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Faculty of Mathematics, University of Cambridge
Faculty of Mathematics, University of Cambridge
Faculty of Mathematics, University of Cambridge
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Centre for Mathematical Sciences, Cambridge

The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics (DPMMS) and the Department of Applied Mathematics and Theoretical Physics (DAMTP). It is housed in the Centre for Mathematical Sciences site in West Cambridge, alongside the Isaac Newton Institute. Many distinguished mathematicians have been members of the faculty.

Some current members

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DPMMS

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Statistical Laboratory

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DAMTP

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Pure Mathematics and Mathematical Statistics

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The Department of Pure Mathematics and Mathematical Statistics (DPMMS) was created in 1964 under the headship of Sir William Hodge.[1] It was housed in a converted warehouse at 16 Mill Lane, adjacent to its sister department DAMTP, until its move around 2000 to the present Centre for Mathematical Sciences where it occupies Pavilions C, D, and E.

Heads of department

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Statistical Laboratory

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The Statistical Laboratory is a Sub-Department of DPMMS.[2] It was created in 1947 with accommodation in a "temporary hut", and was established on 21 March 1953 within the Faculty of Mathematics.[1] It moved in 1958 to the basement of the new Chemistry Department in Lensfield Road, and then formed part of the new Department (DPMMS) in Mill Lane on its creation in 1964. It occupies Pavilion D of the Centre for Mathematical Sciences.

Directors of the Statistical Laboratory

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Applied Mathematics and Theoretical Physics

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Department of Applied Mathematics & Theoretical Physics is based at Centre for Mathematical Sciences.

The Department of Applied Mathematics and Theoretical Physics (DAMTP) was founded by George Batchelor in 1959, and for many years was situated on Silver Street, in the former office buildings of Cambridge University Press.[3] However since the opening of the Isaac Newton Institute in 1991, the Department has been located at the Centre for Mathematical Sciences (Cambridge). Theoretical Physics (including cosmology, relativity, and high energy physics) occupies most of Pavilion B, while Applied Mathematics (including fluid dynamics and solid mechanics) occupies most of Pavilions F, G, and H.

Heads of department

[edit]

See also

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References

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Faculty of Mathematics, University of Cambridge

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The Faculty of Mathematics at the is a prestigious academic division renowned for its world-class research and education in pure and , , and , comprising two primary departments: the Department of Pure Mathematics and (DPMMS) and the Department of and (DAMTP). Housed primarily at the Centre for , it offers undergraduate programs through the , a historic honors degree structure, as well as advanced postgraduate courses including the one-year Master of Advanced Study (Part III) and PhD opportunities, emphasizing both theoretical depth and practical applications. The faculty fosters interdisciplinary collaborations with industry, government, and global partners, contributing to solutions in areas such as , healthcare, and cosmology, while maintaining a commitment to outreach for teachers, students, and the public. Mathematics at Cambridge traces its roots to the 16th and 17th centuries, when figures like introduced the equality symbol (=) around 1550, and , , and elevated the discipline's global stature through foundational work in and . The , formalized by 1790 as a rigorous examination held in the Senate House, became a of the faculty's identity in the , producing luminaries such as James Clerk Maxwell, Lord Kelvin, , and , and driving innovations in physics and computing through reformers like . By the early , milestones included G.H. Hardy's 1908 publication of A Course of , which revitalized pure math , and Fawcett's groundbreaking 1890 performance as the top female candidate, advancing women's access to higher education. The modern faculty structure emerged around 1960 with the establishment of DPMMS and DAMTP, culminating in the 2000 relocation to the £61.4 million Centre for Mathematical Sciences, funded partly by private sources. Today, the faculty's research spans diverse fields, with DPMMS focusing on , , probability, and , while DAMTP addresses applied areas like , , , and . Notable recent achievements include DAMTP researcher Dr. Miles Cranmer's 2025 receipt of the Schmidt Sciences AI2050 Early Career Fellowship as part of a $18 million global initiative for AI-driven scientific advancements. Educationally, it supports hundreds of undergraduates through the , which evolved from its competitive 19th-century origins—abolishing the order of merit in 1909—to a flexible, college-supervised system across Cambridge's 31 colleges. The faculty also hosts the , a national hub for international workshops and long-term programs since 1992. Looking forward, the Faculty of Mathematics aims to sustain its leadership by attracting global talent, expanding inclusive outreach, and tackling societal challenges through pioneering research that bridges pure theory and real-world impact. Its network and ongoing innovations, such as AI2050 fellowships, underscore its enduring influence on and related sciences worldwide.

History

Origins and Early Development

The study of at the traces its origins to the medieval period, when the university, founded in 1209, incorporated as a core component of the arts curriculum within the , encompassing arithmetic, , music, and astronomy. This early instruction drew from classical and scholastic traditions, emphasizing logical reasoning and practical applications, though the syllabus gradually became outdated by the . A notable early figure associated with Cambridge was , who earned his M.D. there in 1545 and may have lectured on shortly thereafter; he is credited with inventing the equals sign (=) in his 1557 work The Whetstone of Witte, which popularized algebraic notation in English textbooks. In the , mathematics gained prominence through the establishment of dedicated professorships, beginning with Isaac Barrow's appointment as the first in 1663, a chair endowed to advance geometric studies. Barrow's lectures on and laid foundational work, but it was his successor, , appointed in 1669 and holding the position until 1702, who transformed the field at . During his tenure, particularly in the 1660s and 1670s amid the university's closure due to plague, Newton developed the —his version of infinitesimal —alongside groundbreaking contributions to and , elevating mathematics from a pedagogical tool to a cornerstone of scientific inquiry in Britain. The 18th century saw the evolution of assessment practices, with voluntary oral examinations in introduced around 1725 to challenge advanced students beyond the standard curriculum, fostering a competitive culture. By 1790, these had formalized into the , featuring printed questions and a rigorous written format that became the pathway to honors degrees, though it emphasized Newtonian methods over continental innovations. In the 1820s, reformers including , George Peacock, and , through the Analytical Society, modernized the Tripos by integrating , , and Leibnizian notation, bridging with European advancements and broadening the syllabus. The system's intense focus on ranking persisted until 1909, when the order of merit was abolished to reduce pressure and encourage balanced education. By the early 20th century, the 's coaching-oriented approach began shifting toward research emphasis, reflecting broader academic trends. In 1934, Part III of the Tripos was established as a distinct postgraduate course, previously an optional extension of the undergraduate honors, providing advanced training that influenced subsequent programs in mathematical research.

Modern Expansion and Milestones

In the mid-20th century, the Faculty of Mathematics underwent significant organizational changes to support its growing research and teaching ambitions. Around 1960, the faculty was formally organized into distinct departments, reflecting a shift toward a more structured, research-oriented model inspired by international developments. This reorganization addressed the increasing specialization in mathematical disciplines and facilitated better resource allocation in the post-war era. A key milestone was the founding of the Department of Applied Mathematics and Theoretical Physics (DAMTP) in 1959 by George Batchelor, who served as its first head. Batchelor, a leading figure in fluid dynamics, established DAMTP to foster advanced research in applied fields, separating it from the broader mathematical faculty to promote interdisciplinary collaboration. Complementing this, the Department of Pure Mathematics and Mathematical Statistics (DPMMS) was created in 1964 under the leadership of Sir William Hodge, incorporating the Statistical Laboratory founded in 1947 as a sub-department. These establishments marked the faculty's evolution into a dual-department structure, enabling focused development in pure and applied mathematics. By the late , the faculty experienced rapid growth in research output and personnel, leading to overcrowding in its original locations on Silver Street for DAMTP and Mill Lane for DPMMS. To address this, the was constructed off Wilberforce Road, with the new facility opening in October 2003 after planning that began in the 1990s. The project, costing £61.4 million, was funded through a mix of sources: £30.8 million (50%) from private donations, £14 million from public funds, and the remainder from the . This relocation consolidated the faculty's operations, providing modern laboratories, offices, and collaborative spaces that enhanced research productivity and interdisciplinary work. Entering the 21st century, the faculty continued to expand, with DPMMS alone hosting over 100 academic and research staff alongside around 80 PhD students, contributing to a faculty-wide community of hundreds in these roles. This growth supported intensified research across pure and applied domains. Outreach efforts also advanced, with programs like the Millennium Mathematics Project—encompassing NRICH and Plus magazine—promoting mathematical engagement for ages 3 to 19 and the public through free resources and events. The Institute for , closely affiliated with the faculty, received a transformative £10 million grant in 2021 from the Engineering and Physical Sciences Research Council, doubling its research funding and enabling expanded programs on themes like AI and mathematical applications. Today, the faculty operates under a Faculty Board overseeing DPMMS and DAMTP, maintaining its position as a global leader in .

Structure and Governance

Departments and Divisions

The Faculty of Mathematics at the consists of two primary departments: the Department of Pure Mathematics and Mathematical Statistics (DPMMS) and the Department of Applied Mathematics and Theoretical Physics (DAMTP). Both departments are housed within the Centre for Mathematical Sciences on Wilberforce Road in , a purpose-built facility that centralizes mathematical teaching and research activities. DPMMS encompasses , probability, and , with the Statistical Laboratory serving as a key sub-unit dedicated to statistical research and applications. The department supports approximately 95 academic and research staff members and around 90 PhD students, who are distributed across three pavilions in the Centre for . DAMTP addresses and , structured around specialized research groups including and High Energy Physics. It employs about 135 academic and research staff and oversees approximately 110 PhD students, all based in the Centre for . Governance of the faculty is managed by the Faculty Board, which oversees academic policies and operations across the departments. Additionally, the Isaac Newton Institute for Mathematical Sciences functions as an affiliated yet independent resource, hosting collaborative programmes closely linked to the faculty's work.

Leadership and Administration

The Faculty of Mathematics is governed by the Faculty Board, which oversees strategic direction, teaching, and research across the faculty, meeting six times per year in accordance with University Statutes and Ordinances. The Board comprises heads of the two departments, appointed and elected faculty members, co-opted experts, and student representatives, with no single permanent director; instead, it is chaired by an elected member serving a fixed term, such as Professor Peter Haynes until 2026. Administrative support is provided by the Faculty Office, which coordinates faculty-wide operations including finance, human resources, and facilities. At the departmental level, the Department of Pure Mathematics and Mathematical Statistics (DPMMS) is headed by Professor Ivan Smith as of 2025. DPMMS was founded in 1964 under (1964–1969), followed by J. W. S. Cassels (1969–1984), D. J. H. Garling (1984–1991), John H. Coates (1991–1997), W. B. R. Lickorish (1997–2002), and others. While the Department of Applied Mathematics and (DAMTP) is led by Professor Nick Dorey, who assumed the role on 1 October 2025, succeeding Professor Colm-cille Caulfield. Each department maintains its own head, appointed for terms typically lasting five years, to manage academic and operational affairs. Historically, DAMTP leadership has included founder George Batchelor (1959–1983), Keith Moffatt (1983–1991), David Crighton (1991–2000), Timothy J. Pedley (2000–2005), Peter Haynes (2005–2015), Nigel Peake (2015–2020), and Colm-cille Caulfield (2020–2025). Administrative functions are handled separately by each department, with dedicated finance and personnel teams supporting around 50 in DPMMS and a similar number in DAMTP. Undergraduate advising is facilitated by Directors of Studies appointed in each , who guide students on course selection and academic progress. Faculty-wide committees, such as the Teaching Committee and Curriculum Committee, oversee admissions processes, examination standards, and program development under the Board.

Education

Undergraduate Programs

The undergraduate program in the Faculty of Mathematics at the is delivered through the , a rigorous three-year course leading to a (BA) with Honours upon successful completion of Parts IA, IB, and II. This structure emphasizes deep conceptual understanding, problem-solving skills, and a balance between pure and applied . Students admitted to the program, numbering approximately 260 per year, follow a cohort-based progression with lectures, supervisions (small-group teaching sessions), and example classes to support learning. The Tripos has included women since 1881, marking early inclusivity in higher . Part IA, undertaken in the first year, establishes foundational knowledge across pure and applied mathematics, with two pathway options: Pure and Applied Mathematics or Mathematics with Physics. In the Pure and Applied track, students complete eight 24-lecture courses covering topics such as vectors and matrices, analysis I (including sequences and continuity), groups, numbers and sets, differential equations, vector calculus, probability, and dynamics and relativity. The Mathematics with Physics option substitutes two mathematics courses with a physics module involving lectures and practical work. Assessment occurs via four three-hour written examinations at the end of the year, with no continuous evaluation except for optional non-examinable computational projects (CATAM). This part ensures all students build essential prerequisites regardless of prior specialization. Part IB in the second year deepens these foundations and introduces greater breadth, comprising four 24-lecture courses, eight 16-lecture courses, three 12-lecture courses, and CATAM projects. Key topics include linear algebra (vector spaces and eigenvalues), (metric spaces and uniform convergence), groups, rings and modules, topological spaces (compactness and manifolds), methods ( and PDEs), , , , , (inference and models), and Markov chains. Courses are distributed across terms, with Easter-term options like optimisation and variational principles available flexibly. Building directly on Part IA, this stage prepares students for specialization by expanding core areas in algebra, , geometry, mechanics, and probability. Evaluation consists of four exam papers with short and long questions scaled to course length, emphasizing analytical rigor. Part II, the third and final year for the BA, focuses on advanced electives and specialization, offering 37 courses (10 intensive 24-lecture C-courses and 27 shorter D-courses) in pure and , alongside CATAM. Students select from topics such as , , , statistical modelling, and , allowing tailoring to interests in , , or . The emphasis shifts toward independent problem-solving, supported by supervisions that provide personalized feedback on challenging exercises. Assessment is through four written exams, with questions designed to test depth and application, leading to classification (first, second, or third class honours) upon graduation. High-performing students may transition to the optional fourth-year Part III for the integrated MMath, which builds on this foundation for advanced study.

Postgraduate Programs

The Faculty of Mathematics at the offers a range of postgraduate programs, with the flagship being Part III of the , a nine-month taught master's course leading to the MMath degree for continuing Cambridge undergraduates or the MASt (Master of Advanced Study) for external applicants. This program features approximately 75 courses across , probability, statistics, , and , allowing students to select around 16 core and elective modules based on their interests. Lectures are supplemented by example classes and an optional extended essay, with assessment primarily through written examinations in late May or early June. Around 280 students enroll annually, including about 90 from Cambridge's undergraduate Tripos and the remainder from other institutions worldwide, fostering a diverse and international cohort. Research degrees form another cornerstone, with PhD programs in and (offered by the Department of Pure Mathematics and Mathematical Statistics, DPMMS) and in and (offered by the Department of Applied Mathematics and Theoretical Physics, DAMTP), each lasting 3-4 years. These research-based programs involve original thesis work under the supervision of 2-3 faculty members, with no mandatory taught components but opportunities for seminars, optional training, and limited teaching experience such as supervisions. Approximately 270 PhD students are enrolled across the faculty at any time, with admissions emphasizing alignment of research interests and prior postgraduate experience, often including completion of Part III or an equivalent master's. Funding is available through sources like EPSRC Doctoral Training Partnerships, STFC studentships, and Cambridge Trusts, though not guaranteed for all admits. Additional postgraduate options include the occasional one-year MPhil by Research in Mathematics, available in either DPMMS or DAMTP, which emphasizes focused with minimal structured teaching and culminates in a . Admissions across all programs require a first-class honors degree or international equivalent in or a related field, with applications assessed on academic record, potential, and references; the process is highly competitive and international in scope. Graduates frequently pursue academic careers, with many Part III alumni proceeding directly to PhD programs at or leading institutions, while others enter industry roles in , , or consulting, leveraging the program's rigorous training in advanced mathematical methods.

Research

Pure Mathematics and Mathematical Statistics

The Department of and (DPMMS) at the conducts across a broad spectrum of theoretical and , emphasizing foundational advancements in abstract structures and probabilistic models. With over 100 academic and staff, as well as around 80 PhD students, the department fosters an environment where explores core theoretical questions, while develops rigorous tools for uncertainty and . in DPMMS is housed within the Centre for , facilitating interdisciplinary interactions without delving into applied modeling. In , key areas include , , and partial differential equations, , and topology, foundations (encompassing ), and . Researchers employ abstract proof techniques to establish fundamental theorems, often complemented by computational verification for complex conjectures. For instance, investigations, led by figures such as Professor Mark Gross, focus on mirror symmetry and , advancing understandings of Calabi-Yau manifolds through algebraic frameworks. In , Professor Imre Leader's work on extremal combinatorics and utilizes extremal set theory to resolve problems in graph structures and intersecting families. efforts explore Diophantine approximations and arithmetic geometry, while logic research addresses set-theoretic foundations and , contributing to consistency results in axiomatic systems. These pursuits often involve collaborative , such as the DPMMS Pure Mathematics series, which host international experts to refine methodologies and share proofs. Mathematical statistics research within DPMMS, primarily through the Statistical Laboratory, centers on probability theory, statistical inference, and applications to machine learning and data science. The laboratory emphasizes Bayesian methods for posterior and nonparametric estimation techniques to handle high-dimensional data. Probability studies investigate processes and mixing times for Markov chains, while statistical inference develops robust methods for shape-constrained and multiple testing. Machine learning applications integrate theoretical statistics with , such as in high-dimensional regression and causal models. Collaborations occur via the Statistical Laboratory Seminar series and joint workshops, promoting the integration of probabilistic tools with computational simulations. Recent highlights underscore the department's impact, driving seminal contributions. In 2025, Professor Perla Sousi received the London Mathematical Society for her work on mixing phenomena and cutoff in Markov chains, highlighting advances in probabilistic analysis. Additionally, Professor Richard Samworth and Dr. Julian Sahasrabudhe have been invited to deliver invited lectures at the 2026 in , recognizing their innovations in and combinatorial , respectively. These achievements reflect DPMMS's role in producing high-impact theoretical results, often published in leading journals like the and the Journal of the .

Applied Mathematics and Theoretical Physics

The Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge conducts pioneering research at the intersection of mathematics and physical sciences, emphasizing practical modeling and theoretical advancements to address complex real-world problems. Established as a hub for interdisciplinary inquiry, DAMTP's work spans foundational theories and computational tools that influence fields from climate science to quantum technologies. Researchers employ partial differential equations (PDEs) and numerical simulations to model phenomena such as fluid flows and gravitational dynamics, often leveraging high-performance computing resources like the COSMOS supercomputer for large-scale analyses. In applied mathematics, DAMTP excels in fluid and solid mechanics, where studies explore the behavior of fluids in turbulent environments and the deformation of solids under stress, with applications ranging from industrial processes to geophysical events. The G.K. Batchelor Laboratory supports experimental validations of these models, enabling precise predictions of phenomena like granular flows in engineering contexts. Geophysics research, active since 1959, investigates the dynamics of the atmosphere, oceans, cryosphere, and solid Earth, integrating fluid mechanics to simulate natural disasters and planetary processes. Mathematical biology initiatives apply these tools to model biological systems, such as population dynamics and disease spread, while computational analysis develops algorithms for solving high-dimensional PDEs in heterogeneous media. A prominent example is the work on environmental fluid dynamics led by Colm-cille Caulfield, which examines buoyancy-driven flows in stratified environments to inform climate resilience strategies. Theoretical physics at DAMTP advances understanding of fundamental forces through high-energy physics, where researchers probe quantum field theories, , and lattice simulations to unravel particle interactions beyond the . General relativity and cosmology efforts focus on , , and the early universe, using techniques to simulate emissions from merging compact objects. Quantum information research, via the Centre for Quantum Information and Foundations (CQIF), develops protocols for and error-correcting codes, bridging theory with emerging hardware. Cosmology studies integrate observational data with theoretical models to constrain parameters and scenarios. has made seminal contributions to research, including the Gibbons-Hawking formula for entropy, which has profoundly shaped paradigms. DAMTP's methodologies emphasize PDE-based modeling and advanced numerical simulations, such as finite element methods for and spectral methods for fluid instabilities, often implemented on clusters to handle multiscale problems. These tools facilitate interdisciplinary collaborations with engineering for optimized designs in and , and with climate science to predict patterns through coupled atmosphere-ocean models. For instance, geophysical simulations inform sustainable by modeling subsurface flows in porous media. Recent achievements underscore DAMTP's impact: in 2025, received the Dirac Medal from the for his foundational work on gravity and black holes. David Abrahams was awarded the 2024 Institute of Mathematics and its Applications (IMA) Gold Medal for outstanding contributions to , particularly in wave propagation and . Miles Cranmer, an assistant professor in DAMTP, secured a 2025 Schmidt Sciences AI2050 Early Career Fellowship to advance AI-driven discovery in physical sciences, enhancing for cosmological models. Additionally, in 2026, Lorenzo Gavassino earned the American Physical Society's George E. Valley Jr. Prize for innovations in relativistic , highlighting DAMTP's role in bridging and .

Notable People

Prominent Faculty Members

The Faculty of Mathematics at the University of Cambridge boasts a diverse body of approximately 240 academic staff, including prominent international researchers and women leaders, who have made seminal contributions across pure and applied domains. In the Department of Pure Mathematics and Mathematical Statistics (DPMMS), Timothy Gowers serves as a Royal Society Research Professor, renowned for his foundational work in and , particularly his development of Gowers uniformity norms that advanced understanding of arithmetic progressions in dense sets, earning him the in 1998. Béla Bollobás, a retired professor with ongoing affiliation, is a leading figure in and extremal , whose influential results on random graphs and the Bollobás-Riordan index have shaped modern probabilistic methods in . Jason Miller, Professor in the Statistical Laboratory, has pioneered techniques in , including rigorous constructions of Liouville quantum gravity surfaces and mating-of-trees theorems for random planar maps, recognized with the 2017 and election as a in 2025. Wendelin Werner, the Rouse Ball Professor of Mathematics, received the 2006 for his breakthroughs on Schramm-Loewner evolution (SLE) and conformal invariance in two-dimensional critical , establishing key convergence results for random planar curves that bridge probability and . Within the Department of Applied Mathematics and Theoretical Physics (DAMTP), Hannah Fry was appointed the inaugural Professor of the Public Understanding of Mathematics in January 2025, advancing mathematics communication through bestselling books like The Mathematics of Love and television series that demystify algorithms in everyday life, fostering broader societal engagement with quantitative reasoning. Carola-Bibiane Schönlieb, Professor of and head of the Cambridge Image Analysis Group, has developed variational methods and partial differential equation-based models for image processing and inverse problems, with applications in and AI-enhanced reconstruction, earning her an invitation to speak at the in 2026. Lorenzo Gavassino, a in relativity and gravitation, resolved longstanding paradoxes in relativistic viscous hydrodynamics through novel thermodynamic frameworks that reconcile causality and stability in ultra-relativistic fluids, securing the 2026 American Physical Society George E. Valley Jr. Prize for his high-impact contributions to .

Distinguished Alumni

The Faculty of Mathematics at the University of Cambridge has produced numerous distinguished alumni whose contributions have profoundly influenced mathematics, physics, computing, , and beyond. Among the earliest notable graduates is , who entered Trinity College in 1661 and developed foundational work in and during his time there, laying the groundwork for . Similarly, , who arrived at Trinity College in 1896 on an open scholarship, advanced and , notably through his collaboration with on partition functions and the circle method. , entering King's College in 1931, pioneered with his 1936 paper on computable numbers and the , which formalized algorithms and computation, and later applied his expertise to cryptography during . In the 20th century, alumni extended these legacies into cosmology, , and dynamical systems. , who won a to in 1902 for and , applied probabilistic reasoning to , authoring The General Theory of Employment, Interest and Money (1936), which revolutionized macroeconomic policy and influenced global fiscal strategies. , after completing his PhD in and at in 1966, advanced understandings of black holes and cosmology through theorems on singularities and , holding the Lucasian Professorship of from 1979 to 2009. , who obtained his PhD from Clare College in 1980, proved in 1994 using elliptic curves and modular forms, resolving a 358-year-old and earning the in 2016. Collectively, these alumni have shaped diverse fields, with graduates linked to numerous Nobel laureates through direct degrees or faculty ties in physics, , and chemistry.

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