D'Math University | Education & Specialist Mathematics
MSc History & Philosophy of Mathematics
A unique interdisciplinary programme exploring mathematics as a human endeavour — tracing its intellectual history from ancient Babylon to Grothendieck's revolution, and interrogating its philosophical foundations from Plato to Wittgenstein. For those who believe that understanding how mathematics came to be is inseparable from understanding what it truly is.
Programme Overview
Mathematics as a Human Story
This MSc positions mathematics not as a body of timeless truths handed down from some Platonic realm, but as a human creation — contested, evolving, and deeply embedded in cultural, political, and social contexts. Students encounter the drama of mathematical discovery: the crisis of incommensurability in ancient Greece, the bitter priority disputes of Newton and Leibniz, the shattering impact of Cantor's infinities on the mathematical establishment.
- Ancient traditions: Babylonian, Egyptian, Greek, Indian, and Islamic mathematical traditions studied in depth
- Philosophical rigour: Primary texts from Plato, Kant, Frege, Russell, Wittgenstein, and Lakatos
- Gödel's legacy: A full module on the incompleteness theorems and their philosophical ramifications
- No equivalent programme: One of fewer than 20 programmes worldwide with this specific focus
Who Should Apply?
This programme attracts two distinct kinds of student: mathematicians who sense that their discipline has a rich intellectual history they have never been taught, and philosophers who want to grapple seriously with mathematics as a test case for their epistemological and metaphysical commitments. Both groups leave with a richer, more nuanced understanding of what mathematics is and why it matters.
- Mathematicians: Discover the story behind the theorems — the people, controversies, and conceptual revolutions
- Philosophers: Engage with mathematics as the hardest test case for theories of knowledge and truth
- Educators: Develop the historical perspective that transforms how mathematics is taught
- Historians of science: Situate mathematics within the broader scientific and cultural revolutions of each era
Core Modules
History of Ancient Mathematics
Babylonian algebra and astronomy, Egyptian geometry, the Rhind Papyrus. The emergence of mathematical proof and rigour in ancient civilisations across three continents.
Greek & Islamic Mathematical Traditions
Euclid's Elements, Archimedes, Diophantus, and the transmission of Greek mathematics through Islamic scholars — al-Khwarizmi, al-Biruni, and the House of Wisdom.
17th–19th Century Revolutions
The calculus controversy, the invention of non-Euclidean geometry, Galois theory, and the arithmetisation of analysis — mathematics reinvented in three centuries.
Philosophy of Mathematical Truth
What makes a mathematical statement true? A priori knowledge, necessary truth, the epistemological status of proof, and the demarcation of mathematics from empirical science.
Foundations: Logicism, Formalism, Intuitionism
Frege's logicism, Russell's paradox, Hilbert's formalist programme, and Brouwer's intuitionism — the foundational crisis and its three proposed solutions.
Gödel's Incompleteness & Impact
A rigorous, conceptually-focused treatment of the incompleteness theorems, their proof strategy, and their profound implications for the foundations of mathematics and human cognition.
Mathematical Platonism vs Constructivism
Do mathematical objects exist independently of minds? Platonism, nominalism, structuralism, and constructivism debated through primary texts and contemporary analytic philosophy.
Social History of Mathematics
Mathematics as a social institution — who has been included and excluded, how mathematical communities form and police their boundaries, and the sociology of mathematical knowledge.
Mathematics & Scientific Revolutions
Kuhn's scientific revolutions applied to mathematics. Is there such a thing as a mathematical paradigm shift? Case studies: non-Euclidean geometry, abstract algebra, category theory.
Dissertation in HPoM
An original 15,000-word dissertation in the history or philosophy of mathematics. Students pursue a focused argument under expert supervision in a genuinely under-explored area.
Click any course to view its objective and learning outcomes.
HPM 501 History of Ancient Mathematics +
Objective
To trace the development of mathematics from antiquity to the medieval period.
Learning Outcomes
- Analyse Egyptian, Babylonian, Greek and Indian mathematics.
- Discuss the role of geometry in Greek thought.
- Trace the transmission of knowledge through the Islamic world.
- Analyse medieval European contributions.
- Compare ancient mathematical traditions.
AND OR NOT XOR -> <->
HPM 502 History of Modern Mathematics +
Objective
To examine the development of mathematics from the Renaissance to the 20th century.
Learning Outcomes
- Analyse the development of calculus.
- Discuss the rise of modern algebra.
- Trace the foundations crisis of the 19th-20th century.
- Discuss the development of set theory.
- Analyse 20th-century mathematical movements.
AND OR NOT XOR -> <->
HPM 503 Philosophy of Mathematics +
Objective
To examine the philosophical foundations of mathematics.
Learning Outcomes
- Analyse Platonism, formalism and intuitionism.
- Discuss the foundations crisis.
- Apply philosophy to questions of mathematical truth.
- Discuss structuralism in mathematics.
- Analyse the role of proof.
AND OR NOT XOR -> <->
HPM 504 Foundations of Mathematics +
Objective
To examine the logical foundations of modern mathematics.
Learning Outcomes
- Apply Zermelo-Fraenkel set theory.
- Discuss Gödel's incompleteness theorems.
- Apply categorical foundations.
- Discuss type theory and homotopy type theory.
- Analyse the continuum hypothesis.
HPM 505 Logic & Proof Theory +
Objective
To study the logical structure of mathematical reasoning.
Learning Outcomes
- Apply propositional and predicate logic.
- Use Gentzen-style natural deduction.
- Apply cut elimination.
- Discuss intuitionistic logic.
- Apply proof theory to consistency.
AND OR NOT XOR -> <->
HPM 506 Sociology of Mathematics +
Objective
To examine mathematics as a social and cultural practice.
Learning Outcomes
- Analyse mathematical communities and institutions.
- Discuss gender and ethnicity in mathematics.
- Apply sociological frameworks to research culture.
- Examine mathematical publishing and peer review.
- Discuss the politics of mathematics education.
HPM 507 Ethnomathematics +
Objective
To study mathematics in cultural context across societies.
Learning Outcomes
- Analyse counting and measurement systems globally.
- Discuss indigenous geometric traditions.
- Examine mathematics in art and music.
- Discuss mathematics and colonialism.
- Apply ethnomathematics to teaching.
HPM 508 Mathematics & Society +
Objective
To examine the role of mathematics in modern society.
Learning Outcomes
- Analyse mathematics in policy and governance.
- Discuss mathematics in war and surveillance.
- Examine algorithmic decision-making.
- Discuss mathematics and inequality.
- Analyse public understanding of mathematics.
HPM 509 Biographies of Mathematicians +
Objective
To study the lives of major mathematicians and their contexts.
Learning Outcomes
- Analyse the careers of Newton, Gauss, Euler and Cantor.
- Discuss the role of patronage and institutions.
- Examine excluded voices in mathematical history.
- Analyse the lives of Ramanujan, Noether and Galois.
- Discuss the role of correspondence and collaboration.
HPM 510 History of Statistical Thought +
Objective
To trace the rise of statistics from probability to modern data science.
Learning Outcomes
- Analyse the origins of probability.
- Discuss the rise of frequentist statistics.
- Examine the Bayesian-frequentist divide.
- Discuss the rise of computational statistics.
- Analyse data science as a discipline.
AND OR NOT XOR -> <->
HPM 511 Research Methods for HPS +
Objective
To apply scholarly methods to historical and philosophical research.
Learning Outcomes
- Use primary sources in mathematical history.
- Apply textual criticism.
- Use philosophical argumentation.
- Apply qualitative research methods.
- Communicate scholarship effectively.
HPM 512 Master's Dissertation +
Objective
To complete an original dissertation in history or philosophy of mathematics.
Learning Outcomes
- Identify a research-quality topic.
- Conduct primary source research.
- Apply rigorous historical or philosophical methods.
- Write a 15,000-word dissertation.
- Defend orally to a panel.
Career Outcomes
Academic Philosopher of Mathematics
Pursuing doctoral and academic positions in philosophy departments with specialisation in philosophy of mathematics — one of analytic philosophy's most vibrant and technically demanding sub-disciplines.
Science Historian
Research positions in history of science departments, museums, and research institutes. The history of mathematics is a distinct and valued specialism within the broader history of science community.
University Lecturer
Teaching history and philosophy of mathematics modules within mathematics, philosophy, or science studies departments. The combination of mathematical and philosophical competence is rare and highly valued.
Museum of Science Curator
Curating mathematical and scientific heritage collections at institutions such as the Science Museum (London), the Smithsonian, or national mathematical archives. A specialist role requiring deep historical expertise.
Education Policy Writer
Bringing historical and philosophical perspective to mathematics curriculum policy — arguing for the inclusion of mathematical history in school curricula and advising examination boards on content selection.
Mathematics Communicator
Translating deep mathematical ideas for general audiences — through books, podcasts, documentary films, and public lectures. Graduates with both mathematical depth and humanistic breadth are extraordinarily rare.
Top Universities for History & Philosophy of Mathematics
Why D'Math University for This Unique Programme?
Mathematical Depth
Unlike philosophy programmes that skim the mathematical surface, our HPoM MSc demands genuine mathematical engagement. You will work through primary mathematical texts — Euclid, Euler, Cantor, Gödel — and understand their arguments from the inside.
Philosophical Rigour
Unlike history of mathematics programmes that avoid philosophical controversy, we engage directly with the hardest questions: What is mathematical existence? Can we know mathematical truths? Are proofs discovered or invented?
Primary Sources
Modules are built around primary texts rather than secondary summaries. Students read Plato's Meno, Frege's Foundations of Arithmetic, and Wittgenstein's Remarks on the Foundations of Mathematics in translation alongside expert commentary.
A Rare Academic Community
Our faculty includes mathematicians who have turned to philosophy, philosophers trained in mathematics, and historians who work across disciplines. This rare intellectual climate cannot be replicated at a mainstream mathematics department.
One of fewer than 20 programmes worldwide with this exact focus. Applications close March 2026.