I defended my mathematics thesis yesterday. It’s done.
Three years. Two degrees. Stage 3 cancer. And now: MS in Mathematics and Statistics from SIUE.
October 13, 2023: Defense complete.
Time for a post-mortem on what worked, what didn’t, and what I learned.
The Decision (2020)
I started this degree for specific reasons:
- Needed deeper statistical foundations
- Wanted to understand proofs, not just applications
- Suspected mathematical maturity would unlock better research
All three turned out to be true, but not how I expected.
What I Actually Learned
Not just statistical methods, but statistical thinking:
Before: “Run this test, get p-value, make decision” After: “What’s the generative model? What are we assuming? What could go wrong?”
Not just probability theory, but measure-theoretic probability:
Before: Probability is counting favorable outcomes After: Probability is a measure on σ-algebras and everything flows from Kolmogorov’s axioms
Not just computing estimates, but understanding why they work:
Before: “Maximum likelihood works because stats textbook says so” After: “MLE is consistent under these regularity conditions because of this proof…”
The Thesis
My thesis: Maximum Likelihood Estimation for Series Systems with Masked, Censored Failure Data
Translation: When you have a system that fails if any component fails, some systems haven’t failed when testing stops (censoring), and you don’t know which component caused failures (masking), how do you estimate component reliability?
This required combining:
- Survival analysis (censored data)
- Mixture models (masked causes)
- EM algorithm (hidden variables)
- Bootstrap methods (confidence intervals)
- Simulation studies (validation)
It’s not groundbreaking work. But it’s complete, rigorous, and useful.
What Worked
Starting with clear goals: I knew what gaps I was filling. No wandering.
Choosing thesis topic early: Spent 2+ years with the problem. Got deep.
Coding while learning theory: Implemented methods as I derived them. Theory stayed concrete.
Cancer as deadline: Stage 3 diagnosis in 2020 made me finish. No lingering perfectionism.
Strong mathematical foundation: The CS degree gave me coding. This gave me proofs.
What Didn’t Work
Took some irrelevant courses: A few classes didn’t connect to my research. Time tax.
Should have published earlier: Waited for thesis completion. Should have pushed papers out incrementally.
Didn’t 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.
Good aspects:
- Mathematics worked when biology didn’t
- Having structure helped between treatments
- Research gave me something controllable
- Thesis deadlines kept me moving forward
Hard aspects:
- Chemo brain made proofs harder
- Medical appointments ate time
- Energy unpredictable
- Had to accept reduced pace
But I finished. That counts.
Key Insights Gained
1. Statistical inference is philosophy formalized
Every statistical method embodies beliefs about:
- What’s knowable from data
- What uncertainty means
- What constitutes evidence
- What trade-offs matter
Understanding this makes you a better researcher.
2. Proofs force clarity
Can’t handwave in a proof. Every step justified. This discipline carries over to everything else.
3. Computation and theory need each other
Pure theory becomes disconnected. Pure computation becomes unprincipled. The magic is in the synthesis.
4. 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.
5. Mathematics is a mode of thought
Not just a toolkit. A way of seeing structure, abstraction, and pattern.
How This Changed My Research
I now approach problems differently:
Before: Find existing method, apply it, report results
After:
- What’s 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: “Was a second master’s degree worth three years?”
Absolutely.
I’m a better researcher because of:
- Mathematical foundations
- Statistical rigor
- Comfort with proofs
- 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’s Next
Planning to start PhD in Computer Science soon.
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
If you’re thinking about a second degree in a related field:
Do it if:
- You have specific gaps you need to fill
- You’re willing to go deep, not just collect credentials
- You have research questions that require it
- You can afford the time investment
Don’t do it if:
- You just want credentials
- You’re not willing to struggle with proofs
- You could learn what you need from textbooks
- You’re doing it because it sounds impressive
If you do it:
- Start with clear goals
- Choose thesis topic early
- Code while you learn
- Publish incrementally
- Accept that it’s hard
Final Thoughts
Three years. Stage 3 cancer. Two master’s degrees.
The work is done. The defense went well. The degree is complete.
On to the next thing.
MS Mathematics and Statistics, 2023. Next: PhD in Computer Science.
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