Mark Warner was a prominent theoretical physicist working in the field of soft-matter and polymer science. He was a pioneer in discovering liquid crystalline elastomers as a concept and was the key figure in establishing this subject as a thriving area of research and development. The idea of a material that couples the entropic rubber elasticity with the orientational order of network elements was a complete novelty and a surprise to many. Largely driven by Mark's efforts, this concept, stemming from the coupled order parameters, has been now recognized as a universal phenomenon in several fields: from martensitic transition in shape-memory alloys to engineering and applied mathematics of quasi-convexification. ‘Liquid crystalline elastomers’ will firmly remain as his lasting legacy in science. Mark also made major contributions to physics education, his final legacy being to co-found the national physics education programme, Isaac Physics, in 2013. The ideology of the programme focuses uniquely on students ‘learning by doing’—reassuring students that making mistakes and trying again are fundamental and crucial for learning and developing confidence. Isaac Physics has demonstrated quantifiable impact in raising the aspirations and attainment of hundreds of thousands of students since its inception.

Part I: life

Mark Warner was a pioneering physicist in the study of elastomers who predicted the complex physics and technology of novel elastic materials and opened new opportunities in physics education throughout the UK. Mark passed away on 24 December 2021, just a month short of his seventieth birthday, leaving behind his wife Adele, who sadly passed away in April 2024, his children Maximilian and Jessica, and four grandchildren Mathilde, Harry, Cecilia and Sophie. Mark also leaves behind a great many friends and colleagues by whom he was greatly respected and who held him in high esteem.

Early life

Mark was born in Wellington, New Zealand, to father Gunter and mother Patricia (née Raven). Mark was the eldest of three children; his brother John and sister Kirsten both still live in Auckland where the family settled. His parents were both schoolteachers and placed great importance on education. His father arrived in New Zealand in 1939 as an 18-year-old German-Jewish refugee. His mother's family emigrated to New Zealand from London's East End. She died at a young age while Mark was studying in Cambridge as an undergraduate.

Mark attended Auckland Grammar, which is the best school in New Zealand even today, and had an excellent education there, especially in science and mathematics. These early formative years were essential to Mark and created the solid foundation upon which he based all his professional life. On top of the generally good schooling this institution afforded, his cohort was exceptional, as is alluded to in an article in The New Zealand Herald published on 14 December 2001, entitled ‘The amazing class of ‘69’ (Watkin 2001). Among the 15 classmates, there are a Field Medal winner in mathematics, six senior university professors, a top New Zealand taxation lawyer, a senior World Trade Organization official and several prominent businessmen. The striving for success, the demand for intellectual rigour and excellence and the feeding of energy between the group members both in and outside the classroom have been remarkable. For the rest of his life, Mark was convinced that bringing interested and gifted young people together to encourage each other to strive for success is the best way to lift them up, individually and collectively. His tutorial work in Corpus Christi College, Cambridge, the Senior Physics Challenge and later the Isaac Physics project were reflections of this deep conviction.

Even in this exceptional company and environment, Mark was outstanding. His exam results were the top of New Zealand national rankings in 1969, which resulted in the award of the Girdlers’ Scholarship. The Girdlers, one of the City of London's livery companies, had a long association with New Zealand and awarded its annual scholarship to an outstanding New Zealander to study for a degree at Corpus Christi College, Cambridge. This scholarship is how Mark came to Cambridge, where he stayed for the rest of his life, with a few short stints abroad in his early career.

University education

Mark took a long route to arrive in Cambridge, choosing to travel slowly in a cabin on a cargo ship over other means of transport. This was partially to ‘see the world’, partially to fit the timing with university term dates and partly because he wanted to have time ‘to prepare’. Among other useful things, during these long weeks onboard, Mark learned the skill of fast blind typing, which in later years was astonishing for his friends to observe in action. Another of his rare skills, which few people know about, was his swimming ability. Mark was a very accomplished athlete, achieving a Cambridge Blue among other accolades, but he never regarded it as anything special, and certainly never celebrated these very significant achievements. True modesty and refusing to advertise himself formed one of his key personality traits.

In the last year of his undergraduate degree in natural sciences in 1972, Mark met his future teacher and mentor Sam (later Sir) Edwards FRS, who had just moved back to Cambridge from Manchester. Their first encounter was in a statistical mechanics course, which Sam was giving for the first time. He was delighted to discover two keen students, Mark and Jacob Klein, who followed the lectures closely and often visited him for discussions. In his memoir of Sam (25)^*, Mark wrote:

I certainly recall being worried about the lectures since they presented statistical mechanics in a formidable and uncompromising way, with difficult notions expressed in very difficult mathematics. A second problem was that the hastily handwritten notes were riddled with errors. I focused my reading and analysis by correcting these errors, as best I could, using red ink which could cover the entire page. Finally presenting Sam with my efforts, I suddenly thought, ‘this is not the way to start a relationship with a senior and famous physicist’. Things did not come to an end, but progressed according to most people's memories of scientific interactions with Sam—he respected those who engaged intellectually and valued their engagement, however junior they were. The upshot for me was a PhD place with him in London.

It was lucky that Mark, just before graduation, finally met his match in Sam Edwards: a senior scientist with a very similar set of inner values, but also a great deal of knowledge and wisdom to pass on. When Sam accepted the government post of chair of the Science Research Council in 1973 and had to move to London, Mark decided to follow. Sam suggested that, as his time available for PhD supervision would be limited, he wanted his student to be nearby. This was a difficult period for Mark, as the actual contact time was in the end much less than they both wanted or hoped for. He certainly learned a lot of science, and significant theoretical skills, but they had not completed any specific problem to the point of joint publication in that time. Several of their papers were written later, during and after Mark's return to the UK from a short postdoctoral term in the USA. Those familiar with the field would recognize that the papers they published were on the central topics of interest at the time, and touch the hotly debated issue of ‘lozenges’ in polymer scattering, the defect-mediated ordering transitions and the effects of quenched disorder on thermodynamical averages, all of which are now recognized by separate Nobel Prizes. These early papers were:

•	With Karl Freed and Sam Edwards (1976): excluded volume effect in concentrated polymer solutions (1)
•	With Sam Edwards (1978, 1979 and 1980): neutron scattering from strained polymer networks (2)
•	A dislocation theory of crystal melting and of glasses (3)
•	The effect of disorder on the spectrum of a Hermitian matrix (4).

Mark defended his PhD thesis, ‘Molecular motion of polymeric systems’, in 1977. The thesis abstract describes the depth of his studies, which Mark and Sam preferred in those early years, as opposed to the route of simpler problems and faster publications:

A reformulation of statistical mechanics to handle the effects of non-linearities and lack of timescale separation is used on the excluded volume problem in polymer dynamics. This ‘Lagrangian Liouville Theory’ allows for non-exponential decays and frequency dependent transport coefficients that result from interactions. A framework is developed in which the frequency dependence, due to interactions, of the density fluctuation spectrum can be calculated. Preliminary calculations show an effect in the resultant coherent neutron scattering cross sections. In good solvents the half-width is dominated by the usual RPA k2 term. Excluded volume initially only re-scales the incoherent results through an excluded volume-dependent step length. Various functional problems are still to be overcome to fully investigate the r-coordinate dynamics. The long-time behaviour of a Brownian sphere, and the implications for scattering are derived. A review of glass thermodynamics and conclusions about the role of kinetics are presented. A dislocation theory of melting is also given, following Edwards’ calculation of the screening between dense dislocations. Screening makes the details of the transition more precise (first order). This has much in common with the dislocation and crystallite theories of melting and liquids. Supercooling past this first order transition leads to glass behaviour. We outline a systematic experimental procedure for well characterizing glasses. Then we make predictions about the ‘thermodynamic’ properties of glasses in terms of their corresponding crystals and thermal histories.

Also in that year, Mark married Adele—his partner for life, whom he met in a class on brass rubbing at St Benet Church in Cambridge, right next to Corpus Christi. She followed him through all his positions and continents—to London, then to California, then to Oxford and then back to Cambridge in 1988.

Postdoctoral work

After his PhD, Mark had a choice of several postdoctoral positions in the USA, and decided to work with Paul Flory at Stanford, where he learned about liquid crystals. The paper with Flory, ‘The phase equilibria in thermotropic liquid crystalline systems’ (5), was just a marker for that period of learning. Later, combined with the Edwards-inspired polymer field theory, Mark produced his first large body of work on nematic polymers. This effort was shared most prominently with Mike Gunn in the mid 1980s (6), and with Xin-Jiu Wang in the late 1980s (7). The result was that Mark gained a really good understanding of how liquid crystallinity arises in polymers with their peculiar entropy function, much like the Maier–Saupe or Onsager theories that deal with simple nematic liquid crystals. As with the theory of orientational order in ordinary nematic liquids, there must be some anisotropic effect in the problem: either an anisotropic pair-interaction potential, reduced to the mean-field by Maier and Saupe, or the anisotropic excluded volume entropy of Lars Onsager ForMemRS. In polymers, such an effect most naturally arises from the chain bending stiffness, often called ‘semi-flexibility’. During the nematic transition, such a chain must fold into locally aligned straight segments separated by sharp ‘hairpins’, reflecting the trade-off for the chain forming the long parallel segments demanded by the nematic order and retaining some conformational entropy; without the hairpins, the long straight chain would represent a prohibitive loss of entropy. One remarkable result of this theory is the singular relation between the average length of straight nematic segments $L_{segm}$ , which could be called persistence length in this context, and the nematic order parameter $Q$ :

L_{segm} \propto exp (4.5 / (1 - Q)) .

Of course, such a relation in retrospect is obvious: as the order becomes saturated (

Q \to 1

), there could be no hairpins left and the whole chain must become one straight ‘stick’, but it was Mark's first significant individual achievement to develop the consistent statistical theory that leads to it. A curious follow-up of this theory was that, when one of us (ET) had written his own paper in 1991 on the ordering of nematic polymers, obtaining the same result unaware of Mark's work. That paper was sent to be refereed by Mark, who wrote a rejection because of the lack of novelty, but then followed it up in a personal email in which he explained, and apologized for, the rejection, saying that he knew that the theory was valid—it was close to his own—and suggested further communication on this subject of mutual interest. That exchange began many years of close friendship and collaboration when ET moved to Cambridge to work with Mark on liquid crystal elastomers in 1992.

Part II: works

Research activities and achievements

Liquid crystal elastomers

In 1988 Mark published a paper, ‘Theory of nematic networks’ (8), with his student, K. P. Gelling, and Thomas Vilgis from the Max Planck Institute in Mainz. It was a major deviation from his previous research themes and was perhaps influenced by interactions with P. G. De Gennes ForMemRS, who was a frequent guest and friend of Sam Edwards in Cambridge (figure 1). Indeed, De Gennes had long anticipated that something remarkable must occur if one manages to create an elastic solid with sufficient internal freedom to permit nematic orientational order—this is very different from a mere uniaxial elastic lattice, where the special direction is not free to rotate independently from the elastic matrix. The Warner–Gelling–Vilgis 1988 paper formulated the framework of a complete theory of such a system, including the anisotropic elasticity, the spontaneous length change on ordering and the Landau–De Gennes nematic phase transition analysis.

Figure 1. Sam Edwards and Pierre-Gilles De Gennes, September 1995. Photograph kindly provided by the Warner family; credit: Professor Maso Doi.

It turns out that, simultaneously and independently, S. Abramchuk and A. Khokhlov published a paper with almost identical results (Abramchuk & Khokhlov 1987), and for a short while this was developing into a ‘competition’ in this new research area. But in the end Khokhlov never followed that first paper, which was published in a source that was hard to access, while Mark and his various colleagues ran away with it. They created a whole new domain in the broad ‘soft condensed matter’ area, which is now called ‘liquid crystalline elastomers’ and is firmly associated with the name of Mark Warner, as well as that of Heino Finkelmann, the German chemist who first made these new materials in the laboratory. As a result, the pair were awarded the 2003 Agilent EuroPhysics Prize ‘for the discovery of a new class of materials called liquid crystal elastomers’.

Mark stayed with this research area until the end, and it is interesting and instructive to map the key milestones of this journey, a large portion of which was shared with one of us (ET). The first step was the forementioned Warner–Gelling–Vilgis 1988 paper, which opened up the subject but in retrospect was limited in only considering one uniform orientation of the nematic director. The early 1990s were very exciting because several new experiments were emerging from Finkelmann, and also from Rudolf Zentel in Germany and Geoffrey Mitchell in Reading, and others. In these different experiments and physical settings, it was clear that the mechanical deformations of these elastomers were causing rotations of the director. The next key step was made in 1993, when the ‘Trace Formula’ was first formulated (9). In the soft-matter and rubber-elasticity fields it was not necessary to use tensor algebra, but since the anisotropic tensors, separately, control the elastic deformation and the average chain conformation, their coupling to produce the scalar elastic energy has been crucial:

F_{elastic} = \frac{1}{2} G Tr [{\bar{\bar{ℓ}}}_{0} \cdot {\bar{\bar{λ}}}^{T} \cdot {\bar{\bar{ℓ}}}^{- 1} \cdot \bar{\bar{λ}}],

where just two parameters describe all the rich physics: the overall rubber modulus G, proportional to the crosslinking density and temperature, and the average chain anisotropy

r = ℓ_{| |} / ℓ_{⊥}

, which is proportional to the nematic order parameter. In the Trace Formula, the tensor

\bar{\bar{ℓ_{0}}}

, describing the state of local nematic order before deformation, is coupled in a particular way with the local deformation tensor

\bar{\bar{λ}}

and the order tensor

\bar{\bar{ℓ}}

describing the nematic order after deformation, which could alter both the degree of order and its orientation. Or, vice versa, the change in the nematic order could cause a spontaneous deformation by altering the shape of the body. This was a goldmine: in just a space of three to four years a large number of problems in the field were solved with great ease, and two key novel phenomena understood fully.

The first was the spontaneous shape change, which is now called large-stroke actuation and is the driving force of the 30 plus years of active development of applications in engineering fields such as soft robotics or active textiles.

The second was ‘soft elasticity’. This term was coined in 1994 after much deliberation and agony: Mark and ET fully realized how important it is to have a catchy, but also informative, name for this new phenomenon (11). The Trace Formula predicted that there is a large set of possible elastic deformations, which, if accompanied by an appropriate director rotation, would result in zero elastic energy. And it was actually true, the experiments confirming it once they knew what deformations to apply! The engineering and the elasticity communities became very excited about this elegant way of identifying these zero-energy modes, which had been long anticipated in systems with a complex internal microstructure, for example in shape-memory alloys. The circle of friends and colleagues who dived deeply into the theoretical implications has grown rapidly. Various established and emerging experimental groups rushed into liquid crystal elastomers, realizing that this was a ‘cool’ and promising area. Mark is also remembered by essentially initiating the concept of photo-actuation in these elastomers, the idea that held his attention for many years after their discovery (16).

The third significant conceptual step Mark and his colleagues achieved was making the Trace Formula compatible with the ‘real world’. Indeed, the compact and elegant expression was very attractive for mathematicians, but in real elastomers there are always imperfections of various kinds. Usually, accounting for deviations from an ideal scenario is a tedious task, but the momentum and experience acquired in describing the system with several key tensors, observing the key symmetries present, have allowed the development of an almost equally elegant and general model of what is now called ‘semi-soft elasticity’. The term is much weaker than the original, but ET and Mark felt it was important to keep the kernel of the expression because it was relying on the same ‘soft’ symmetries of the tensors involved. The non-ideal semi-soft correction to the Trace Formula could be caused by many different effects, which determine the amplitude α, but its form remains compact and universal:

\begin{aligned} F_{elastic} = \frac{1}{2} G Tr [{\bar{\bar{ℓ}}}_{0} \cdot {\bar{\bar{λ}}}^{T} \cdot {\bar{\bar{ℓ}}}^{- 1} \cdot \bar{\bar{λ}}] + \frac{1}{2} α T r [(\bar{\bar{δ}} - n_{0} n_{0}) \cdot {\bar{\bar{λ}}}^{T} \cdot n n \cdot \bar{\bar{λ}}], \end{aligned}

where the unit vector

n

is the principal axis of the order tensor

\bar{\bar{ℓ}}

, so that the deformations of the type

\bar{\bar{λ}} = {\bar{\bar{ℓ}}}^{1 / 2} \cdot \bar{\bar{W}} \cdot {\bar{\bar{ℓ}}}_{0}^{- 1 / 2}

, where

\bar{\bar{W}}

is an arbitrary rotation tensor, would achieve the lowest-energy pathway, even if not a completely zero elastic energy. The small constant

α

is determined by a particular physical mechanism, and Mark with his student G. C. Verwey have studied at least three very different kinds (13, 14). Another strong year in Mark's research was 1977, when all these ‘soft’ and ‘semi-soft’ theories were formulated and their key manifestation in what we called ‘stripe domains’ was discovered, both theoretically, and experimentally with H. Finkelmann (12).

There have been endless variations on this theme, and multiple papers developing them, notably:

•	Exploring the lamellar (smectic) phase of elastomers (with Tom Lubensky), where the concept of ‘locking’ the network crosslinks between the layers was shown to have many remarkable mechanical implications (10)
•	Discovering the effects of mechanical deformation on chiral (cholesteric) elastomers (with Yong Mao), where the coarse-graining of the helix led to localization of the photonic bandgap (17)
•	Raising a piezoelectric response (15)
•	Exploring linear hydrodynamics and viscoelasticity, covered in a series of strong papers in 2001 (18).

Tom Lubensky, who remained a good friend with Mark until the very end, jokingly complained sometime around 1997–1998 that Mark has not left much for others to do in this field—interested and capable people like himself struggled to find a topic where Mark and his colleagues had not yet published a foundation paper. The definitive book, Liquid crystal elastomers (19), was a major adventure: Mark and ET started writing it around 1996 on the back of the Trace Formula excitement, but the field was exploding and, every time they thought they would finish, a new discovery or a twist of understanding came along and they had to re-write or add things. In the end, using Mark's words in the context of DIY housework, you can never finish it, only stop. They stopped to have it published in 2003 and immediately regretted it, because all the smectics, cholesterics and hydrodynamics developments came along—so they started adding and re-writing chapters for the 2007 edition. Many things happened in the field after that, but ET and Mark simply ran out of energy to do it again.

In the later years, Mark got excited about the particular set of implications of actuation, especially photo-stimulated actuation, in liquid crystal elastomers: the induced bending and complex curvatures of flat bodies. Carl Modes and Kaushik Bhattacharya shared this interest and contributed to its progress. Starting from the simpler cantilever bending (20) and moving to more complex curvatures and implications (21), Mark once again stimulated exciting new experiments, once his experimental colleagues had been shown what to aim for (26, 27). His last papers, some published after his passing away, were in active pursuit of deeper understanding of this field: with John Biggins, Mark's student in the early 2000s and a close colleague until the end, he made strong inroads into the mechanics of flat metrics (29).

Even though ‘liquid crystal elastomer’ had the largest place in Mark's heart, his unstoppable curiosity and striving for complete understanding produced several remarkable side tracks. Just two examples are so characteristic of him. How many of us are concerned by the problem of why a bicycle stays upright? Having cycled all his life, it really bothered Mark that the question had no clear answer, which resulted in a paper (with Daniel Corbett) on what makes the moving bicycle stable (22). Similarly, having taught Part 1B electromagnetism for over 30 years, Mark got excited about a problem in electric engineering, which resulted in a paper with Robin Hughes on ‘LEDs driven by AC without transformers or rectifiers’ (28).

Physics education

Mark was a master of many things, aided by his apparent ability to create an infinite amount of time. His interests spanned many fields, but the personal quality that transcends all of them was his generosity—sparing his time for others who shared the same interests or who sparked an interest in a new area of discovery for Mark. The field of physics education was no exception.

As a director of studies at Corpus Christi College in Cambridge, Mark encouraged and supported many up-and-coming physicists. Whether the students were incredibly talented and able or required some extra support and supervision, Mark was always willing and eager to discuss physics with them. He would inspire the light-bulb moment that would leave them satisfied to move on to the next concept and a new set of problems to solve. Within the department, Mark was part of the group of university lecturers tasked with the design and development of the curriculum for the four-year integrated Masters that was first examined in 1997—in Mark's view to address changes in the school curriculum that required what used to be spread across a three-year degree to be adjusted to a four-year programme. This evolution of the degree, in combination with his experience of interviewing and admitting new students through the Collegiate system, stimulated Mark to investigate the changes in physics education and consider how one might address the educational disadvantages experienced by some students but not all.

In 2006 the Gatsby Foundation commissioned a report from Alan Smithers and Pamela Robinson to investigate the flow of physics students from school to university using available data (Smithers & Robinson 2006). Their findings were that, since 1990, A-level physics entries had fallen by 35.0% while entries overall had risen by 12.1% (figure 2). Between 1990 and 1996, the annual rate of decline was 2.5 times greater and occurred mainly in comprehensive schools, sixth form colleges and further education colleges, with independent schools and grammar schools less affected (figure 3). Female students were not only less likely than males to take A-level physics (22.4% in 2006) but also less likely to read physics at university (18.5% in 2006) despite achieving better results. Sadly, A-level statistics for physics have remained broadly consistent—in 2021 22.9% of students taking A-level physics were women. It was in 2006 that Mark Warner founded the Senior Physics Challenge with the financial support and encouragement of The Ogden Trust. The aim of this four-day residential programme was to raise the aspirations of talented year 12 students from across the UK to consider applying for physics at university. The programme began with special relativity as its focus, with experimental sessions, Fermi problem solving and a social programme that allowed those who were perhaps isolated in their schools to engage with other like-minded students. The programme evolved from a focus on special relativity to a focus on quantum mechanics, and led Mark to create the Cavendish quantum mechanics primer (23). This book, authored with Anson Cheung, was designed to provide a resource that begins at a level suitable for A-level students, but develops into material that would support first- and second-year undergraduate study too.

Figure 2. Chart 2.1 from Smithers & Robinson (2006) showing the number of A-level physics entries compared with the total number of A-level entries between 1950 and 2005. The key point of the figure occurs around 1990, when A-level entries fell by 35% while overall entries to A-level had risen by 12.1%. Image used with permission from Alan Smithers.

Figure 3. Chart 2.2 from Smithers & Robinson (2006) showing the decline in physics A-level entries from 1990 in maintained schools, sixth forms and further education colleges in contrast to a consistent number of students in independent schools. Image used with permission from Alan Smithers.

The under-recruitment of students from UK schools to study physics and engineering, as well as the limited diversity of undergraduate students in physics at university, remained a concern. Mark was puzzled as to the cause of the decline in the number of students taking A-level physics given the upturn in the number of students taking A-levels, and why those who did take physics A-level were choosing other courses at university. A-level curriculum changes took place in 2000. In physics there was a hope that these changes would address the downturn in the number of students taking physics, with mathematical content significantly reduced in A-levels (Smith 2014). Outreach initiatives were beginning to flourish, providing inspirational activities for students to engage with and to encourage their continued participation and study of physics. However, the combined efforts of outreach interventions and changes to the curriculum had no effect on A-level physics numbers or the ca 23% of female entries.

Numbers aside, concerns were also being raised about students’ preparation for university study in physics. Peter Barham of the University of Bristol studied the physics knowledge test results of students entering Bristol for physics over a 35-year period from 1975 (Barham 2012). He noted that the ability of students to answer the same test fell from 75% up to 1990 to below 50% after 2000, against a background of increasing A-level grades of the incoming students. He specifically noted that changes to teaching and examinations had caused students to be less able to carry out multi-stage calculations. Further research in Cambridge into the importance of scaffolding for first-year undergraduate students showed that the lack of prior experience of multi-stage problems had a particular impact on the percentage of women achieving first class results in the first year of their physics course within the natural sciences degree (Gibson et al. 2015).

In 2011 the Institute of Physics commissioned the Mind the gap report (Morgan 2011) to investigate anecdotal reports that physics and mathematics A-levels were not preparing students sufficiently for undergraduate physics and engineering courses and, in particular, were not providing encouragement for students to take physics at university level. Students who were studying for mathematics degrees reported being unaware that physics contained so much mathematics and problem solving and so had taken a mathematics degree rather than physics. Students and academics reported that the separation of mathematics and physics at A-level in school examinations did not equip them to apply their mathematical knowledge to physics but instead had inadvertently caused students to compartmentalize their knowledge and understanding.

Mark undertook his own analysis of 2011 A-level physics examinations in comparison with O-level, Common Entrance, Special Paper and Oxford entrance exams from the 1980s. The conclusion was a removal of the need for students to make connections across topics within the mathematics and physics curricula—a change from succinctly stated problems without scaffold, to problems being broken down into singular steps without the need to make connections or understand the bigger picture. In the 2011 examination paper nearly all effort was spent injecting numbers into formulae that were often provided on a formula sheet. Given students were able to do the problems in the 1980s there is no suggestion that the intrinsic inability to attack such problems had disappeared but the demands on language were higher. However, despite the more challenging examinations of the 1980s, it should be noted that around 57 000 sat A-level physics at this time compared with just under 40 000 in recent years.

In his role as a director of studies in physics (academic tutor) at Corpus Christi, Mark saw first-hand the inequalities that students experienced in their education—disadvantaged through no fault of their own, for example, based on geography and access to schools with teachers who were physics specialists. Following his own research in this landscape and the research of those cited here, Mark wrote to the secretary of state for education, Michael Gove. In his letter he outlined the inequality of access to university, and the problems for universities and consequently for the UK economy, and proposed a programme to bridge the gap between school physics and physics, engineering and mathematics in higher education. Thus, in 2013 Isaac Physics, initially known as the Rutherford Schools Physics Project, was founded by Mark and one of us (LJW) (figure 4).

Figure 4. Warner (right) receiving the Lawrence Bragg Gold Medal at the Institute of Physics awards in 2019 with Jardine-Wright (centre) and IOP President, Jonathan Flint (left). Photograph kindly provided by Lauren Thomas.

Isaac Physics began with a focus on providing A-level students with access to high quality resources that would stretch and challenge them but would have interactive online support and scaffolding to help them succeed with such challenges. Mark's ability to foresee connections and seize the opportunity of every encounter led to Isaac securing the expertise of Alastair Beresford and Andrew Rice of the Department of Computer Science and Technology in Cambridge. They had recently developed a new undergraduate course that was accessed online and was presented as short interactive videos interleaved with formative questions to enable students to assess their own progress. Lisa, Mark, Beresford and Rice's mutual aspirations were aligned, and they planned to develop a bespoke open platform for active learning (OPAL) that would present students with live interactive feedback and enhance their learning through bespoke technology.

Mark and LJW were clear that, based on their experience of delivering the Senior Physics Challenge and other outreach programmes, Isaac would have both face-to-face and online engagement, and it soon became obvious that teachers were key to increasing student engagement and enabling students to attend workshops and events. Furthermore, teacher recruitment and retention in physics had become a key issue in schools, and the shortage of physics teachers continued to grow. These issues catalysed an evolution of the OPAL to enable teachers to set work, for it to be automatically marked and to present to the teachers a live mark-book that could be viewed as students answered their classwork or homework through Isaac. In the first year of its implementation, teachers using Isaac reported an average saving of two hours per week. Now teachers are reporting 3.9 hours saved a week and in the school year of 2023–2024 it is estimated that over 400 000 teacher hours were saved. The numbers of students, teachers and schools engaged with Isaac is hard to report because, as soon as the numbers are written down, they have increased. At the time of writing, more than 520 000 students (37% of those who declared their gender were women) had registered on Isaac, with more than 12 000 teachers from 3265 English state schools. The number of questions that had been attempted reached over 150 million in May 2024.

Mark was passionate about teaching and about inspiring the next generation of physicists, and never missed an opportunity to spark their interest. There are several memorable moments along the Isaac journey as it grew to serve GCSE students and their teachers, as well as A-level, pre-university and foundation year students around the UK. One such moment was when, while writing problems for the Isaac Physics platform, Mark happened upon a video by science communicator and presenter Steve Mould demonstrating the fountain effect of a chain of beads (Mould n.d.). The chain fountain—named the Mould Effect by Mark, to Steve Mould's great delight—was not understood, and Mark worked with John Biggins to publish yet another ‘side-track’ paper explaining the effect (24) as well as making an excellent outreach demonstration. The crucial and fascinating connection between Mark's research, the chain fountain problem and Isaac was that the effect could be explained using school-level physics. Mark developed a lecture so that school students could predict how high a chain would rise. Isaac Physics is hoped to remain another lasting legacy of Mark, and a testament to his commitment to mentoring and to physics education.

Outstanding features of Mark were his modesty and humility; he made no assumptions about the knowledge or ability of his audience but took them on a journey of discovery—his calm and considered approach meant that they were never lost along the way. He gave people the confidence to try, demonstrated that failure was not a weakness but a necessary part of learning and that the satisfaction that follows from practice is success and just reward. An extensive body of work in liquid crystal elastomers and closely conceptually related fields that has germinated and fed a whole new area of international research is his legacy and a testament to his own implementation of these ideals.

Awards and recognition

1989	IOP Maxwell Medal and Prize
2000	Alexander von Humboldt Research Prize
2002	Honorary Fellow, Royal Society of New Zealand
2003	EuroPhysics Prize, the European Physical Society
2009	Cambridge Philosophical Society Hopkins Prize
2013	Colwyn Medal, the Institute of Materials, Minerals and Mining
2014	G. W. Gray Medal, British Liquid Crystal Society
2017	Founders’ Prize, IOP Polymer Physics Group
2019	IOP Lawrence Bragg Medal and Prize

Acknowledgements

We are grateful to many colleagues for their recollections of Mark Warner. We are particularly grateful to the late Professor Tom McLeish, who began writing this biographical memoir with us, but who was sadly taken ill and passed away in 2023. The principal sources are given in the text. Permissions to reproduce extracts from Mark's work and photographs of him are also acknowledged in the text.

Author profiles

Professor Eugene Terentjev

Inline Graphic

Eugene is the professor of polymer physics at the Cavendish Laboratory. After being trained in Moscow, with a PhD in 1985, he arrived in Cambridge in 1992 to spend the rest of his career. He started as a theoretical physicist, working with Sir Sam Edwards FRS and Mark Warner on many problems in soft-matter and polymer physics, before setting up a laboratory in materials chemistry to develop new functional polymers and composites. He supervised over 50 PhD students and postdocs, at least 20 of whom are now professors in Cambridge and various universities around the world. He has published over 400 original research papers and invited reviews and three books, and about a half of this output focuses on liquid crystalline elastomers, where Warner and Terentjev's legacy remains strong. He is a fellow of Queens’ College, Cambridge, where he was the director of studies in natural sciences for over 15 years.

Dr Lisa Jardine-Wright OBE

Inline Graphic

Lisa is the director of Isaac Physics and co-founded the project with Mark Warner in 2013. She was awarded an OBE in the Queen's birthday honours in 2022 for her services to education and in 2019 was awarded the IOP Lawrence Bragg Gold Medal and Prize jointly with Mark Warner for co-founding Isaac Physics. She began her career as an undergraduate in natural sciences (physics) at Trinity College, Cambridge, and remained for her PhD and postdoctoral research in cosmological simulations of galaxy formation at the Institute of Astronomy. Her current research focus is on technology-enhanced learning and physics education. She is an affiliated lecturer in physics at the Cavendish Laboratory and a fellow and director of studies in physical natural sciences at Churchill College in Cambridge.