Overview
About the Program
A doctorate built on specialized scientific inquiry, with close supervision from researchers working at the frontier of their fields.
Four principles shape the program: complete flexibility, a research-driven structure, a debt-free model, and a global scientific community.
100% Online & Flexible
Complete your online PhD in the natural sciences from anywhere in the world, with personalized supervision and a global research community.
Rigorous & Research-Driven
Grounded in sustained analysis, disciplined writing, and original inquiry. You work under close supervision by an expert in your specific field.
Oideachas Saor ó Fhiacha
Pursue advanced research without tuition debt. Studying online also saves on relocation and living costs, keeping your focus on the science.
Global Community
Join a research community spanning continents and disciplines, and build lasting scientific networks through seminars, research groups, and conferences.
Disciplines
Fields of Study
The program supports specialized doctoral research across the natural, mathematical, and computational sciences, with a focus on projects that confront significant scientific or engineering challenges.
Mathematics & Logic
- Pure & Applied Mathematics
- Mathematical Logic
- Game & Decision Theory
- Optimisation
- Category Theory
Physics & Chemistry
- Theoretical Physics
- Quantum Foundations
- Chemistry
- Pharmaceutical Sciences
Computation & Engineering
- Computational Sciences
- Artificial Intelligence
- Quantum Computing
- Signal Processing & Telecommunications
- Engineering
Earth & Life Sciences
- Climate Science
- Agricultural Science
- Environmental & Energy Systems
This list is not exhaustive. If your research falls outside these fields, contact us to discuss whether we can support it. In all cases, the degree awarded is the Doctor of Philosophy in Natural, Mathematical, and Computational Sciences.
Program Structure
Your Doctoral Journey
The Doctor of Philosophy in Natural, Mathematical, and Computational Sciences (EQF level 8), awarded by Woolf, is structured as a focused three-year research program, requiring approximately 1,500 research hours per year.
Click each year to follow the path.
1 Year 1 · Laying the FoundationsLiterature review, research architecture, methodology ›
You work with Dr. Fernando Tohmé, Director of the PhD Natural Science Programme, who supervises every incoming researcher through the foundational stage.
- Narrow your research question and define the problem your work will address
- Develop a literature review that establishes what is already known in your field, and where your contribution lies
- Design your research architecture and methodology
- Move on to Year 2 once this groundwork is secure—not before
2 Year 2 · Research & WritingSustained dissertation work with your chosen supervisor ›
The heart of the PhD: sustained research and dissertation writing, with regular supervisory meetings and feedback.
- Help choose the dissertation supervisor who will guide you through Years 2 and 3—a GCAS researcher or an expert at another institution
- Carry out your core research and develop your results
- Write your dissertation chapter by chapter, with regular feedback
- Prepare work for peer-reviewed publication where appropriate
3 Year 3 · Completion & DefenceComplete, prepare, and defend your dissertation ›
You bring your research to completion and defend it before an academic committee.
- Complete and revise the full dissertation
- Prepare your final manuscript for submission
- Defend your dissertation before an academic committee
Supervision
How Doctoral Supervision Works at GCAS
Most doctoral programs assign you a supervisor and expect your research to fit their agenda. GCAS reverses that order: your research question comes first, and we find the expert who fits it. Read more about supervision at GCAS →
Year One
Narrowing the question
In your first year you work with Dr. Fernando Tohmé, Director of the PhD Natural Science Programme, who supervises every incoming researcher through the foundational stage. His job is to help you narrow your topic and bring your literature review to the standard required to proceed—establishing what has already been established in your field, and where the opening is for you to contribute.
You move on to Years 2 and 3 once that groundwork is secure—not before.
Years Two and Three
Choosing your dissertation supervisor
Years 2 and 3 are given over to the dissertation itself, and you help choose the supervisor who will guide it. That supervisor may be a GCAS researcher, or may be based at another institution entirely—what matters is that they are a genuine expert in your specific research area, not that they happen to sit on our staff list.
The right supervisor gives you rigorous guidance on the thesis and, just as importantly, opens a professional network that carries into your working life after the PhD.
Mentorship
Meet the Supervisors
Our supervisors are working researchers in mathematics, physics, and engineering, publishing at the frontier of their fields.
Fernando Tohmé is a mathematical economist working on the foundations of game-theoretic and economic formalisms and their extension into artificial intelligence, engineering, and the computational sciences. His research centres on decision problems, game theory, social choice, and optimisation in socio-economic settings, with further work on abductive cognition, argumentation systems, and evolutionary models of economic development.
He is a Principal Researcher of CONICET, Argentina’s National Research Council, and Full Professor in the Department of Economics at the Universidad Nacional del Sur in Bahía Blanca, where he has taught game theory and microeconomic theory since 1993. He holds an undergraduate degree in Mathematics and a PhD in Economics, and is a former Fulbright Scholar who has held visiting positions at UC Berkeley, Washington University in St. Louis, the University of Luxembourg, and the British University in Dubai. His work appears in Artificial Intelligence, Theory and Decision, Mathematical Social Sciences, Annals of Operations Research, and Omega, among others.
At GCAS he directs the doctoral programme in the natural, mathematical, and computational sciences, supervising researchers across the sciences and mathematics.
Muhammad Hamza Waseem is a Research Scientist at Quantinuum. His current research focuses on quantum foundations, quantum science education, applied category theory, mathematical linguistics, and quantum natural language processing. Hamza completed his DPhil in Physics at the University of Oxford, funded by the Rhodes Trust and Magdalen College. His thesis explored applied process-relational philosophy and employed string diagrams to study interpretations of quantum theory, constructor theory, wave-based logic, quantum computing, and natural language processing.
During his undergraduate studies in electrical engineering at UET Lahore, Hamza helped establish Pakistan’s first laboratory for single-photon quantum physics. He also co-authored the book Quantum Mechanics in the Single-Photon Laboratory, published by the Institute of Physics (IOP), UK, now in its second edition. Passionate about public engagement with science, Hamza has played a key role in organising the Lahore Science Mela, the largest annual science festival in Pakistan, and co-founded Spectra, an online magazine dedicated to training popular science writers in Pakistan. For his contributions to science popularisation he has been awarded the 2021 Diana Award, a High Commendation at the 2021 SEPnet Public Engagement Awards, and the 2024 MPLS Public Engagement with Research Impact Award.
At Oxford, Hamza teaches mathematics and physics at Magdalen College, the Mathematical Institute, and the Department of Computer Science, and has served as a Lecturer in Physics at Magdalen College. He is also a Senior Research Fellow at the Global Centre for Advanced Studies in Dublin.
Dr Brian Tyrrell-Nic Dhonncha was awarded his DPhil in mathematics from the University of Oxford in 2023, with a specialisation in mathematical logic. After a year at Oxford as a postdoctoral researcher and stipendiary lecturer, he joined California Polytechnic State University, San Luis Obispo, where he lectures core mathematics courses in calculus, linear algebra, and differential equations.
His research interests are split between mathematical logic and mathematics education. His PhD and postdoctoral research focused on undecidability results — such as Gödel’s First Incompleteness Theorem — applied to specific problems in number theory and algebraic geometry, with implications for automated theorem proving and Hilbert’s axiomatisation of mathematics programme. His recent research at Cal Poly focuses on the theory of embodied cognition — that thought is physically rooted in the body, and that abstraction, including mathematical reasoning, becomes grounded by bodily actions such as hand gestures — applied to the teaching and learning of undergraduate students, especially those with communication disorders.
Juan Felipe Miranda Medina is a Peruvian researcher and artist who integrates different knowledge fields: engineering, music-dance, and philosophy. As an engineer, Miranda holds a PhD in telecommunications and specialises in microwave design and analysis, with a strong background in signal processing. In music and dance, Juan is the first Peruvian to graduate from the prestigious Choreomundus Programme in Dance Knowledge, Practice and Heritage, and holds an undergraduate degree in musicology.
Juan has conducted fieldwork with the Afro-Peruvian community since 2013, which led to the publication of the book Freedom, Laughter and the Void (2022). In philosophy, Juan is interested in topics regarding philosophy of mind and cognition in relation to the production of meaning at the syntactic, semantic, and pragmatic levels. He is currently applying the philosophical framework of hylomorphism to the study of zapateo dance battles known as contrapuntos.
See all PhD supervisors
Browse the full range of GCAS doctoral supervisors across the sciences, mathematics, and the humanities.
View PhD Supervisors →Outcomes
Your Career
A doctorate in the natural, mathematical, and computational sciences is a research credential first—and it opens doors well beyond the university. Hover over each path to learn more.
Academic Research & Faculty Positions
+Pursue postdoctoral fellowships and tenure-track appointments at research universities and colleges. A completed dissertation, peer-reviewed publications, and a supervisor who is active in your field are the three things hiring committees look for—and the programme is built to produce all three.
Industrial R&D & Deep Tech
+Join research teams at technology firms, quantum computing companies, pharmaceutical and biotech laboratories, materials and semiconductor manufacturers, and engineering consultancies—settings where a doctorate is often the entry requirement rather than an advantage.
Data Science, AI & Quantitative Modelling
+Apply advanced mathematics, statistics, and computational methods in machine learning research, algorithm design, quantitative finance, operations research, and risk modelling. Doctoral training in formal reasoning transfers directly to problems where the modelling itself is the hard part.
National Laboratories & Public Science
+Conduct research at government laboratories, space and defence agencies, meteorological and geological surveys, public health institutes, and international scientific bodies—institutions where independent, publishable research is the core of the role.
Climate, Energy & Agricultural Science
+Work on the problems that will define the century: climate modelling and adaptation, renewable energy systems, sustainable agriculture, water and food security. These fields need researchers who can build defensible models and communicate what the models actually show.
Science Policy & Technical Advisory
+Advise governments, regulators, NGOs, and standards bodies on questions where technical judgement carries real consequences—emerging technology regulation, research funding, public health, environmental standards. Evidence-based reasoning is the qualification.
Entrepreneurship & Technology Transfer
+Take research from laboratory to venture. Doctoral projects in deep tech can produce patentable methods, and graduates go on to found start-ups, join technical leadership at early-stage companies, or work in technology transfer and scientific venture capital.
Teaching & Scientific Communication
+Teach at university and secondary level, or work in scientific publishing, editing, and public engagement. At a moment when scientific expertise is widely contested, the ability to explain difficult material honestly is a public good in short supply.
Investment
Tuition & Scholarships
Tuition for each year before the guaranteed tuition-reduction scholarship is applied
€6,000
All accepted students receive a tuition-reduction scholarship of up to 50%. Tuition can be paid in instalments, and there is no application fee.
When you graduate, you become a co-owner of GCAS College Dublin.
Questions
Ceisteanna Coitianta
What are the admission requirements?
How long does the program take to complete?
Can I finish the degree in under 3 years (36 months)?
Is the program fully online?
What is the total cost of the program?
How do I choose a supervisor?
Is the degree accredited?
When can I apply?
Get Started
Ready to Begin?
Applications are open year-round. Not sure yet? Talk with one of our PhD researchers or graduates to find out whether the program is a good fit for you.