Julio Garavito Armero

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5 January 1865
Bogotá, Colombia
11 March 1920
Bogotá, Colombia

Julio Garavito was a Colombian mathematician and astronomer who also contributed to political economy.


Julio Garavito was the son of the merchant Jose Vicente Hermógenes Garavito Oropesa (1829-1881) and his wife Dolores Armero de la Cala (-1900) both of whom had been born in Bogotá. Hermógenes and Dolores had seven children who were all born in Bogotá: José María Garavito Armero (1860-1904); Jorge Garavito Armero (1862-1920); Julio Garavito Armero (1865-1920), the subject of this biography; José Felipe Hermogenes Garavito Armero (1868-1869); Justino Garavito Armero (1871-1926); Fernando Garavito Armero (1874-1927); and María Teresa Garavito Armero (1877-1927).

Colombia had achieved independence from Spain in 1810 becoming the Republic of Gran Colombia, then became the Republic of New Granada before changing its name to the United States of Colombia in 1863, two years before Julio Garavito was born. This last name change was the result of a civil war in 1860-62. Another civil war in 1876-77 was a result of a dispute over education, with the Liberal Party attempting to introduce public education while the Conservative Party wanted education under the control of the Roman Catholic Church. In 1875, at the age of ten, Julio Garavito began his schooling at the Colegio de San Bartolomé in Bogotá. This college had been run by the Jesuits but, by the time that Julio began his studies there, it had been nationalised and was being run by the state. Already he had a strong interest in astronomy and, when only eleven years old, he produced his first almanac.

Hermógenes Garavito faced bankruptcy, probably due to fluctuations in the foreign markets, and moved to Fusagasugá, about 55 km southwest of Bogotá, with the three youngest children Justino, Fernando and María Teresa while Julio and his two older brothers remained in Bogotá for their education. We note that by this time there were only six children, José Felipe Hermogenes Garavito having died in 1869.

At the Colegio de San Bartolomé, Julio Garavito was taught mathematics by Luis María Lleras (1842-1885). Lleras was an excellent mathematician who had translated Legendre's Éléments de Géométrie into Spanish and published it in 1866. In 1883 Lleras talked about his pupil (see for example [6]):-
... Julio Garavito is that young man who expresses himself with such difficulty, yet he is, of all the students I have known, the only one who has a true mathematical spirit. Look at the way he reasons, at the rigour of his logic and at the depth of his analysis, and you will see that he is truly a superior intelligence.
Garavito graduated from the Colegio de San Bartolomé in 1884 but again in this year the United States of Colombia saw a civil war which grew more serious in 1885, with a rebellion by radical groups from the Liberal Party against the government, leading to the Battle of La Humareda. Luis María Lleras, Garavito's former mathematics teacher, was killed in this battle. The civil war saw the universities closed from 1885 to 1887. It also led to the declaration of the Republic of Colombia in 1886. When the National University of Colombia, which had been founded in 1867, reopened in 1887, Garavito began his studies of mathematics and civil engineering by enrolling in Practical Geometry, Trigonometry and Analytical Geometry. He graduated in 1891 having submitted three theses [23]:-
For his first mathematics thesis, he proposed a probabilistic approach to calculating π, while for his second, he calculated all the mathematical possibilities that a pressure gauge could have. In his final thesis, this one in engineering, Julio Garavito proposed a triangular structure to build bridges just like the Sydney Harbour Bridge.
Garavito's mathematical thesis was entitled El Juego de la Aguja which looked at probabilistic approaches to calculating π in the spirit of the Comte de Buffon's needle experiment. He was appointed to the chairs of Infinitesimal Calculus, Rational Mechanics and Astronomy at the National University of Colombia.

Due to his outstanding performance, Garavito was appointed as head of the National Observatory of Colombia in 1892. This observatory, built in 1803 on the initiative of the Spanish priest, botanist, and mathematician José Celestino Mutis 1732-1808), had seen periods when scientific activity ceased as for example from 1816 to 1823 after it had been used by those conspiring to overthrow Spanish rule, between 1848 and 1859 when it had been a military college and even an ice cream shop, and in the 1860s when it had been used as a fortress and a prison.

Garavito married María Luisa Cadena (1872-1917) on 23 May 1893 in Bogotá. She had been born in Fusagasugá, the daughter of Guillermo Cadena and Lucinda Reyes Vargas. Let us note that María Luisa Cadena had a sister Isabel Cadena who married Julio Garavito's younger brother Justino Garavito who became a mathematician, astronomer and cartographer. Justino Garavito graduated from the National University of Colombia, became a Professor of Mathematics and Engineering and an official at the Office of Longitudes. He was a founding member of the Geographical Society of Colombia.

Another civil war had broken out in Colombia in 1899 and, known as the War of a Thousand Days, lasted until 1903. It was fought between the Liberal Party who represented coffee plantation owners and import-export merchants, and the ruling Conservative Party. It started when the international price of coffee fell heavily. It is estimated that around 100,000 people died in the war which resulted in widespread damage to property and was a disaster for the economy of Colombia. It was during this war that the Nine Point Circle Society formed around Julio Garavito; for more information on this Society, named after Euler's nine point circle, see THIS LINK.

In 1897 Garavito published Latitud del observatorio de Bogotá which contained the series of observations he had made to determine the latitude of the Bogotá Observatory. This document, however, went much further in advocating a plan to measure the country. He had conceived a cartographic plan for a country which he described as "sparsely populated, without communication routes, covered by thick forest, extensive moors, lagoons and inaccessible swamps, crossed by very high mountain ranges, and exposed to continual political shocks that make any technical organisation temporary." Also in 1897 he published Los números inconmensurables , and two years later Reseña histórica del Observatorio Astronómico de Bogotá .

The War of a Thousand Days had a major impact on Colombia and engineers, professors and students decided to take refuge in the Observatory during the conflict. Garavito organised informal teaching sessions, seminars and other activities for this broad range of scientists. The civil war caused government finances to collapse and it decided to suspend and close activities in various state agencies and institutions, among them the Faculty of Mathematics and Engineering, and the National Astronomical Observatory. Garavito became the informal director of the Faculty of Mathematics and Engineering, set up in the Observatory. Ricardo Lleras Codazzi, a mining engineer, geologist, mineralogist and naturalist, writes [15]:-
During the great revolution from 1899 to 1902, the Director of the National Observatory was not idle; apart from the many questions of mathematics that he studied conscientiously as a distraction, he busied himself putting his notes in order to write the mechanics course that he developed by an original method, and tackled the analysis of the most difficult problems of algebra: the general solution of equations of degree higher than the second. He departed from the best known path of science, which consists of finding out the number of real and imaginary roots that the equation admits, the limits within which they are included and their general properties, to determine them by successive approximations, and preferred to relate the properties of the roots with certain lines of the star polygons that came to be the key to the desired solutions. In order to achieve his goal, it was necessary for him to establish new theories and to investigate hitherto unknown properties of figures, in a word, almost to create a science to which the name of polygonometry would be appropriate. Once these foundations were established, he based on them his analysis of binomial, trinomial, reciprocal equations, etc., and advanced a great deal in the general equation of degree m, by rigorous methods and admirable ingenuity. This work, which reveals a complete mastery of the most intricate questions of the field of analysis, as well as a rare intuition in the geometric field, is known only to a small number of his friends. One day it will be published and it will then be seen how far he has come in the field of abstract speculation and how much this privileged spirit was capable of.
In 1901 Garavito published Beobachtungen des Cometen 1901 in Astronomische Nachrichten in which he writes:-
In the observation of 6 May, the Comet shone in such a way that the tail was clearly perceived in the field of the telescope of the theodolite strongly illuminated by a reflector. The tail was perceived as a single one of uniform thickness with a dark stripe that extended lengthwise from the middle part to the end. Bad weather prevented seeing it again on some nights. On the nights of the 12th and 16th the brightness had diminished so considerably that the illumination of the field of the telescope had to be made just sufficient to be able to perceive the threads at the same time as the nucleus; but observing with the dark sky two tails that formed an angle of 30 to 40 degrees were clearly visible.
As an Observatory publication, El Cometa de 1901 by Garavito was also published. He wrote:-
The method used in the observations was imposed by the class of instruments that we could take advantage of, given the low height at which the comet was visible.
In 1902, while the civil war was still in progress, the Office of Longitudes was founded with the Observatory as the centre of all its work. Garavito submitted the paper La teoría racional de las curvas planas y de reverso, sus conexiones posibles con la teoría de las covariantes e invariantes to the third Latin American Scientific Congress that met in Rio de Janeiro in 1905. It was published in volume 2 of the Proceedings. The Brazilian mathematician Otto de Alencar e Silva (1874-1912) criticised Garavito's paper in various sessions of the Congress and Garavito answered these criticisms in a paper in the Anales de Ingeniería. Garavito wrotes:-
It is very painful for us to make a critical judgment of the cited memoir, but we are morally obliged to do so having been tacitly challenged by Otto Alencar Silva, as recorded in the minutes of the 5th, 6th, 7th, and 8th sessions of the Congress.
Garavito continued to publish on mathematical and astronomical topics, particularly on mathematical optics, but, from 1906 onwards, he also published essays on political economy and philosophical criticism. His interests in political economy were prompted, no doubt, by the harsh effects of the civil wars on the economy of the country and, as a consequence, on the available funding for science [2]:-
In 1909 Garavito delivered an interesting lecture in Samper Hall in Bogotá, to expose his ideas related to topics of political economy. For a long time, his attention had been fixed on the fluctuations of the exchange rate and on the devaluation of paper money, a devaluation that, due to the frequent and large issues made by the government during the developing situation of the 1899 war, reached limits never seen before. ... Garavito realised, before anyone else in Colombia, that paper money was nothing more than a forced contribution imposed on the country because it was not prepared for a more rational tax regime. He said: "The belief that currency has an effective and unconventional value had become so ingrained in the spirit of our landowners that many came to believe in the total ruin of the country for this reason, and to speak in gloomy terms of the cancer of paper currency."
In May 1910 Halley's comet made a close approach to the Earth, in fact the Earth passed through the tail of the comet. People eagerly anticipated the event while others were frightened and some panicked. Garavito was interviewed by the press, wrote popular and academic articles such as El cometa Halley 1910 and tried to demonstrate the unfoundedness of people's apprehensions.

He continued to write articles on political economy. For example at the Farmers Congress of 1911 he presented a paper on Seguro agrícola in which he also analysed the background of the Colombian civil wars. In 1912 he published a booklet that he called the Evolución de la distribución de la riqueza y fundamento científico del impuesto [2]:-
This pamphlet is a fairly complete exposition of the economic foundations that in future ages will support society by the State and for the State.
In May 1916, in the Revista del Colegio del Rosario, he published an essay entitled Causa principal de la guerra europea . He had predicted World War I since 1909 and in 1914 the truth of his predictions sadly came true. His essay analysed the causes of the war.

He continued his work on light, publishing Teoría de la Aberración de la Luz (1912), Notas Sobre Óptica Matemática (1913) and La Paradoja de la Óptica Matemática (1916).

In 1905 Albert Einstein published what is today called the special theory of relativity and in 1915 he published the definitive version of the general theory of relativity. Garavito, however, was reluctant to view space as non-euclidean, publishing Bancarrota de la ciencia? (1917) and Nota sobre las Geometrías Planas no Euclídeas (1918), and he did not accept the theory of relativity. He was certainly not alone in his opposition at this time and he did not live long enough to see the experimental verifications of the theory.

Due to an illness he had contracted in his youth through spending long hours down a flooded coal mine without proper ventilation, his health began to deteriorate visibly from 1916. In the following year he received a severe blow with the death of his wife on 25 May 1917. For twenty-three years she had supported him through some very difficult times [2]:-
He could not recover from this loss, so the two years that he survived his wife were nothing but slow agony. He no longer attended the Observatory, the centre of his world for so long; it was almost impossible for him to attend his classes at the Faculty of Engineering; he only rarely left his house, spending long hours in front of the notes in his last years. Many friends visited him in such circumstances and all were amazed at the lucidity of that privileged brain, which did not lose its lucidity until the very night of his death. At that time he had the satisfaction that the Colombian Congress had enacted Law 128 of 1919, which ordered the publication of his works and the erection of his bust in the garden of the Observatory. This law, long unfulfilled, was finally carried out in part when his bust was inaugurated on 20 August 1945. In the early hours of 11 March 1920, after many days spent in bed suffering unspeakable torture caused by the disease and suffering pecuniary hardships that made it impossible for him to lessen the pain of which he was a victim, he gave his soul to the Creator. He died in the same poverty in which he lived; he never had anything; what was left over he gave to the poor ...
He was buried in Bogotá's central Cemetery. His tomb [3]:-
... has long been the unlikely destination of the superstitious, who believe that it can bring good luck and even wealth. Although Garavito, a man of science, would undoubtedly have rejected the superstition, the belief does have a connection to reality: Garavito is on the 20,000 peso bill. Visitors often left flowers coloured blue, the same as the 20,000 peso bill, and even painted parts of the tomb blue. Recently, the cemetery administration renovated Garavito's tomb, raising it and erasing the messages believers had written to Garavito, asking him for miracles or thanking him for favours received. The cemetery folks also put signs on neighbouring trees reminding visitors that leaving flowers, writing messages, burning incense and other activities were strictly prohibited in the cemetery. Naturally, and thankfully, believers have ignored the warning and the tomb is decorated once again.
In his lifetime Garavito received many national and international honours, including honorary membership of the Colombian Society of Engineers, of the Geographical Society of Lima, of the Astronomical Society of France and of the Belgian Astronomical Society.

The Julio Garavito Order of Merit in the Degree of Grand Cross, the highest distinction awarded by the national government of Colombia in the field of engineering, was established on 5 January 1965, the centenary of the birth of Julio Garavito. On 27 August 1970 the International Astronomical Union named a crater on the far side of the Moon 'Garavito crater'. It lies to the north-northwest of the huge walled plain named 'Poincaré'. On 24 April 1949 Colombia issued a 4 Colombian centavo commemorative stamp in his honour. In 1996 the Banco de la Republica issued the 20,000 Colombian Pesos banknote with a portrait of Garavito on the front and on the back side of the note is the crater on the Moon's far side named after Garavito. The banknote was withdrawn from circulation in 2012. See THIS LINK.

The Julio Garavito Colombian School of Engineering, founded in 1972, is named in his honour. The National University of Colombia's engineering building was remodelled and given Garavito's name in a ceremony on 21 November 2014. On 13 August 1993, the District Institute of Culture and Tourism awarded their "Honour to cultural merit" Medal to Garavito. The award was received by his great-nephew, Clemente Garavito Baraya, President of the Geographic Society of Colombia, during the closing ceremony of the Conference on Geography and Astronomy.

References (show)

  1. L C Arboleda and M P Anacona, Las geometrías no euclidianas en Colombia. La apuesta euclidiana del profesor Julio Garavito (1865-1920), Quipu 11 (1) (1994), 7-24.
  2. A D Bateman, Julio Garavito Armero, Boletín de la Sociedad Geográfica de Colombia 13 (45-46) (1955), 1-16.
  3. M Ceaser, You Can't Prohibit Faith, Mikes Bogota Blog (20 June 2011).
  4. C J Cuartas Chacón, Julio Garavito A: Guía Biográfica Ilustrada (Asociación Colombiana de Facultades de Ingeniería, 2015).
  5. G Duque-Escobar, Julio Garavito Armero (1865-1920), godues (2 October 2007).
  6. R Gallego, Julio Garavito Armero en el Cementerio Central de Bogotá, Revista de historia y literatura, getas de tinta (1) (February 2010).
  7. J Garavito Armero died, 1920 (b. 1865), Vatican Observatory (11 March 2020).
  8. Julio Garavito Armero, Escuela Colombiana de Ingeniería Julio Garavito (2021)
  9. Julio Garavito Armero, La Enciclopedia Biográfica en Línea (2004)
  10. Julio Garavito Armero, British Museum.
  11. D Obregón Torres, Julio Garavito Armero: a propósito de una biografía, Boletín Cultural y Bibliográfico 38 (58) (2001), 28-36.
  12. D Ortega Ricaurte, Julio Garavito Armero, Universidad del Rosario.
  13. F Ortiz Guzman, Una demostración del teorema fundamental del álgebra por Julio Garavito, Lecturas matemáticas 40 (1) (2019), 73-101.
  14. F Ortiz Guzman, Cáculo de primas y reservas de seguros de vida por Julio Garavito según el texto de E Dormoy, Lecturas matemáticas 35 (1) (2014), 59-85.
  15. F Ortiz Guzman, Cáculo de primas y reservas de seguros de vida por Julio Garavito según el texto de E Dormoy, Lecturas matemáticas 35 (1) (2014), 59-85.
  16. C D Pérez Ruiz, El ingeniero colombiano Julio Garavito ante las geometrías no euclidianas 1890-1920, Master's Thesis (Universidad Nacional de Colombia, 2016).
  17. G Portilla and C H Sánchez, Centenario de la muerte de Julio Garavito Armero, Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 44 (170) (2020), 9-13.
  18. C Quintero, Julio Garavito y la aplicación de la Astronomía a los intereses del país (1892-1919), Recursos de información científica y tecnológica 19 (3) (2001), 15-23.
  19. S Romero Rey, Julio Garavito: de Colombia a la luna, Recursos de información científica y tecnológica (1998).
  20. C H Sánchez, Los cuadernos de Julio Garavito una antologia comentada, Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales 31 (119) (2007), 253-.
  21. C H Sánchez, Julio Garavito Armero y el desarrollo de la ciencia en Colombia, in La hegemonía conservadora (Centro Editorial de la Facultad de Ciencias Humanas de la Universidad Nacional de Colombia, 2014), 291-322.
  22. The First ICRANet Julio Garavito Meeting on Relativistic Astrophysics, International Center for Relativistic Astrophysics Network (November 2015).
  23. J C Zapata Trujillo, Julio Garavito Armero, University of New South Wales.

Additional Resources (show)

Honours (show)

Honours awarded to Julio Garavito

  1. Lunar features Crater Garavito
  2. Google doodle 2022

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update March 2022