The slide appeared.
And somewhere in the middle of it, a symbol I had seen before but never really understood:
dW_t
My honest reaction: Hmm… I think I’ve seen this before… What does it actually mean? I’ll just write it down and ask Claude later.
That is what I do. That is what I have always done. Write it down. Move on. Come back when there is time.
There is never really time. And two days later, I could not explain it to you.
I am studying the CQF — the Certificate in Quantitative Finance — and at the same time preparing for a Master of Science in Financial Engineering at NUS. I have a computer science background. I have been building software products for five years.
I am, in every way, new to quant finance.
And I am writing this letter not as someone who has figured it out. I am writing it as someone still in the middle of figuring it out — often confused, but slowly learning to read the language. That process is what this letter is about.
The Wrong Reason You Think You Are Struggling
When people find it hard to learn something technical — quant finance, maths, a new industry — they all say the same thing: I am just not smart enough for this.
That is almost never the real reason.
The real problem is usually one of three things:
- You are learning the language and the ideas at the same time
- You are reading and watching, but not actually processing
- You are measuring the wrong thing to know if you have learnt anything
Let me explain each one. Because until you find your real problem, working harder will not help.
I — The Notation Trap
Every difficult subject has two layers: the ideas, and the language used to write down those ideas.
In quant finance, the language is maths symbols. σ means volatility. μ means drift. E[·] means expected value. dW_t means a very small random movement.
Most courses teach you both at the same time — here is the idea, here is the symbol, next slide. But your brain can only handle one new thing at a time. When you are trying to understand the symbol and the idea at the same moment, both fail.
The symbol is not the maths. It is a short way of writing the maths — built on top of the idea.
Learn the idea first. Then the symbol will make sense on its own.
Here is what that looks like in real life.
Instead of writing down the definition of dW_t and moving on, try to understand the idea behind it using plain English — no symbols at all. Let me show you exactly how this worked for me.
II — The Questions That Showed Me How
Recently, someone helped me understand dW_t by asking me questions instead of explaining it.
No formula. No definition. Just:
“If you were watching a stock price every second, what two things would you need to describe the tiny random change from one second to the next?”
My answer: “Delta P..?”
“Good. What is missing from that?”
My answer: “The random part..?”
I said it like a question. I was not confident. But I was right.
“Can it go up or down?”
Yes — both directions.
“Would the change over one full day be bigger than the change over one second?”
Yes, obviously.
“Would it grow at the same speed as time? If one second gives a change of size x, would four seconds give 4x?”
“Hmm… I think… it would be somewhere between x and 4x? Because some changes would cancel each other out..?”
Again — said like a question. But correct.
And then something became clearer. Not fully. But a little. The random changes partially cancel each other across many small steps. So the total size does not grow at the same speed as time. It grows with the square root of time.
That is dW_t. A random step — up or down — with a size that grows by √dt.
The symbol did not teach me that. The questions did.
Here is what I noticed: I had the right answer inside me the whole time. The problem was not intelligence. It was confidence. I was so used to being given answers that I did not trust my own thinking when I had to work things out myself.
This taught me a rule I now use every time I enter a new field: translate before you accumulate. Every time you see a new symbol or a new word you do not understand, your first job is not to copy the definition. It is to build the idea in plain English until you can explain it to someone who knows nothing about the subject. Only then does the symbol become useful — not a wall, but a shortcut.
III — The Feeling of Learning That Is Not Learning
I used to study by reading. Then reading again. Then highlighting. Then writing cleaner notes.
It felt like I was working. My notes looked good. But my understanding was thin.
Here is what the research on learning says, and it is not gentle: reading again, highlighting, and reviewing passively are some of the least useful ways to study ever tested. They create what researchers call the fluency illusion — the material starts to feel familiar, and your brain mistakes that feeling for understanding.
But feeling familiar and being able to recall are two very different things.
Feeling familiar means you can recognise something when you see it. Being able to recall means you can produce it from memory when you need it. Every exam, every real situation, every moment where the knowledge actually matters — requires recall, not just recognition.
The fix is active recall: close the book, close your notes, and try to rebuild what you just learnt from nothing. Do not skim. Do not re-read. Rebuild it. Make mistakes. Then check. Then try again.
Research is very clear on this. The act of trying to remember — even when it feels hard — is what makes the memory stronger. The difficulty is not a sign that the method is failing. The difficulty is the method.
There is another trap worth naming: the notes trap. Neat, organised notes feel like knowledge. You look at a clear summary and feel like you own it — because it looks like you do. But the notes have the answers, not you. The moment the notes are gone — in an exam, in a real decision — the knowledge goes with them.
Take fewer notes. Try to remember more.
Not knowing where to start when the page is blank is not failure. It is the beginning of real learning.
IV — You Are Measuring the Wrong Thing
Most people measure their study progress by time. Hours spent. Pages read. Videos watched.
These are inputs. They tell you nothing about whether you actually understood anything.
The right question is: can you explain this clearly to someone who knows nothing about it? Can you use it on a problem you have never seen before? Can you find exactly where your understanding breaks down?
The Feynman Technique is the best tool I have found for this. Pick one concept. Take a blank page. Explain it in plain English as if you are talking to a 12-year-old. No technical words. No symbols until you have first explained the idea behind them.
Where you stop — where the words do not come, where you reach for a technical term because you cannot find the plain English version — that is exactly where you do not understand yet. Not a general fog. One specific gap.
And one specific gap has one specific fix.
This is why most studying does not work well: people put effort everywhere, when the real gain comes from finding the exact place where the understanding is missing.
V — The Four-Phase Framework
You can learn any subject — no matter how technical or new — through the same four steps. Most people spend almost all their time in Phase 1.
Phase 1 — Acquire. You see new material. You read, watch, listen. You build a rough picture. This is where most students stay.
Phase 2 — Consolidate. You test yourself. You use active recall and spaced repetition — reviewing things at increasing time gaps, just before you would normally forget them — to move knowledge from short-term memory into long-term memory. This is where most students do not spend enough time.
Phase 3 — Transfer. You mix this topic with other topics. You do different types of problems in one session. This forces your brain to think about which approach to use, not just how to do the approach. This is where real understanding forms.
Phase 4 — Apply. You use the knowledge in a real situation, with real consequences. Projects, real decisions, real stakes — these make knowledge stick in a way no textbook question can, because the real problem becomes the memory itself.
The ratio for most learners: 80% Phase 1, 15% Phase 2, 4% Phase 3, 1% Phase 4.
The ratio for fast learners: 40% Phase 1, 30% Phase 2, 20% Phase 3, 10% Phase 4.
Phases 2 to 4 feel harder and slower. They are harder. But they give you 10x better memory — and the understanding that is still there when the exam or the real decision arrives.
VI — The Difficulty Is the Moat
Here is something I have come to understand about the methods that actually work.
They are uncomfortable. Active recall. Spaced repetition. Building ideas from scratch instead of copying definitions. They feel harder than re-reading. They feel slower. They feel like you are not making progress, even when you are.
But that uncomfortable feeling is also what keeps most people out.
Most people will re-read their notes tonight. They will highlight. They will feel like they studied. Six weeks later, when the same formula appears in a new situation they have not seen before, it will not be there.
The difficulty of doing it the right way is the moat. Not the knowledge itself — the willingness to learn it properly.
There is a very specific satisfaction that comes from finally understanding something hard. Not just recognising it — actually owning it. Feeling like you have earned the right to call yourself programmer, doctor, lawyer, or someone who knows this. Like you can now read the language as an insider, not just look at the words as a layman.
That feeling is worth the struggle.
And the struggle is exactly what makes it rare and builds you into a competent person.
VII — How I Apply This
Right now I am learning across four areas at the same time: quant finance for CQF and MFE, building a family office system in code, applying what I learn to my family’s real wealth, and writing about all of it publicly.
These are not four separate learning problems. They are the same framework applied to four different types of material.
For CQF and MFE, the work right now is mostly Phases 1 and 2. The content is dense, the symbols are new, and there is a lot of it. My rule: translate first. Build the idea in plain English before I touch the symbol. Then I use Anki — a free flashcard app that uses spaced repetition — to remember the exact definitions and formulas I need. For the harder concepts — stochastic calculus, measure theory, and derivatives pricing — I use the Feynman method every week. I pick one concept, explain it on paper until I find where I stop, and that gap becomes what I study next.
For the family office system, this is mostly Phases 3 and 4. I am building something real — a codebase that will actually manage my family’s financial position. Every design choice is a problem I have not faced before. The knowledge I build here does not need Anki. It is built into something I made with my own hands.
For applying quant knowledge to family wealth, this is the Feynman method at its most important. Every time I want to act on an idea, I have to explain it in plain English first. If I cannot explain why a strategy makes sense without using technical words, I am not ready to use it on real money.
For writing, every letter I publish is Phase 3 and Phase 4 at the same time. The act of writing is the act of learning. Every essay is a Feynman test made public — and the feedback is immediate. If the writing is not clear, the thinking is not clear.
Why I Am Actually Doing This
I want to end this letter the way I started it — honestly.
I still do not fully understand dW_t. I understand it more than I did before. I can now build the idea from scratch, even if I cannot yet use the symbol easily. That is my honest position today.
But I am not learning this to pass a module.
I am learning it because I want to be truly qualified — not just someone with a certificate — to manage my family’s wealth responsibly. To understand what our investments are actually doing and why. To earn the right to that responsibility, not just receive it because I happen to be family.
There is a phrase I keep coming back to: from everyone who has been given much, much will be demanded.
That is not pressure I resent. It is the clearest job description I have ever had.
The difficulty of learning quant finance from the beginning, the uncomfortable study methods, the struggle to truly understand things rather than just recognise them — that is not the obstacle.
That is the qualification.
A Note To You
I want to say something before you close this.
If you are at the beginning of something that feels very big — a new field, a new industry, a subject that seems to assume you already know things you do not — I want you to know that the confusion you feel is not a sign you are in the wrong place.
It is a sign you are in exactly the right place.
The people who find this easy are not learning anything new. You are. And the gap between where you are now and where you want to be — that is not something to feel embarrassed about. That is the most honest place to learn from.
I am not writing these letters because I have it all figured out. I am writing them because I am still figuring it out, and I think there is someone reading this who is one or two steps behind me on the same road. If that is you — keep going. The discomfort you are feeling right now is the moat being built.
Thank you for reading. Genuinely. Every letter I write, I write with one specific reader in mind — someone curious, honest about what they do not know yet, and building toward something that matters. If that is you, I am glad you found this.
— Jeremy