HOëNé-WROńSKI (OR HOEHNE), JóZEF MARIA

(b. Wolsztyn, Poland, 23 August 1776;d. Neuilly, near Paris, France, 8 August 1853)

philosophy, mathematics.

Hoehne was the son of Antoni Hoehne, the municipal architect of Poznan, and Elzbieta Per-nicka. Educated in Poznan and Warsaw, he took part as a young artillery officer in the national uprising of 1794, commanding a battery during the siege of Warsaw by the Prussian army. In the same year he was taken prisoner by the Russian army, which he joined for a short period. He was released about 1797 and, living on money left to him by his father, spent the next few years studying philosophy at several German universities. In 1800 Hoehne settled in Marseilles, where he became a French citizen and addressed himself to scientific research. At first he took occasional jobs in scientific institutions, working at the Marseilles astronomical observatory and as secretary of the local medical association. In later years he earned his living by giving private lessons in science and philosophy. At various periods he was supported by patrons who had been converted to his philosophical doctrine and thus obtained the funds for his prolific publishing activity.

About 1810 Hoehne married Victoire Henriette Sarrazin de Montferrier, sister of the mathematician Alexandre Montferrier. At approximately the same time he adopted the surname Wroński, which he used alternatively with Hoehne; but most of his writings are signed Hoëné-Wroński, without a first name.

In 1810 Hoëné-Wroński moved to Paris and submitted to the Institut his first memoir on the foundations of mathematics, “Premier principe des méthodes analytiques.” The paper received a rather sketchy review by Lacroix and Lagrange, and the ensuing polemic initiated by Hoëné-Wroński quickly led to a break in relations with the Institut. During his first years in Paris, he conducted intensive research in mathematical analysis, subsidized by the financier Pierre Arson, who was at first a devoted disciple. Their relations dissolved in a violent quarrel over financial arrangements that resulted in a trial, famous at the time, in 1819.

From 1820 to 1823 Hoëné-Wroński tried unsuccessfully to obtain the award of the British Board of Longitude for research on the determination of longitude at sea. He also failed in attempts to interest the Royal Society in his writings on hydrodynamics. In both cases Hoëné-Wroński became embroiled in polemics that quickly extended to ex-trascientific matters. He continued his mathematical research after returning to Paris, although his main interest had turned to the explication of his Messianic philosophy. In the 1830’s Hoëné-Wroński investigated locomotion and sought to build vehicles that could compete both technically and economically with the newly developing railways, but the caterpillar vehicles that he designed did not progress beyond the model stage. His last years were spent in poverty.

Hoëné-Wroński’s extant manuscripts and published writings cover a wide range of knowledge. His philosophy, which is central, forms the basis for reforming various branches of the exact and social sciences. Hoëné-Wroński’s philosophical notions were formed under Kant’s influence; and his first published work. Philosophie critique decouverte par Kant (Marseilles, 1803), was the first exhaustive presentation of Kant’s teachings in French. Hoëné-Wroński’s philosophical system was based on the sudden revelation of the “Absolute,” a concept never made precise, from which all aspects of existence evolve. This universal and rationalistic “absolute philosophy” could, according to its author, solve all theoretical and practical problems. Three main concepts constitute its framework: the “highest law,” the foundation of reality independent of human influence; the “universal problem,” man’s supplementing of the Creation by introducing new realities; and the “final concordance,” that harmony among various aspects of reality which is humanity’s ultimate aim.

Hoëné-Wroński applied his philosophy to mathematics in a series of works that began with Introduction a la philosophie des mathematiques. In these writings rigorous mathematical proof retreated before arguments of the absolute philosophy—which, with the specific nomenclature introduced, made the reception and evaluation of his works difficult. Hoëné-Wroński criticized the standpoint taken by Lagrange in his Théorie des fonctions analytiques, disagreeing with both Lagrange’s insufficient grounds for the use of the series development and his opposition to the introduction of infinite quantities in analysis. According to Hoëné-Wroński, the “highest law” in mathematics consisted in the development of any function in the series

F(x) = A₀Ω₀(x) + A₁Ω₁(x) + A₂Ω₂(x) +…,

where Ω_i denotes any function of the variable x The “highest law” was to constitute the basis of the entire theory of differential equations. The lack of proof and imprecise range of applicability rendered its evaluation difficult; it is functional analysis that can determine the scope of Hoëné-Wroński theorem. The determinants used to compute the coefficients A[_i] are known as Wronskians, a term introduced by Thomas Muir in 1882.

In 1812 Hoëné-Wroński published his universal solution of algebraic equations, Resolution generate des equations de tons les degres. Al-through Ruffini’s research had already demonstrated that this solution cannot be correct, it is applicable in particular cases. Several errors were found in Hoëné-Wronski’s papers in other branches of sciences, for instance, in his treatment of the laws of hydrodynamics. His celestial mechanics—although based on a law allegedly more general than Newton’s —was in fact equivalent to it. On the other hand, his method of resolving perturbative functions contained new ideas and was later found to be feasible.

A recurrent pattern in Hoëné-Wronski’s relations with various institutions, both academic and social, indicates a marked psychopathic tendency: grandiose exaggeration of the importance of his own research, violent reaction to the slightest criticism, and repeated recourse to nonscientific media as allies against a supposed conspiracy. His aberrant personality, as well as the thesis of his esoteric philosophy (based on a revelation received on 15 August 1803 or, according to his other writings, 1804), tempt one to dismiss his work as the product of a gigantic fallacy engendered by a troubled and deceived mind. Later investigation of his writings, however, leads to a different conclusion. Hidden among the multitude of irrelevancies are important concepts that show him to have been a highly gifted mathematician whose contribution, unfortunately, was overshadowed by the imperative of his all-embracing absolute philosophy.

BIBLIOGRAPHY

I. Original Works. A bibliography of Hoëné-Wroriski’s writings and a catalog of MSS preserved at the library of the Polish Academy of Sciences at Kórnik is in S. Dickttein. Hoene Wroński. Jego lytic i prace (“… His and Works”;Cracow. 1896). Subsequent literature is in B. J. Gawecki, Wmriski i o Wron-skint. Katalog prat filozofieznvch fitene Wrońskio oraz literatury dotyczqeej jego osohy i zycia (“Wroński and About Wronski Catalog of Philosophical Works by Hoëné-Wroński and of Works on the Man and His Philosophy’’; Warsaw, 1958). An incomplete ed. of Hoëné-Wroński’S philosophical works is F. Warrain. ed., L’oeuvre phiiosophique tie Hoene Wroński, 2 vols. (Paris, 1933–1936). A selection of philosophical works published in Italian is Collezione italan degli scritti filosofici di Hoene Wroński 4 pts. (Vicenza. 1870–1878). The mathematical works appeared as J. M Wroński, Oeuvres mathématiques, 4 vols, (Paris, 1925).

II. Secondary Literature. An introduction to Hoëné-Wronskfs philosophy is P. d’Arcy, Hoëné-Wroński, une philosophie de la création (Paris, 1970). On the mathematical “supreme law” see S. Banach.“Über das Moi supreme’ von J, Hoëné Wroński’’: in Bulletin international de ’#x2019;Academic polonaise des sciences et des lettrcs, ser. A (1939). 1-10: and C Lagrange. “Démonstration élémcnlaire de la loi suprême de Wroński, in Mémoires couronnés… publiés per I’Académic royale des sciences . . . de Befcique.47 , no. 2 (1886). His astronomy is discussed in F. Koebcke, “Über Hoëné-Wroriski’s Überiegungen zur Himmeismechanik.” in Ada astwnomiau sen C, 3 (Feb. 1938), 73-81.

Jerzy Dobrzycki

Hoene-Wronski, Jozef Maria (1776-1853)

Polish mathematician and inventor who developed a philosophy of messianism, derived from the Kabala and Gnosticism. He claimed to have discovered "the secret of the Absolute," which he revealed for 150,000 francs to Pierre Arson, a businessman who agreed to publish Hoene-Wronski's messianic works. When Arson backed out of the deal, Hoene-Wronski declared him to be the beast of the Apocalypse and published a pamphlet with the immortal title Yes or No—that is to say, have you or have you not, yes or no, purchased from me for 150,000 francs my discovery of the Absolute? Not surprisingly, Hoene-Wronski lost his court battle to obtain the remainder of the money, but the unfortunate Arson had already expended some 40,000 francs on the works of Hoene-Wronski.

About 1850 Hoene-Wronski became the occult teacher of Alphonse Louis Constant, who later wrote many books on the occult under the pseudonym Éliphas Lévi.

Sources:

Hoene-Wronski, Jozef Maria. Hoene-Wronski: Une philosopie de la creation. Paris: Seghers, 1970.