Juan Manuel Cajigal y Odoardo

Quick Info

10 August 1803
Barcelona, Venezuela
10 February 1856
Yaguaraparo, Venezuela

Juan Manuel Cajigal was the founder of mathematical and engineering studies in Venezuela and trained many mathematicians. He founded the first astronomical observatory in Venezuela.


Juan Manuel Cajigal was the son of Gaspar de Cajigal y Pontón Gobernador de Cumaná (born in Ávila, Spain in 1773) and Matilde Odoardo Bouchet de Grand Pré (born in Cumana, Venezuela) who was ten years younger than her husband. Let us note at this point that there are two spellings of Juan Manuel's family name, Cajigal and Cagigal. Of the 35 references below that include his name in their title, 21 give the spelling Cajigal and 14 give Cagigal. We shall say a little more about this later in our biography. Juan Manuel had a brother Alejandro Manuel Cajigal.

Gaspar de Cagigal y Pontón was a Spanish army officer who was governor of Cumaná, Venezuela from 1795 and lived in Barcelona, Anzoátegui. At this time Venezuela was a colony of Spain but there was a strong movement for independence. Gaspar died on 5 July 1810 [25]:-
... poisoned by the patriots in the midst of the independence events of 1810. His house in Barcelona was burned by order of Colonel Agustín Arriojas. This forced Matilde to return to her family in Cumaná, where, a few years later, she married the surgeon Alonso Ruiz Moreno.
After the death of his father, Juan Manuel and his brother Alejandro Manuel were left in the care of Juan Manuel Cagigal de la Vega y Martinez Nino (1757-1823), a cousin of Gaspar de Cajigal. This cousin was also a Spanish military man who fought against the Venezuelan independence fighters. He returned to Spain, landing in Cádiz on 8 February 1816, after a stay in San Juan de Puerto Rico. He took both Juan Manuel and his brother Alejandro Manuel to Spain with him.

Juan Manuel studied as a cadet in the Corps of Mounted Hussars and then at the University of Alcalá de Henares. His love of mathematics took him to Paris in 1823 where he took courses at the École des Ponts et Chaussées and the Collège de France given by Augustin-Louis Cauchy, Sylvestre François Lacroix, Adrien-Marie Legendre, Siméon Denis Poisson and Pierre-Simon Laplace. He showed outstanding abilities and he was offered a position as professor of mathematics at the Complutense University of Madrid. He decided, however, to return to South America. At the École des ponts et chaussées, Cajigal had met Lino de Pombo, a Columbian engineer and diplomat, who had written on 13 January 1828 to General Carlos Soublette, the Minister of War of Colombia, saying that Cajigal was a young man of great talents who would be a great asset to Columbia. We note that at this time Venezuela was effectively a province of Colombia.

Having completed his studies in Paris, Cajigal returned to Venezuela where, in 1829, he approached José María Vargas who had been appointed by Simón Bolívar to restore the Royal and Pontifical University of Caracas. Vargas had created the new Central University of Venezuela in Caracas and was keen to employ Cajigal as the first professor of mathematics. He wrote to the Minister of Education (see [35]):-
By one of those lucky chances to the country, Juan Manuel Cajigal has appeared among us, a young man filled with the noble desire to be useful to his country, whose record proves his outstanding abilities are the best criterion in these inquiries, they make him a precious find for the country and present him as the most calculated to fill the indicated position.
The political situation was, however, very difficult at this time and there was no response from the Minister of Education, so Cajigal went to Cumaná where he became the secretary of General José Francisco Bermúdez, the military chief of that province.

Although there had been no immediate response to Vargas's approach to the Minister of Education concerning Cajigal, by 1830 things began to move when Congress met in Valencia, and decreed on 14 October to establish a Military and Mathematics Academy in Caracas. The purpose of the Academy was to give mathematical and military training to men in both the civil and military fields. The Military and Mathematics Academy was formally founded on 26 October 1831 as part of the University of Caracas and Cajigal took up his duties as Director of the Academy on 4 November 1831. It is not surprising to see that the syllabus which was set up by Cajigal was based on the teaching that he had experienced in Paris. He created a cycle of three courses, each course being two years in length.

The first of the three courses taught arithmetic, algebra and geometry in the first year, then conic sections, plane and spherical trigonometry, and topography in the second year. The second of the three courses taught analytic geometry, descriptive geometry (with applications to shadows, perspective and stone cutting), and differential calculus in the first year, followed by integral calculus, and analytic mechanics (with its applications to machines, architecture and other civil works) in the second year. The third course was designed for military students aspiring to the Corps of Engineers. The first year topics were tactics of weapons in general, artillery, strategy, making a military camp, and military bridges. The second year involved eight months studying field fortification and mines while the remaining four months involved practical skills learning how to build batteries, parapets, etc. There were also technical drawing classes which were taken by all students.

Cajigal spent ten years directing the Military and Mathematics Academy. In December 1832 he made a plea for the setting up of a library and the purchase of instruments. He wrote (see for example [13]):-
Most of the students cannot afford the classic works, nor the academic collections, because of their great cost, and for Venezuela it would be very easy to allocate two thousand pesos for the time being to buy books and instruments ...
He was also very concerned about the well-being of his students, realising that to be able to profit from the teaching, the students required good living conditions. He wrote to the Secretary of State in the Offices of War and Navy (see for example [13]):-
... it will not be out of place to include my opinions about what can be done to improve the situation of the students and offer them the necessary incentives so that they continue with zeal and consecration the important and difficult studies that must form their institution. It is not enough that the Government, desirous of giving impetus to public education, and with the wise object of forming a body of engineers, has achieved the establishment of a school, fixed the subjects that must be taught there and indicated the final reward for those who apply and laboriously reach the term indicated for their incorporation into it. It is necessary, in addition, to ensure a comfortable existence while the studies last, that by having them sheltered from misery, leave them the necessary time to dedicate themselves exclusively to the tasks that are demanded.
During his time running the Military and Mathematics Academy, Cajigal was also involved in other activities. On the academic side he directed the Literature Chair at the Central University of Venezuela. He installed the first telescopes in Venezuela when he founded the first astronomical observatory in the country in Caracas and he computed the first astronomical charts in the country. But his work was not restricted to academic issues for he became involved in politics, the first time in 1833 when he became Deputy for Caracas. This was a difficult period following the separation of Columbia into various countries such as Venezuela. The Michelena-Pombo Treaty was an agreement drawn up to deal with issues such as friendship, trade, and navigation rights between Venezuela and Columbia. Cajigal worked on evaluating this controversial treaty which was signed on 14 December 1833.

He was a founding member and correspondence secretary of the Economic Society of Friends of the Country in 1829, 1830 and 1841. In the Memoirs of that Society he published an article about specimens of flora he had collected in 1833. For an extract from a talk he gave to the Economic Society of Friends of the Country in 1839, see THIS LINK.

He also took part in debates on the adoption of the metric system and the immigration of workers from the Canary Islands. A second involvement in politics came in 1835 when he became a senator for Barcelona in Anzoátegui.

The year 1835 was a difficult one for during that year the Military and Mathematics Academy had to close for a while. José María Vargas, who had played a role in Cajigal's career, became president of Venezuela in that year. There was, however, an attempted coup led by Pedro Carujo which began as an insurrection on 7 June 1835 [3]:-
The Academy of Mathematics suspends its activities and Cajigal himself must abandon books and scientific instruments to lead a battalion destined to defend the civilian and legitimate government.
The Dictionary of the History of Venezuela gives information about some other of Cajigal's activities [13]:-
... during this time he worked on the War and Navy, and Foreign Relations commissions. His work in Congress was linked to issues as important such as the Michelena-Pombo Treaty, the Organic Law of the Provinces, and the exile of Archbishop Ramón Ignacio Méndez. He also acted in the Electoral Colleges, in the Provincial Council, and in the General Directorate of Public Instruction (1840) .... He founded and edited, together with José Hermenegildo García and Fermín Toro, the newspaper 'Correo de Caracas' (1838-1841). He wrote about the layout of the highway to the valleys of Aragua, on the Caracas-La Guaira highway, and was the first to point out the advantages of the railway between that port and the capital.
Given the remarkable number of different activities that Cajigal was undertaking, it is not too surprising that his mental health began to deteriorate. In 1841 he left the Military and Mathematics Academy and travelled to London as secretary to Alejo Fortique (1797-1845), Minister of Venezuela in London. He soon moved to Paris as an official of the Government of Venezuela, spending a couple of years there. In Paris he met with colleagues who had been his friends when he had studied there in the 1820s. They entertained him with a banquet and told him that he had made a mistake returning to Venezuela after his studies. They were convinced that had he would have had a better career had he remained in Europe as a professor of mathematics [8]:-
In a burst of nationalistic enthusiasm, Cajigal replied that he preferred the glory of founding mathematical studies in his homeland to all the honour that standing out as a man of science in Paris could bring him. To reciprocate the entertainment of his hosts, Cagigal ordered the manufacture of gold and silver tableware engraved with his initials: JMC. The Venezuelan also dedicated himself to updating his scientific knowledge, visiting museums and libraries and participating in Parisian social life.
In 1843 Cajigal returned to Venezuela but by this time his mental health had deteriorated further. Some have blamed this on a passion he had for a young theatre artist, Marie Duplessis, who had rejected him but there is no solid evidence for this. Back in Venezuela Cajigal retired from public life and from all his teaching activities. He spent the last ten years of his life in Yaguaraparo on the Paria Peninsula in the Sucre State of Venezuela. He spent several years in a state of melancholy silence before he finally passed away [8]:-
The misfortune began with calm, shy monomania. He believed that people were going to persecute him, that they wanted to kill him. And those ideas were slowly isolating such a luminous intelligence from the scientific and social world.
Following his death he was buried in the Río Caribe Church but his remains are no longer there. Maximilian Kopp Marcano writes [24]:-
Unfortunately, and like other great men from the East such as Antonio José de Sucre and José Antonio Anzoátegui, the remains of the Barcelona wise man Juan Manuel Cagigal are not in Caracas, in the National Pantheon. In 1889, the then President of Venezuela, Doctor Juan Pablo Rojas Paúl, decreed his transfer to the temple reserved for illustrious Venezuelans, for which his bones were exhumed from the Río Caribe Church where they had rested since his death, next to his mother and his stepfather, however, as confirmed by research carried out in 1952 by his biographer Don Ángel Grisanti for the National Academy of History, the remains of Juan Manuel Cagigal were lost, but not his indelible example of dignity, dedication and work for current generations.
Cajigal is rightly credited as the founder of mathematical and engineering studies in Venezuela. He did not, as far as we know, produce any original mathematics, at least he certainly never published results from original research. He did, however, write a Memoir on Definite Integrals. It is not known when he wrote that work but it originally circulated as a handwritten text for students in his Military and Mathematics Academy. The book follows closely Cauchy's approach to the subject and was clearly strongly influenced by courses that Cajigal had taken while he had been a student in Paris. Walter Beyer discusses this work in detail in [5] giving this Abstract:-
This study consists of a description and critical analysis of the book 'Memoria sobre las integrales limitadas' , written by Juan Manuel Cajigal (1803-1856) and published posthumously in 1929. Prepared on a date not yet precisely determined, it is the only mathematical writing of his that still exists. It initially circulated in handwritten form and was used as a text in the Academy of Mathematics of Caracas. His 'Memoria' does not pretend to be an original contribution to mathematics having a didactic purpose and to disseminate the advances in Integral Calculus of its time, closely following Cauchy's ideas.
Cajigal also wrote the texts Treatise on astronomy and Treatise on elementary mechanics for use by students but neither has been published.

Today Cajigal's name is remembered for Avenida Cajigal and in Caracas as well as Avenida Cajigal in Barcelona, Anzoátegui. The Cagigal Naval Observatory is named for him. Asteroid 12359 was named "Cajigal" in his honour.

Finally we promised at the beginning of this article to say a little about the fact that his name appears sometimes as Cajigal and sometimes as Cagigal. The version Cajigal is an older spelling which changed over time to Cagigal. We suspect that he was given the name Cajigal when he was born but one fact is certain and that is that he signed himself using the form Cagigal. Several versions of his name written in his own hand still exist and they quite definitely are Cagigal with a 'g' instead of a 'j'.

Let us end with this description by José Sant Roz of how the brilliant Cajigal was destroyed by the times through which he lived [34]:-
Juan Manuel Cajigal was not a man with the qualities of a warrior, nor of a politician, despite the fact that he suffered through an era in which without these two "qualities" it was practically impossible to survive. Still, with all the "progress" of which we boast, we see how certain luminaries of science, certain people anointed with intellect, find it impossible to escape from the small world of partisan diatribe. They end up changing the solitary rooms of libraries and laboratories, the silent battle of ideas, for the bitter confrontation with the personal interests of groups possessed of foolish ambitions: the tropical caprice of leadership, the enjoyment of honours and prebends.

It was impossible for Juan Manuel Cajigal to overcome the stupidity of his time, and his tragic end is nothing but the result of a man before the defeated vision of his Destiny. He is a man who watches his talent shattered by the pack of dogs playing games. His life and his talent is irretrievably lost. He never had peace to think, to order his ideas in the midst of the demanding discipline required by the study of the exact sciences.

References (show)

  1. 10 de Agosto 1803 Natalicio de Juan Manuel Cajigal, Compañía Anónima Venezolana de Industrias Militares (CAVIM) (10 August 2022).
  2. 10 de agosto: Natalicio de Juan Manuel Cajigal, Venelogía (4 February 2014).
  3. 160 años de la muerte del sabio Juan Manuel Cagigal, Colegio de Ingenieros de Venezuela (10 February 2016).
  4. Admin, Natalicio de Juan Manuel Cajigal, Circuito Regional de Noticias (10 August 2017).
  5. W O Beyer K, Juan Manuel Cagigal (1803-1856) y su Memoria sobre las Integrales Limitadas: Una Aventura del Pensamiento, Paradigma (December 2020), 253-285.
  6. L D Correa (ed.), Juan Manuel Cagigal, Escritos literarios y científicos (Americana, Caracas, 1930).
  7. N Días, Juan Manuel Cagigal | Venezolano con todos los hierros, Venezolanos Ilustres.
  8. El sabio que inspiró el Observatorio Cagigal, La Guía de Caracas (18 September 2022).
  9. Elogio a la locura de Cajigal de mi tío Caupolicán, El Nacional (2 March 2002), 4.
  10. Y Freites, Un Esbozo Histórico de las Matemáticas en Venezuela. I Parte: Desde la Colonia Hasta Finales del Siglo XIX, Boletín de la Asociación Matemática Venezolana 7 (1-2) (2000), 9-37.
  11. E Fuguet, Juan Manuel Cagigal: Fundador de los estudios de matemáticas en Venezuela, El Carabobeño (16 de agosto de 2018).
  12. N Garcés, Nace Juan Manuel Cajigal, Ciudad Maracay (10 August 2022).
  13. R F Heres, El Proyecto Cientifico-Educativo de Juan Manuel Cagigal, Bulletin of the National Academy of History, Caracas 86 (343/344) (2003), 47-82.
  14. Juan Manuel Cagigal y Odoardo, Matematicos Venezolanos (2 February 2015).
  15. Juan Manuel Cajigal y Odoardo, dbpedia.org.
  16. Juan Manuel Cajigal y Odoardo, Diccionario de Historia de Venezuela (Fundación Polar, 1997).
  17. Juan Manuel Cajigal, EcuRed.
  18. Juan Manuel Cajigal, La Venciclopedia.
  19. Juan Manuel Cajigal, Official Website of the Respectable Lautaro Lodge No. 197.
  20. Juan Manuel Cagigal, in J Méndez and D Mendoza, Historia de la Universidad Central de vénezuela II (Caracas, 1924), 93-96.
  21. Juan Manuel Cajigal nació hace 214 años, Radio Mundial (10 August 2017).
  22. Juan Manuel Cajigal fundador de la Academia Militar de las Matemáticas y el Observatorio Astronómico de Caracas, Otilca Radio.
  23. B I de Lusinchi, Juan Manuel Cajigal, Blanca Ibáñez de Lusinchi Blogspot (9 August 2011).
  24. M K Marcano, Juan Manuel Cagigal (10 de agosto de 1803 - 10 de febrero de 1856), Asociación Larense de Astronomía.
  25. E Marín, Cajigal y la vajilla para la Dama de Las Camelias: una ingeniosa y divertida fábula, Estampas (13 October 2019).
  26. A Mijares, Juan Manuel Cagigal, in Lo Afirmativo vénezolano (Caracas, 1970), 172-173.
  27. O G Moreno, El sabio Juan Manuel Cajigal, En Oriente (11 April 2021).
  28. Nace en Venezuela el sabio Juan Manuel Cagigal y Odoardo, Radio Reloj (10 August 2021).
  29. C Pacheco, L B Linares and B G Stephan, Nación y literatura: itinerarios de la palabra escrita en la cultura venezolana (Equinoccio, 2006).
  30. I T Pampols, El masòn Juan Manuel Cajigal y Odoardo dirigió la instalación de los primeros telescopios en Caracas, Revista Masónica Malletes (9 January 2016).
  31. C A Di Prisco, Breves comentarios sobre la vida y obra matemática de Juan Manuel Cagigal, Boletin de la Academia de Ciencias Fisicas, Matematicas y Naturales 63 (3-4) (2003), 63-68.
  32. N Rivero, En la Venezuela del siglo XIX: Juan Manuel Cajigal compendio de Ciencias y Humanidades, Correo del Orinoco (10 August 2016).
  33. N Rivero, Venezuela: Juan Manuel Cajigal compendio de Ciencias y Humanidades, Agibilis 10 August 2016).
  34. J S Roz, El matemático Juan Manuel Cajigal, quien murió loco en Yaguaraparo, Aporrea (4 September 2010).
  35. G J Schael, Los Grandes Matemáticos Juan Manuel Cagigal, Homotecia 8 (6) (2010).
  36. E Subero, Juan Manuel Cajigal, in Del Ideario Pedagógico Venezolano (Ministerio de Educacion, Caracas, 1968), 49-52.
  37. S Verenzuela, Juan Manuel Cajigal, Venezuela e Historia (20 February 2016).

Additional Resources (show)

Other pages about Juan Manuel Cajigal:

  1. Juan Manuel Cajigal on science versus the arts

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update February 2023