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The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers not because it is abstract, but because it is a representation of actual things.
In N. Rose, Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Francois-Joseph Servois: Priest, Artillery Officer, and Professor of Mathematics
The Mathematics of Servois: Other Works
During the years 1811 to 1817, Servois had the majority of his work published in Gergonne's Annales des mathématiques pures et appliquées. Some of his works were either solutions to problems posed by other mathematicians, or his remarks on other articles in the journal. In 1813, Servois published his “Calendrier perpétuel” [Servois 1813] (Perpetual Calendar). This work was not mathematically significant; however, Jacques Frédéric Français (1775-1833, brother of François Joseph Français) called it an “ingenious table” [Français 1813].
Figure 6. The Mathematical Philosophy section of the Table of Contents of volume 5 of Annales des mathématiques pures et appliquées (public domain). Note Servois' article [Servois 1814b], Argand's response to Servois' letter [Servois 1814c], and two pieces by the editor.
The majority of Servois' contributions to the field of mathematics can be described by the term “algebraic formalism.” This idea was very important to Servois, and he severely criticized individuals who followed paths he considered to be non-rigorous. One such incident occurred within the pages of the Annales, in which a heated debate took place among Servois, Jean Robert Argand (1768-1822), and Jacques Français. Français published a paper in 1813, based on the work of Argand, in which he viewed complex numbers geometrically. This view of the complex plane is now commonly known as the Argand Diagram or the Argand Plane. Servois criticized the work of these two mathematicians, saying: “I had long thought of calling the ideas of Messrs. Argand and Français on complex numbers by the odious qualifications of useless and erroneous …” [Servois 1814c, p. 228].
Servois published two more articles in the Annales before his retirement in 1827. In 1817 he published his “Mémoire sur les quadratures” [Servois 1817] (Memoir on quadratures). Then he published his final work in 1826, called “Sur la théorie des paralleles” [Servois 1826] (On the theory of parallels). These last two papers were not very influential. Bradley  states that at the “courtesy” of an old friend, Gergonne placed this final paper as the first article in volume 16, number 7.
Petrilli, Jr., Salvatore J., "Francois-Joseph Servois: Priest, Artillery Officer, and Professor of Mathematics," Loci (June 2010), DOI: 10.4169/loci003498