- Mathematical maturity develops several critical capabilities: systematic thinking about complex problems, mental acuity for abstract reasoning, comfort with rigorous analysis, and skill in building reliable models. These tools enable one to navigate uncertainty, construct mathematical frameworks that model reality, and make sound decisions in high-stakes situations where intuition proves insufficient.
- In late 2024, I explored trading options as a way of generating income (primarily selling call/put spreads and CSPs). As I went further into it, I realized my mathematical foundation was weak, and hindered my learning. Tried reading Natenburg, but felt like I was missing something.
- In early 2025, I was trading Solana/meme coins I realized having a strong base in mathematics, statistics, probability, would help me to trade more profitably, think more clearly, focus on finding an edge, testing it, and building a model/system around a thesis.
- In early 2025, I realized more and more how much LLMs and AI have changed the way we work and solve problems. In order to understand AI/ML/LLMs, at a baseline level, one needs mathematical literacy.
All roads lead back to building a strong foundation in Mathematics.
Indiana University | Mathematics, B.S.
Admitted August 2025.
- Core (Required)
- Calculus I, 215 (fulfilled by prior coursework)
- Calculus II, 216 (fulfilled by prior coursework)
- Calculus III, 311 (Sagara) - (in progress)
- Linear Algebra, 303 (Thomas) - (in progress)
- Bridge to Abstract Mathematics, 393
- Introduction To Modern Algebra I, 403
- Introduction To Analysis I, 413 (Udita)
- Mathematical Models I, 447 (Young)
- Senior Seminar
- Elective Choices (15 Units, 5 courses in total)
- Schedule
- 2025 Fall: Calculus III, Linear Algebra
- 2025 Winter: Differential Equations, Elements of Statistical Inference
- 2026 Spring: Bridge to Abstract Mathematics, Introduction to Probability I
- 2026 Summer: Mathematical Models I, Senior Seminar
- 2026 Fall: Modern Algebra I, Mathematical Statistics
- 2026 Winter: Analysis I, Mathematics of Finance
- Resources
- Mathematical Foundations I (Completed 2025-05-01)
- Mathematical Foundations II (Completed 2025-07-20)
- Mathematical Foundations III (21% | 2025-08-10, 41% | 2025-09-11))
- Linear Algebra
- Probability & Statistics
- Multivariable Calculus
- Methods of Proof
- Discrete Mathematics
- Mathematics for Machine Learning
- Differential Equations
- Abstract Algebra
- Incorporated Math Academy into my Daily Practice. 30 points a day. It's backed by data, one of the best ways to re-learn the foundations of Math.
- Progress, 64% through MF2
- Completed MF2, now on to MF3. It's not easy, but I'm making progress.
- I just had a call with Tom Burdo, a HF recruiter. It's clear, that the places I'm considering joining almost exclusively hire people with Math/CS backgrounds. You need to show you are quantitatively adept. You need to be able to pass the interview.
- If one wants to get into UChicago Financial Math, mathematical maturity is required.
- e.g. Quant Foundation Series or Baruch Pre-MFE
- The path is long, but rewarding. Find joy in the process.
I'm starting to see how beautiful math is. It's like there is a "reason" for things. There is a truth. Things came from observations. And those blossomed into useful applications and uses in real life. Like from flipping a coin and intuitively expecting 50/50, but only with enough sample sizes. Which led to the question of is independence necessary to do probability? Boom, Markov with his work on proving you don't need independent events to do probability, you could do it with dependent events. Which then played a part in modeling "how much" uranium-235 do you need for a neutron bomb? When does the chain reaction reach critical point? Markov Chain. Another one, PageRank in the early 90s. Another one, how many times to shuffle a deck (riffle shuffle) to be "random enough". It's crazy how you can build on a simple observation, flipping a coin. Or approximating things geometrically and build off of it. It's like a mental fortress of knowledge, a way of understanding the world and how it works. To get answers to "why". So fucking beautiful.
Literally tearing up, like it "clicks".
https://www.youtube.com/watch?v=KZeIEiBrT_w&ab_channel=Veritasium
Another "when it clicks" observation. I'm learning about using Cofactor Expansion to find the Determinant of an n x n matrix, and it just blew my mind that you can use any row or column, multiply each element by its respective cofactor, and you get the same value - the determinant for that matrix.
ANY row, ANY column. For a n x n matrix, that means there are n! ways to get the same determinant.
That just feels like black magic. It feels like this mathematical property of matrices was meant to be "found". We didn't create this property, we didn't design this property. It "emerged". More archeology than invention.
Insane.
The mathematician Eugene Wigner wrote about "the unreasonable effectiveness of mathematics in the natural sciences" - why should abstract mathematical relationships have such perfect predictive power in physics? Why should the universe "speak" mathematics so fluently?
- Euler's identity: e^(iπ) + 1 = 0 (connecting the five most fundamental constants in a single equation)
- The fact that prime numbers, despite seeming random, follow deep statistical patterns (what patterns?)
- How the same mathematical structures (like differential equations) describe everything from planetary orbits to quantum mechanics to population dynamics