Federico Villarreal , was born in Túcume (Lambayeque) on August 3, 1850, in a very modest family. He began his studies in his hometown and then attended high school at the San José de Lambayeque national school. Due to the economic hardship he was going through, he was forced to work since his adolescence, working as a cashier in a cotton gin company. He took exams (1870) to be admitted as a preceptor of first letters before the departmental instruction commission of Trujillo, after which he went on to direct the official primary school of Túcume (1871-1873). In 1874 he founded a private primary school in that town, whose direction he exercised at the same time that he taught mathematics in a secondary school in Lambayeque. In 1877 he obtained the title of secondary education teacher, a fact that gave him the opportunity to permanently move his residence to Lima.
University life
Among other achievements, he early spread a method to raise any polynomial to any power , by means of such an absolutely original and perfect procedure, that even for the case of binomials it is easier, safer and faster than Newton's binomial method. In 1877 Villarreal entered the Faculty of Sciences of the Universidad Mayor de San Marcos. He was a student with brilliant grades and obtained a bachelor's degree after two years. For his degree, he wrote a thesis entitled Effects of refraction on the disk of the stars (1880). Due to the outbreak of the Pacific War and the imminent Chilean occupation of Lima, he enlisted in the ranks of the Army Reserve. As a second lieutenant of the sixth company of the battalion No. 16, he fought in the battle of Miraflores on January 15, 1881. Despite the sad events of the war, he continued his studies and opted the degree of Doctor of Science Mathematics at the University of San Marcos on September 23, 1881 , with a thesis on Classification of third-order curves . He was the first student of the mathematical section to receive a doctorate there and a gold medal for his outstanding grades. Not satisfied with that training, he began his studies in 1882 at the National School of Engineers, where he successively obtained the titles of civil engineer (1884) and mining engineer (1886). In the Faculty of Sciences in San Marcos he ran the chairs of Astronomy, Review of Mathematics and Rational Mechanics, from 1880, and in the National School of Engineers he was in charge of subjects in Physics, Topography, Geodesy and Infinitesimal Calculus. He also taught at the Military School (1890-1896) and at the Naval School.
Political Life
In the field of politics, Villarreal was elected senator for Lambayeque in the general elections of 1894 and 1912. The deanship of the Faculty of Sciences of San Marcos fell to him by election in 1903, and he was successively re-elected to the position in 1907, 1911, 1915 and 1921.
Other studies
He had the merit of founding the Revista de Ciencias in 1897. The wise man from Lambaye also dealt with some subjects other than mathematical sciences. For example, he was interested in the native languages and came to affirm that there was a link or correspondence between the Quechua, Aymara and Yunga languages. In 1921 he published a reissue of the Grammar of the Yunga or Mochica language by Fernando de la Carrera (original work from the 17th century). He also carried out research on astronomy in the times of the Incas, understanding the environment of comets in the time of Huayna Capac. In addition, he wrote a treatise on The Positivist Doctrine (1891), attempting to harmonize Comte's teachings with Wronski's philosophy. Among the 550 titles that make up his intellectual production, the following stand out: Elevation of polynomials (1886), Esperanto (1901), Beam embedded at both ends (1906), Deformation of beams working in bending (1909) and a manual on Strength of materials . In the words of the historian Jorge Basadre, Villarreal was a brilliant figure who "brought a shine to Peruvian science at the end of the 19th and beginning of the 20th centuries." This illustrious character died in Barranco (Lima) on June 13, 1923, at the age of 72 .