Introduction
Nowadays, Math is comparatively accessible discipline to everyone, who is eager to master it, and has some basic logical skills. It is because of the wide range of contemporary textbooks, hundreds of helpful websites and numerous highly-qualified teachers and professors, who are not only acquainted with the discipline itself, but are also talented in the art of teaching.
However, the situation was not so bright in the old times, when the books on Math could not have been comprehended by a common person. Moreover, many theoretical and practical issues still had not been resolved, which complicated the teaching process even more. Fortunately, thankfully to Raphael Bombelli, whose biographical pages and great contribution to the science of math are considered in this paper, the development of math obtained new tempo.
Biography in Brief
As Katz has pointed out, “Bombelli was educated as an engineer and spent much of his adult life working on engineering projects in the service of his patron, a Roman nobleman who was a favorite of Pope Paul III” (375). Indeed, Bombelli did not receive any higher education in its classical meaning. Instead, he mastered himself in engineering skills both under the supervision of the patrons and also during the independent self-teaching.
As O'Connor and Robertson (n. p.) have maintained, Bombelli participated in the reclaiming of marshes on the Topino River in central Italy, and further, was interested in several another reclamation project, important for neighboring regions. The same authors also provide the readers with the information that Bombelli’s project at the Val di Chiana marshes was a great success, which gained for him a high reputation as an hydraulic engineer.
No doubt, not all the time of Bombelli was dedicated to the engineering projects. In fact, his intellectual work and gradual self-mastering of engineering skills led him to the idea of improving the current algebra books.
Although it is almost impossible to clearly answer what was the main motive of Bombelli, which make him begin the own book, some ideas as regards this issue still do exist. For instance, one of the most popular version concerns Bombelli’s simultaneous fascination by particular math books (namely, Cardan’s one, as is stated by O'Connor and Robertson) and his total discontentment by many other books, written in this field, because of either their too vague and general character, or too high level of sophistication, impossible to be understood by the laypeople.
Such state of affairs was rather unacceptable for Bombelli, and he merely decided to improve the existed knowledge, presenting it in a clearer manner. His aim was to write an informative and profound book, which still could be understood and comprehended by a person, far from special scientific math preparation.
This fact is rather interesting to know about, since the last version of Bombelli’s “Algebra” was far more important than a mere compilation of existing knowledge, instead, he enriched the history of math with new author discoveries, about which it is explained in more details further. In other words, Bombelli’s “Algebra”, designed to put together difficult for comprehension works of other mathematicians, became the new page in the history of math, from which even Newton and Leibniz drew their inspiration (Curtin 41).
Frankly speaking, the fate has presented for Raphael Bombelli rather precious present. In particular, his colleague, Antonio Maria Pazzi, who taught mathematics at the University of Rome, showed Bombelli a manuscript of Greek author Diophantus's “Arithmetica”, which made the great impact on Bombelli’s own work (O'Connor and Robertson n. p.). Having acquainted with the manuscript of Diophantus, whose works were not commonly known, Bombelli was so fascinated that he decided to translate the manuscript for enriching the world with it, and then, he reworked his own book under the influence of Diophantus’ ideas, developing them significantly (Bashmakova, Smirnova 71).
No doubt, even the Raphael Bombelli himself did not in any way deny the inheriting and reworking of Diophantus' ideas. Still, he cannot be blamed for the lack of own contribution of author’s creativity, since firstly, he improved and developed Greek author’s consideration, and secondly, he rescued them from the death in silence and neglect, to which they were doomed. Furthermore, it cannot be excluded that any other mind, apart from Bombelli’s one could have been able to understand the meaning of Diophantus’ work and to develop it with the utility to the humanity.
Contribution to Math
As Bashmakova and Smirnova have mentioned, first three parts of Bombelli’s “Algebra” were published in 1572, whereas the remaining two, which contained methods, even superior to Descartes’ ones, were published after the significant period of time – only in 1929 (71).
The three published books included the mastered comprehension of the known algebraic solution of the XVI century as well as author’s own considerations. What is of utmost importance, the specific style of writing, comparatively easier accessible to the reader of that time, was the distinguishing feature of the “Algebra” by Raphael Bombelli.
As regards Bombelli’s innovations in the math itself, they are numerous and of significant meaning for the development of this science. Namely, rules of computations with negative numbers were not familiar for the common people of that time, whereas Bombelli managed to preserve them in a written form, in a manner, which is possible to be comprehended.
What is more, the issue of imaginary numbers was comprehended in “Algebra” in a great form. Also, the contemporary science has been enriched by Bombelli’s written rules for addition, subtraction and multiplication of complex numbers (O'Connor and Robertson n. p.). In fact, the complex number theory has received the necessary impetus by the efforts of Bombelli, therefore, his contribution to it is estimated as the tremendous one.
In addition, having revised his algebra text in the light of what the discovered Diophantus’ ideas, Bombelli gives in Book III 272 math problems, among which, as O'Connor and Robertson have pointed out, 143 were taken from Diophantus, the fact which he acknowledged.
His further books concerned the ideas in the field of geometry, which were discovered in manuscripts in Bologna, and were published in the XX century, revealing to the world the broad character of Bombelli’s mind.
Conclusion
Under the Bagni’s conclusion, history allows us to see how, bit by bit, complex numbers came into life, revealing the cultural context that made imaginary numbers possible, namely - such a shift in the new algebra of Cardan, Bombelli and other Renaissance mathematicians should inevitably be linked to the rise and spreading of manufacture and a new systematic dimension in human actions (31).
Similarly, this research has come to the similar conclusion. Namely, Bombelli’s professional skills as an engineer made him look into the depth of the math in a more detailed way than any of his contemporaries managed to. Therefore, the first rules of dealing with imaginary and complex numbers emerged in this epoch, when a man, working with engineering communications, become able to think in a different way.
Last but not least, lack of classical higher education turned out to be Bombelli’s advantage rather than the disadvantage, since his self-education made him intolerant to the excessive complexity of math books of that time, granting the world with the best possible in the XVI century version of “Algebra”.
Works Cited
Bagni, Giorgio T. “Bombelli's Algebra (1572) and a New Mathematical Object”. For the Learning of Mathematics, vol. 29, no. 2, 2009, pp. 29-31.
Bashmakova Isabella, Smirnova, Galina. The Beginnings and Evolution of Algebra. The Mathematical Association of America, 2000.
Curtin, Daniel J. "Complex Numbers, Cubic Equations, and Sixteenth-Century Italy." Mathematical Time Capsules: Historical Modules for the Mathematics Classroom, edited by Dick Jardine, Amy Shell-Gellasch, The Mathematical Association of America, 2010, pp. 39-43.
Katz, Victor J. A History of Mathematics: An Introduction. Addison-Wesley, 1998.
O'Connor J J., Robertson E F. Rafael Bombelli. MacTutor History of Mathematics, 2000.
