Gaussian integral
Integral de Gauss
- Date
- 1733 / 1809 · confidence medium
- Place
- Göttingen, Germany
- Credited to
- Abraham de Moivre (first calculation, 1733); precise form given by Carl Friedrich Gauss, 1809
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
The integral of the Gaussian function over the whole real line, whose value is the square root of pi. It is the normalising constant of the normal distribution and appears throughout probability theory and statistical physics.
Gauss published the exact value in 1809, attributing its discovery to Laplace; de Moivre had already found an equivalent result in 1733 while studying the binomial distribution.
What it led to
- Normalisation of the normal distribution
- Calculation of integrals in statistical physics and quantum mechanics