About
What this site is
The Long Math is a growing collection of interactive financial calculators, tools, and explanations designed to make long-term financial trade-offs visible.
The tools model how fees, taxes, compounding, incentives, and time horizons interact over decades. Every input is explicit. Every assumption is stated. The arithmetic behind each result can be inspected directly.
The current tools and articles cover advisor fees, income and capital gains tax, compounding, inflation, mortgages, and Canadian account strategy (TFSA, RRSP, FHSA). The site is actively expanding — into corporate tax structures, deeper investment analysis, and content specific to incorporated professionals.
Alongside the calculators and articles, a separate essay section — Beyond the Numbers — explores the personal and career decisions that connect to the arithmetic: the financial cost of professional training, long-term career cashflows, and trade-offs that rarely get quantified.
Most financial decisions are discussed through narratives — conventional guidance, reassurances of expertise, promises of outcomes. This site approaches those same decisions through arithmetic. The math doesn't tell you what to do. It shows you what's actually happening.
Where this came from
The Long Math was built by Phil, a Canadian emergency physician who became increasingly frustrated by opaque financial narratives, hidden assumptions, and black-box projections.
Early in his career, he made financial decisions based on narratives rather than numbers — and spent two years paying for it through advisor fees and expensive mutual funds. That was the catalyst. What followed was a years-long self-education that went well beyond advisor fee structures: personal and corporate taxation, tax-efficient investing, asset allocation, real estate analysis, stock analysis, and the specific financial structures available to incorporated professionals in Canada.
Many of these tools were built originally in Excel, for personal use, to model real decisions with real money. The website came later, as a way to make them accessible. The calculator set continues to expand — now well beyond the original scope — as new topics are added and existing ones go deeper.
Who this is for
The educational content is for anyone with savings to manage. The arithmetic doesn't care about your profession.
That said, some of the most consequential — and least-discussed — financial decisions belong to high-income professionals. In Canada, many operate through a Canadian-Controlled Private Corporation (CCPC) or professional corporation (PC). The tax deferral, income-splitting, and investment implications of those structures are significant, and they rarely receive clear, quantitative treatment anywhere.
Professionals who commonly use these structures include physicians, surgeons, dentists, lawyers, accountants (CPAs), veterinarians, chiropractors, pharmacists, optometrists, psychologists, and physiotherapists. What they tend to share is a high income, a late start to serious earning, and a professional education that offered virtually no financial training.
This site assumes nothing and explains the math from the ground up.
How the tools are built
- Inputs are explicit and user-controlled. No hidden defaults.
- Assumptions are stated plainly. Disagreement becomes inspectable.
- Outputs follow directly from inputs. No black boxes.
- Understandable over impressive. Every dependency is visible.
What this site is not
This site does not provide financial advice or recommendations. The tools do not tell you what to do, optimize for specific outcomes, or steer decisions toward particular products or strategies. They show how inputs relate to outputs.
Financial advisors are not the target here. Several are known personally to the person behind this site — they are good people doing legitimate work. But the economics of how that work is typically priced in that industry deserves scrutiny. Most advisors charge a percentage of assets under management. That means the fee scales with your wealth, not with the complexity or volume of work performed. Imagine a dentist who charged a percentage of your net worth to perform a filling. The service is the same regardless of what's in your investment account.
Professional advice has genuine value, but the fee structure is worth scrutinizing. A good accountant, tax specialist, realtor, lawyer, or flat-fee advisor can more than earn their fee. The question worth asking is not whether to pay for professional help — sometimes you absolutely should. It's whether the fee structure matches what's actually being delivered.
That question — and what an unexamined fee structure quietly costs over decades — is the subject of dedicated tools and articles elsewhere on this site.
No opinions.
No hidden assumptions.
Just arithmetic.