My Scientific Journey
Every researcher begins with a question. Mine has always been remarkably simple:
How can mathematics help us understand complex systems well enough to make better decisions?
Chapter One
Foundations
Before I had a research question, I had a habit: distrust anything that isn’t precise. That habit didn’t come from a classroom: it came from working with systems where a wrong assumption doesn’t just look bad on paper, it fails in the real world. Mathematics became the language that let me be precise on purpose. Group theory, functional analysis, differential equations, not as subjects to master, but as a discipline of thought: define your terms, state your assumptions, follow the logic wherever it leads, and never mistake an intuition for a proof.
That discipline is still the first filter everything else in this story has to pass through.
Rigor isn't a constraint on creativity. It's what makes an idea trustworthy enough to build on.
Chapter Two
From Theory to Computation
A theorem is true in general. Reality is a specific case, and specific cases rarely have closed-form answers. That gap is where mathematical modelling lives, and scientific computing is what makes a model something more than an equation on paper. I started translating continuous equations (wave propagation, atmospheric flow) into discrete schemes a computer could actually run: finite differences, operator splitting, stability conditions that quietly decide whether a simulation reflects physics or just accumulates numerical noise.
That taught me something the pure theory hadn’t: an elegant model that is numerically unstable is not a working model. Computation isn’t separate from mathematics: it’s mathematics forced to be honest about what it can actually compute.
An unstable numerical scheme is just as wrong as an incorrect proof. It just fails later, and more expensively.
Chapter Three
From Models to Data
Simulated systems are clean. Real ones are not. The moment a model has to face actual measurements, uncertainty stops being a footnote and becomes the main problem: noisy inputs, missing values, distributions that don’t behave the way the theory assumed. Statistics gave me a formal way to reason about that uncertainty instead of gesturing at it, and once the data in question was about human health rather than an abstract system, that same statistical grounding became biostatistics.
Data has a second, quieter problem: it has to be trustworthy before it is ever analyzed. That is what pulled me into data science and data engineering: pipelines, validation, reproducibility. I don’t think of that as software work bolted onto research. It’s scientific methodology: the part that decides whether a conclusion survives someone else re-running the analysis.
A result that can't be reproduced isn't a finding yet. It's a claim waiting for verification.
Chapter Four
Learning Systems
Machine learning entered this story late, and on purpose. I didn’t want a black box that outperforms interpretation; I wanted another modelling framework, one that can find structure I didn’t specify by hand, but that still has to earn trust the same way every other model does: through validation, transparency, and reproducibility.
In practice that means combining approaches rather than replacing one with another: symbolic reasoning for what can be stated precisely, statistical learning for what can only be estimated, and enough documentation that someone else can see exactly how a system reached its answer. Intelligence, in this context, isn’t the goal. Accountable inference is.
A model that can't explain itself isn't intelligent. It's just confident.
Chapter Five
Towards Healthcare
All four of these threads (rigor, computation, data, learning) only matter to me insofar as they can be trusted with something that matters. Healthcare and environmental science are where that stake is highest: a model of contamination exposure, or a triage recommendation, isn’t an academic exercise. It’s an input into someone’s decision, sometimes about someone’s health. That is not a comfortable place to be careless.
It’s exactly why the earlier chapters exist: because decision support in healthcare and public health deserves mathematics rigorous enough to be right, and transparent enough to be questioned. That is the direction this is heading: not artificial intelligence for its own sake, not modelling for its own sake, but scientific tools built carefully enough to be trusted with real consequences.
The question I started with hasn't changed. Only the tools I have to answer it with.
The Shape of the Idea
An Intellectual Timeline
Not a résumé. A record of how one question kept finding new tools to answer it.
- Applied Mathematics
- Mathematical Modelling
- Scientific Computing
- Statistics & Biostatistics
- Data Science
- Artificial Intelligence
- Healthcare Analytics
- Decision Support Systems
How I Work
Research Philosophy
Mathematical Rigor
Every model starts with explicit assumptions and ends with an honest account of its limits. If I can't state what a result assumes, I don't trust it yet.
Computational Reproducibility
A result that only exists on my machine isn't a result. Code, data, and methods should be transparent enough for someone else to verify (or challenge) what I found.
Interdisciplinary Thinking
The most interesting problems don't respect department boundaries. Mathematics, computation, and domain expertise have to work together, not in sequence.
Practical Impact
An elegant model that never touches a real decision is unfinished. I care about work that eventually has to survive contact with reality.
Extensions, Not Separate Activities
Beyond Research
None of the following are a break from research. They are what happens when the same question gets asked out loud, in front of other people.
Teaching
Explaining a model well is often what reveals whether I actually understand it. Teaching is where that gets tested in real time.
Open Source
Publishing code is a form of intellectual honesty: it means the methodology has to be complete enough for someone else to run.
Scientific Writing
Writing forces the same rigor as the mathematics itself: state it clearly enough that being wrong would be obvious.
Knowledge Sharing
Research that stays in one head doesn't compound. Conversations, reviews, and mentoring are part of how ideas actually get better.
Geo's Stories
The unpolished side of the same work (ideas, failures, and unexpected turns) lives on Geo's Stories.
For the concrete version of this story (dates, publications, technical skills), the CV has that.
Looking Forward
Where This Is Headed
This is not a finished trajectory. The next chapter is a PhD, and the questions I want to spend it on haven’t changed; only the scale has. I’m looking for interdisciplinary collaboration at the intersection of scientific computing, artificial intelligence for science, healthcare analytics, environmental modelling, and decision support systems: places where rigorous mathematics has to meet a real, consequential decision.
I don’t think of this as ambition for its own sake. I think of it as the natural next size of the same question I started with.
- PhD
- Scientific Computing
- AI for Science
- Healthcare Analytics
- Environmental Modelling
- Decision Support