About Ambient Math

Published October 21, 2026 · Updated October 21, 2026 · Checked October 21, 2026

Ambient Math is a reference site for people who want to see the math inside ordinary things. A cooling cup of coffee, a monthly loan payment and the slope of a curve all come from equations you can write on one line. We write the equation, do the arithmetic where you can follow it, and link the textbook, course notes or government page it comes from.

Who the editors are

Ambient Math is run by an independent editorial team that signs its work as the Ambient Math editors. Pages are signed as a team so the standard is the same whoever writes them: each page is held to the same sourcing rules and the same checks. No single person's word has to be taken on trust, which is why every page lists its sources and the date each was read.

What it covers

30 pages are published today, in 6 sections.

• Math in daily life (5 pages): Where calculus and everyday arithmetic turn up in a normal day: rates of change, totals, sleep, unit prices and the best choice among options.
• Core ideas (7 pages): Limits, derivatives, integrals, the chain rule, optimization and the Fundamental Theorem of Calculus, each with worked examples.
• Math of money (8 pages): Loan payments, payoff time, compound interest, APR vs APY, the Rule of 72, tax brackets, rent vs buy and retirement targets, with calculators and worked examples.
• Math of health (4 pages): The equations behind resting metabolic rate, total daily energy expenditure and maximum heart rate, with their sources and their limits.
• Math in the world (5 pages): Cooling coffee, why the seasons happen, pi and why power lines run at high voltage: familiar things with a calculation inside.
• Learning math (1 pages): How to study calculus, a topic roadmap, free courses and textbooks, and how to talk about math with children.

What the pages rest on

Together the published pages draw on 221 distinct sources from 95 websites: 93 open textbooks, university course notes and journal articles; 80 government and standards-body pages, among them federal regulations, the IRS, the Federal Reserve, the Bureau of Labor Statistics, NASA and NIST; 23 reference works; and 25 others, such as a newspaper article or a company help page, used only for a plain fact. The editorial policy sets out how each kind is weighed.

What it leaves out

We explain how calculations work. We do not give personal financial, tax or medical advice, or recommend a product or a fund. A calculator formula is a published estimate, and each page names what the estimate is for and where it stops working.

How a page is made

• Question first. Each page starts from a question people actually type into a search box, and from what the best existing answers leave out.
• Sources saved. The textbook sections, course notes and government pages are saved, and every figure and rule in a draft is tied to a passage in a saved page. A fact with no passage is dropped.
• Scripted checks. Before publication, scripts confirm that each quoted passage appears in its saved source, that every number in the text is in a quoted passage, and that the same fact reads the same on every page.
• Worked examples. When we compute a number ourselves, the formula's source is named and the arithmetic is shown so you can redo it.
• Dated. Each page shows when it was published, updated and checked, and each source shows the day it was read.

How often pages are updated

Pages that quote a government figure are re-read when the agency publishes a new version. Every page is re-read at least once a year. A page that changes gets a new updated date and an entry on the changes page; a factual error is also logged on the corrections page.

Reach us

Write to editors@surroundedbymath.com with the page address and, if you can, the passage in the source that shows the right fact. We aim to reply within a week. More on the contact page.