Timeline of a Topic (across the centuries)

ROLE: Act as a meticulous historian who builds clear, accurate timelines of mathematical topics for students.

CONTEXT: I teach [CLASS/GRADE] ([BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]). I want a timeline showing how a topic developed across centuries and cultures, so students see maths as a growing human story, not a fixed set of rules.

YOUR TASK:
1. Build a chronological timeline of 8 to 12 milestones in the topic's development.
2. For each milestone give: the rough date or century, who/where, and what changed in one line.
3. Deliberately include contributions from more than one culture (e.g. Babylonian, Greek, Indian, Arabic, Chinese, European, modern) where true.
4. Mark uncertain dates with 'approx'.
5. End with one line on where the topic is heading or being used now.

INPUT: Here is the topic: [TOPIC] (e.g. numbers, algebra, geometry, trigonometry, calculus, probability, the concept of infinity).

HOW TO WORK IT OUT: First privately list only milestones you are confident about, ordered by date. Do NOT invent precise dates, names, or events; if unsure write 'approx [century]' or omit it. Verify the order is chronologically consistent (no later event placed before an earlier cause) and that each attribution matches the standard historical account. Keep any maths terms simple.

OUTPUT FORMAT:
TITLE: 'Timeline: the story of [TOPIC]'.
Then a numbered chronological list. Each line: '[date/century] - [who/where] - [what changed]'.
Then 'WHERE IT IS GOING:' one line.
Then 'TEACHING TIP:' one line on how to use this timeline in class.

RULES: 350-520 words. Chronologically correct, multi-cultural where true, no fabricated dates. Plain ASCII only.

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return one complete, editable document ready to paste into Word or Google Docs. Use a descriptive title, short section headings, readable paragraphs, numbered actions and tables only where they make the material easier to use. Include every requested section; do not return formatting advice instead of the document.


MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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