied maths to achieve those goals, given their importance within the new fields noble Lords highlighted. It is right that ARIA may fund research in those areas.

We are confident that any activities of this nature that ARIA will seek to pursue are covered by its functions, and that the results of scientific research will encompass the results of mathematical inquiry that might be needed by ARIA. ARIA’s supplementary powers provide further reassurance. When exercising its functions, such as funding a programme with a specific scientific objective, ARIA’s supplementary powers allow it to do whatever is necessary in support of that. It is therefore the case that any mathematical endeavours that ARIA needed to draw on for a programme—for example, in support of a particular objective for machine learning—could be funded under its supplementary powers as well.

On that basis, although the noble and gallant Lord and the noble Viscount have raised important points, I hope they will be satisfied that there is no need for their amendments and feel able not to press them.

My Lords, I thank the Minister and all those who spoke to this. Quite clearly, there is a difference of view between the Government and those of us who have spoken to them about how we should treat mathematical sciences in the present age. It is a pity that it has not been possible for the Government to agree to the Amendment, but, in view of the late hour, I shall withdraw it.

Amendment 12 withdrawn.