École polytechnique (French pronunciation: [ekɔl pɔlitɛknik], lit. 'Polytechnic School'; also known as Polytechnique or l'X [liks]) is a grande école located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.

The school was founded in 1794 by mathematician Gaspard Monge during the French Revolution and was militarized under Napoleon I in 1804. It is still supervised by the French Ministry of Armed Forces. Originally located in the Latin Quarter in central Paris, the institution moved to Palaiseau in 1976, in the Paris-Saclay technology cluster.

French engineering students undergo initial military training and have the status of paid officer cadets. The school has also been awarding doctorates since 1985, masters since 2005 and bachelors since 2017. Most Polytechnique engineering graduates go on to become top executives in companies, senior civil servants, military officers, or researchers.

Its alumni from the engineering graduate program include three Nobel Prize winners, a Fields Medalist, three presidents of France and many CEOs of French and international companies. The school has produced renowned mathematicians such as Augustin-Louis Cauchy, Gaspard-Gustave de Coriolis, Henri Poincaré, Laurent Schwartz and Benoît Mandelbrot, physicists such as Henri Becquerel, Nicolas Léonard Sadi Carnot, André-Marie Ampère and Augustin-Jean Fresnel, and economists Maurice Allais and Jean Tirole. French Marshals Joseph Joffre, Ferdinand Foch, Émile Fayolle and Michel-Joseph Maunoury were also notable Polytechnique engineering graduates.

Founded in 1794 as the École centrale des travaux publics (Central School of Public Works), the school initially provided teaching limited to technical knowledge. In 1795, the school was renamed the "École polytechnique" (Polytechnic School). The neologism polytechnique, appearing for the first time in a document published by Claude Prieur at the beginning of 1795, means "many arts", referring to the plurality of applied arts, sciences, technology, engineering and other academic subjects taught at the school.

Under the Restoration and the July Monarchy, the school was officially renamed the "École royale polytechnique". Under the First and the Second Empire, it was renamed the "École impériale polytechnique". The students, alumni, and graduates were called "Polytechnicians". The school was often simply called "Polytechnique".^{[citation needed]}

The school has been nicknamed "l'X" or the "X" since the middle of the 19th century. Two explanations have been put forward. One points to the two crossed cannons on the school's badge. The other attributes it to the preeminence of mathematics in the training of Polytechnicians. According to L'Argot de l'X, published in 1894: "It is from the very importance given to the teaching of ana [analysis], the whole language of which is made up of x and y, that the nickname X came, universally accepted to designate Polytechnicians. Not all of them are mathematicians, but all have sufficient knowledge of differential and integral calculus for public service applications. Let us further say that in troubled times, such as 1830 and 1848, this knowledge particularly helped them to avoid being confused with all the individuals who disguised themselves as Polytechnicians to give themselves the appearance of defenders of order. When they were encountered, they were asked the differential of sin x or log x, and if they did not answer, they were immediately locked up." However, in the 1994 edition, the origin of the nickname was again reported to be the crossing of the canons on the coat of arms. The nickname "X" also applies to Polytechnicians. Female Polytechnicians are sometimes nicknamed "Xettes" or "X7", which is pronounced [iksɛt].

In the late 19th and early 20th centuries, the school and its students and alumni were nicknamed "pipo". In the early 20th century, the school was also nicknamed "Carva".