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  "body": "\n## Statement\n\nThe number $\\pi$ is [[transcendental|00SW8B91E7]] over $\\mathbb{Q}$.\n\n## Remarks\n\nThe statement follows from the Lindemann–Weierstrass theorem: $e^\\alpha$ is transcendental for every nonzero algebraic number $\\alpha$.\nIndeed, if $\\pi$ were algebraic, then $i \\pi$ would be algebraic and nonzero, but $e^{i \\pi} = -1$ is algebraic.\nSo $\\sqrt{\\pi}$ is also transcendental, and it is not [[constructible|0FMN2MN7TM]].\n\n## History\n\nCharles Hermite proved the transcendence of $e$ in 1873.\nFerdinand von Lindemann proved in 1882 that $e^\\alpha$ is transcendental for every nonzero algebraic $\\alpha$, and so that $\\pi$ is transcendental.\nKarl Weierstrass proved a more general statement in 1885.\n\n## Explanations\n\n### L1 human\n\nThe number $\\pi$ is not a root of any nonzero polynomial with rational coefficients.\nThis is much stronger than the irrationality of $\\pi$, and the proof is much harder.\n",
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