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who created the quadratic formula

Nobody knows a single person who “created” the quadratic formula; it evolved over many centuries, with key contributions from several mathematicians across different cultures.

Quick Scoop: Who created the quadratic formula?

The ultra-short answer

  • The quadratic formula was not invented by one person.
  • Ancient mathematicians solved quadratic equations long before the modern formula was written down.
  • The first fully general formula came in the late 1500s, and the modern-looking version was written in the 1600s.

So if you need one “name” for school, many historians point to Simon Stevin (late 16th century) for the first general formula, and René Descartes (17th century) for the modern algebraic form.

Mini timeline of the quadratic formula

Think of the quadratic formula as a long-running group project rather than a solo invention.

  1. Babylonians (c. 2000–1600 BCE)
    • Used numerical methods equivalent to solving some quadratic equations, often via geometric “completing the square” ideas, though not in symbolic formula form.
  1. Ancient Greeks (Pythagoras, Euclid, Diophantus)
    • Euclid used geometric constructions to solve quadratic-type problems in Elements (c. 300 BCE).
 * **Diophantus** (c. 3rd century CE) solved specific quadratic equations algebraically but usually only gave one root.
  1. Chinese mathematics – Nine Chapters (c. 200 BCE)
    • The classic text The Nine Chapters on the Mathematical Art includes systematic rules for solving quadratic equations, again without our modern symbolic formula.
  1. Indian mathematics – Brahmagupta (7th century)
    • Brahmagupta gave an explicit rule that is essentially a form of the quadratic formula for equations like ax2+bx=cax^2+bx=cax2+bx=c, though not yet completely general and not in modern notation.
  1. Islamic Golden Age – Al-Khwarizmi and others (9th century)
    • Muhammad ibn Musa al‑Khwarizmi wrote a landmark algebra book giving full solutions to several types of quadratic equations (with geometric proofs), but expressed them verbally and case-by-case.
 * His work is a major step toward the general algebraic method behind the formula.
  1. Early modern Europe – Simon Stevin (1594)
    • Simon Stevin , a Flemish mathematician, is often credited with the first general quadratic formula covering all cases (allowing for different signs of coefficients, etc.).
 * This is the closest historical answer to “who first got the whole general formula.”
  1. Modern-style formula – René Descartes (1637)
    • In La Géométrie (1637), René Descartes wrote the quadratic solution in a symbolic algebraic form very close to the formula we memorize today.

Different viewpoints: who “created” it?

Because the history is long and multi-cultural, you’ll see slightly different answers:

  • “Ancient origins” viewpoint
    • Emphasizes Babylonians, Chinese, Indians, Greeks, and Islamic mathematicians who already knew how to solve quadratics , just not with our compact symbol formula.
  • “First general formula” viewpoint
    • Focuses on Simon Stevin (1594) as the first to write a formula that truly works in all coefficient cases.
  • “Modern algebra form” viewpoint
    • Credits René Descartes (1637) for presenting the solution in a recognizably modern algebraic style with symbols.

If a test asks “Who created the quadratic formula?” a safe historically informed answer is something like:

“No single person created it, but the first fully general formula is usually credited to Simon Stevin (1594), and the modern symbolic form to René Descartes (1637).”

Quick HTML fact table (for your notes or blog)

html

<table>
  <thead>
    <tr>
      <th>Era / Region</th>
      <th>Mathematician / Text</th>
      <th>Contribution to quadratic formula</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Babylonia (c. 2000–1600 BCE)</td>
      <td>Unknown scribes</td>
      <td>Numerical methods and completing-the-square style techniques for quadratic problems (no general symbolic formula).</td>
    </tr>
    <tr>
      <td>China (c. 200 BCE)</td>
      <td><em>Nine Chapters on the Mathematical Art</em></td>
      <td>Rules for solving quadratic equations written algorithmically in prose.</td>
    </tr>
    <tr>
      <td>Greece (c. 300 BCE – 3rd c. CE)</td>
      <td>Euclid, Diophantus</td>
      <td>Geometric and early algebraic methods for quadratics; solutions but no universal symbolic formula.</td>
    </tr>
    <tr>
      <td>India (7th century)</td>
      <td>Brahmagupta</td>
      <td>First explicit formula-like rule for certain quadratic forms such as ax² + bx = c.</td>
    </tr>
    <tr>
      <td>Islamic Golden Age (9th century)</td>
      <td>Al-Khwarizmi</td>
      <td>Systematic algebraic solution of quadratics, case-by-case, with geometric justification.</td>
    </tr>
    <tr>
      <td>Europe (1594)</td>
      <td>Simon Stevin</td>
      <td>First general quadratic formula covering all cases.</td>
    </tr>
    <tr>
      <td>Europe (1637)</td>
      <td>René Descartes</td>
      <td>Quadratic formula in a near-modern symbolic algebraic form.</td>
    </tr>
  </tbody>
</table>

Why this is still a “trending topic” in math forums

Even today, people on math forums and YouTube still debate questions like “Who discovered the quadratic formula?” because:

  • It’s one of the first big formulas students memorize, so its origin is a natural curiosity.
  • The answer isn’t a simple one-liner: it’s a story across multiple civilizations , which makes for good videos and explainers.
  • Modern creators like to revisit classics (like the quadratic formula) to show how math evolved over time, especially using historical “completing the square” methods that students still learn.

TL;DR

  • No single inventor.
  • Many ancient cultures knew how to solve quadratics.
  • Simon Stevin (1594): first fully general quadratic formula.
  • René Descartes (1637): modern-looking symbolic version that leads directly to the formula students use today.

Information gathered from public forums or data available on the internet and portrayed here.