Gutiérrez was acquainted with letters from an early age, but did not disdain the sciences, and was especially fond of mathematics. He studied engineering as much as he did law. He earned his doctorate in jurisprudence at age 27 with the thesis Sobre los tres poderes públicos. He was exempt from paying tuition due to his family's poor economic standing, but chose to pay his own way as a surveyor and engineer with the Topographical Department, by producing translations, and by contributing to literary journals. He formed and presided over the Association of Historical Studies and regularly attended meetings of the Literary Salon founded by Marcos Sastre. In 1837 he delivered his lecture Physiognomy of Spanish learning. During the rule of Juan Manuel de Rosas, Gutiérrez's support for Argentine exiles in Montevideo led to his dismissal and imprisonment. He himself moved to Uruguay in 1840 when it was discovered that he had collaborated anonymously to El Iniciador, a periodical critical of Rosas. At the same time he continued to produce works as an engineer and topographer. Along with Juan Bautista Alberdi and Esteban Echeverría, he founded the Asociación de Mayo. In 1843 he and Alberdi traveled through the Americas and Europe. During a sojourn in Valparaíso, Chile, Gutiérrez devoted himself to teaching and writing. Among his works from this period was the critically acclaimed América Poética. He became the first director of the Naval Academy in Valparaíso. He published biographies translated from the French, as well as the results of his investigations of the new world. The fall of Rosas in 1852 allowed Gutiérrez to return to Argentina, where he attended the Constitutional Convention of 1853 as a supporter of the San Nicolás Agreement. As minister of foreign relations of the Argentine Confederation under Justo José de Urquiza, he contributed to the success of the San José de Flores Agreement in 1859, which reunited Buenos Aires and the provinces of the Argentine Confederation. Gutiérrez began a career as a journalist in Buenos Aires and also served as a national deputy. President Bartolomé Mitre appointed him rector of the University of Buenos Aires, in which capacity he served from 1861 to 1874.; he established the university's School of Engineering in 1866. He later attended the Constitutional Convention of Buenos Aires between 1870 and 1873.
