I defended my mathematics thesis yesterday. It is done.
Three years. Two degrees. Stage 3 cancer. MS in Mathematics and Statistics from SIUE. October 13, 2023.
Time for a post-mortem.
The Decision (2020)
I started this degree for specific reasons. I needed deeper statistical foundations. I wanted to understand proofs, not just applications. I suspected mathematical maturity would unlock better research.
All three turned out to be true, but not in the ways I expected.
What I Actually Learned
Statistical thinking, not just statistical methods. Before: run this test, get a p-value, make a decision. After: what is the generative model? What are we assuming? What could go wrong?
Measure-theoretic probability, not just counting outcomes. Before: probability is favorable outcomes over total outcomes. After: probability is a measure on sigma-algebras and everything flows from Kolmogorov's axioms.
Why estimators work, not just that they work. Before: MLE works because the textbook says so. After: MLE is consistent under these regularity conditions because of this proof.
The Thesis
Maximum Likelihood Estimation for Series Systems with Masked, Censored Failure Data.
In plain terms: when you have a system that fails if any component fails, some systems have not failed when testing stops (censoring), and you do not know which component caused failures (masking), how do you estimate component reliability?
This required combining survival analysis (censored data), mixture models (masked causes), the EM algorithm (hidden variables), bootstrap methods (confidence intervals), and simulation studies (validation).
It is not groundbreaking work. But it is complete, rigorous, and useful.
What Worked
Starting with clear goals. I knew what gaps I was filling. No wandering.
Choosing a thesis topic early. Spent two-plus years with the problem. Got deep.
Coding while learning theory. I implemented methods as I derived them. Theory stayed concrete.
Cancer as deadline. Stage 3 diagnosis in 2020 eliminated perfectionism. You finish or you do not.
Strong CS foundation. The CS degree gave me coding. This gave me proofs. Together they cover most of what you need.
What Did Not Work
Some irrelevant courses. A few classes had no connection to my research. Time tax.
Should have published earlier. I waited for thesis completion instead of pushing papers out incrementally. Mistake.
Did not network enough. Focused on work, not relationships. Probably cost me collaboration opportunities.
Underestimated administrative burden. So much paperwork for something that should be about ideas.
The Cancer Context
Doing a math degree while managing stage 3 cancer was complicated.
On the good side: mathematics worked when biology did not. Having structure helped between treatments. Research gave me something I could control. Thesis deadlines kept me moving forward.
On the hard side: chemo brain made proofs harder. Medical appointments ate time. Energy was unpredictable. I had to accept a reduced pace.
But I finished. That counts.
Key Insights
Statistical inference is philosophy formalized. Every statistical method embodies beliefs about what is knowable from data, what uncertainty means, what constitutes evidence, what tradeoffs matter. Understanding this makes you a better researcher.
Proofs force clarity. You cannot handwave in a proof. Every step justified. This discipline carries over to everything else.
Computation and theory need each other. Pure theory becomes disconnected. Pure computation becomes unprincipled. The good stuff lives in the synthesis.
The EM algorithm is everywhere. Hidden variables, mixture models, censored data, missing data. All EM problems. Once you see the pattern, you see it everywhere.
Mathematics is a mode of thought. Not just a toolkit. A way of seeing structure, abstraction, and pattern.
How This Changed My Research
Before: find existing method, apply it, report results.
After: what is the generative process? What are we assuming? Can I derive this from first principles? What breaks under model misspecification?
This makes research slower but more robust.
Was It Worth It?
People ask if a second master's degree was worth three years.
Yes. I am a better researcher because of the mathematical foundations, the statistical rigor, the comfort with proofs, the understanding of asymptotic theory.
But more than that, I think differently now. Computer science taught me to build. Mathematics taught me to reason. Both are essential.
What Is Next
I am planning to start a PhD in Computer Science. Focus areas: machine learning and AI safety, complex networks, statistical computing, computational methods for hard problems.
The math degree was preparation. Now comes application.
For Anyone Considering a Similar Path
Do it if you have specific gaps to fill, you are willing to go deep, you have research questions that require it, and you can afford the time investment.
Do not do it if you just want credentials, you are not willing to struggle with proofs, you could learn what you need from textbooks, or you are doing it because it sounds impressive.
If you do it: start with clear goals, choose your thesis topic early, code while you learn, publish incrementally, accept that it is hard.
Final Thoughts
Three years. Stage 3 cancer. Two master's degrees. The work is done. The defense went well. On to the next thing.
