Ricalde's mathematical talent was noticed very early, and one of the anecdotes tells us that at the end of the last century the authorities and the population of the city of Mérida were concerned about the unsafe situation of one of the towers of the Cathedral. An attempt was made to weigh the great bell that was in the upper part of that tower without lowering it, since being cracked it constituted a great danger for the public, and it was necessary to know if it was possible to make repairs without changing the location of said bell. The teacher Manuel Sales Cepeda, then director of the Literary Institute, was entrusted with this challenge, and he chose Graciano to carry out the calculations and deduce the exact weight of the bell, which he did with complete accuracy.

I would be interested in knowing if the number 189 431 482 030 921 is prime or composite. Could a correspondent provide me with this information?

Since it has not been possible to recover Graciano's writing, we will copy and put together what was explained in the review by Mattínez Becerril: "Ricalde, independently of the works of others, arrives at the elliptical resolution of the quintic equation by first reducing the equation to a trinomial form by suitable artifices, having noticed that in a third degree equation without the quadratic term it was sufficient to substitute one of the coefficients by the sine of an auxiliary angle so that the roots split into three functions. By analogy, he found that to reduce a quintic equation to the aforementioned form requires other transcendental functions, the elliptic ones, to make this separation, a very simple idea but brilliant at the same time. By means of these functions he derived the roots of quintic equations in an explicit form which in turn provides a very practical means of solving quintic equations numerically. This Ricalde method requires the invariant and covariant algebraic elements of the fifth degree forms.

This procedure, inspired by that of Hermite, surpasses it for its simplicity and ease of application ... and so there appears in the 'Annales de l'Académie des Sciences', volume 11 of 1901, an application of this procedure to the calculation of the approximate value of a root of the equation:

$x^{5} - x - 0.53499 = 0$

in which the author shows the goodness and advantages of his method."

This work, written in simple and easy-to-understand language, shows that Graciano Ricalde was aware of the scientific ideas that were held in his time about comets, which is why he was able to explain them very clearly to his fellow citizens. In that booklet he also spoke about the necessary elements to establish the type of orbit that a comet can follow; elliptic, parabolic and hyperbolic and explained each of them. In the next section he dealt with the elements of Halley's orbit, as calculated in 1907 and 1908 by the English astronomers of the Greenwich Observatory, Philip H Cowell (1870-1949) and Andrew C D Crommelin (1865-1939). Based on this data, he described in detail the ephemeris of this comet, mentioning the dates of its closest approach to Earth, both on its journey towards the Sun, and when it began to move away from it. He also explained why and when it was seen as a morning or evening star and stated that on 18 May 1910, the nucleus of this comet was 25 million kilometres from Earth and it was traveling at a speed of 46 km/s.

Graciano Ricalde was born to be a mathematician with a vocation for abstract mental activity. His ethical lineage is of the most aristocratic; his father was a model of honesty, rectitude and a hard-working man. He studied as a young man and reached the pinnacle of arithmetic calculation ... But he did not stop there, he continued to devoted himself to the cultivation of his mind and reached the teaching profession with the titles of professor to transmit mathematical and astronomical knowledge. ... Between demanding daily tasks and duties of a mentor which he fulfilled scrupulously, without wandering, he steals time from deserved rest in order to be able to study, and dominates Mathematics and Astronomy in a vast extension of each one; he understands them, applies them, calculates and supports himself reading advanced books that he acquires and possesses as their spiritual and civil owner. Laplace, Serret, Cauchy, Hermite, Poincaré, Appell, Delambre, ... and others are familiar to him. He collaborates in French in 'L'Intermédiaire des Matémathiciens' and maintains correspondence with Henri Poincaré and Sotero Prieto (a brilliant mathematician and his ill-fated compatriot) and writes gracefully on Halley's comet on the occasion of its presence in the sky in 1910, and calculated in 1923 the elements of the total solar eclipse of September of that year: for Mérida, Campeche and Champotón; and he goes to Champotón harbour in order to accompany the envoy from the Geographical Studies Directorate, contemplates the marvellous phenomenon and returns to his daily work satisfied with his knowledge and crowned with the laurels of the purest modesty.