Leonardo da Vinci was born in 1452 to a lawyer father and a peasant mother. The world mostly recognizes Leonardo as a painter, scientist, and inventor, yet he also contributed significantly to the development of mathematics during the renaissance period, particularly in the field of Geometry.
Leonardo da Vinci, by the societal dictates of the time, was an illegitimate child. Although his father had a respectable position in society, as a lawyer, the fact that he had not married Leonardo’s mother by the time he got her pregnant rendered Leonardo an illegitimate child. This status shaped his life trajectory, at first in a manner that seemed disadvantageous for the young Leonardo, but his status as an illegitimate child left him with much more relative freedom for exploration (O’Connor 13). As an illegitimate child, he was destined to miss university and any form of formal higher education, and thus his mother sent him to the city of Florence to train as an apprentice painter. This led to Leonardo’s amazing rise to become one of the world’s most talented minds – a veritable genius. Because his parents largely left him to his own devices as he grew up, he developed a keen interest in nature and always attempted to satisfy this interest at any cost. As a child, Leonardo was constantly moving homes; occasionally living with his uncle in his early childhood before proceeding to live with his grandparents. He also lived for a short while with his mother, however when she re-married he went to live briefly with his father, who remarried several times. Some scholars believe that Leonardo’s paintings and other works projected his status as an illegitimate child; for instance, Capps states that he never included Jesus’ father Joseph in any of his paintings as a reflection of his sense of loss at never enjoying his father’s immaterial and material possessions (565). Out of ten sons, he was the only one who did not inherit anything from his father.
Florence was the perfect city to satisfy the young Leonardo’s mind. He went on to establish himself as a master painter, scientist, mathematician, and inventor in this city. Later, historical events also coincided to make Florence one of the most intellectually vibrant cities of the Renaissance period. When the Ottoman Turks attacked and conquered the city of Constantinople in 1453, many of the scholars in the city fled to the cities of Italy for protection and asylum. They also sought to begin a new life away from the constant threats of war wrought by the Ottoman Turks (Romei 40). These scholars brought with them much of the academic material that they could salvage, or the ones, in which they had an interest. This way, Greek manuscripts on Leonardo’s favorite mathematical subject, and the one in which he bequeathed the most ideas to succeeding generations – Geometry – found their way to Florence. In a related historical endeavor, Johannes Guttenberg’s invention of the printing press ensured that academic manuscripts, which only privileged few in society owned, were now easily available for public consumption.
Therefore, as was characteristic of the Renaissance period, scholars actively perused and evaluated many of the Greek texts, principles, and ideas. Much of the geometrical drawings that Leonardo did were in support of his mathematician friend’s principles and ideas; a treatise they published together known as “Divine Proportions”. His friend was a monk and a mathematician known as Luca Pacioli. Although it seems a little odd for the contemporary mind, many of the scientists, mathematicians, and engineers of Leonardo’s time received training that cut across both art/humanities disciplines and science (Petto and Petto 49). According to Moon, many of the mathematicians trained on how to draw and illustrate their work as painters/artists (162). Wilson states that Leonardo encouraged scrutiny of his paintings with a ‘mathematical eye’, and even once when writing in a treatise of his paintings stated that anyone who was not mathematically inclined should avoid looking at his paintings (32). Besides geometry, Leonardo da Vinci made significant contributions in the development of Archimedes’s principles, the Pythagoras theorem, the laws of friction, the center of gravity of objects, and other such mathematical concepts that this paper will discuss later.
In geometry, Leonardo contributed to the understanding of the volume of solids and their projected heights. In “Divine Proportions”, which he co-authored with Luca Pacioli, Leonardo illustrated such shapes as polygons, icosahedrons, and dodecahedrons, contributing to the development of the concept of volume and projections of such shapes (Stakhov and Olsen 172; Frere 110). Although earlier biographers tended to portray Leonardo’s understanding of geometrical forms and figures as relatively limited, Dauben and Scriba believe that the basis of such view was on the limited study of his works, and the latter-day understanding of Leonardo’s works reveal a deeper knowledge of this subject (87). Leonardo’s method of operation in representing these mathematical figures, according to Moon, does not involve equations (162). Instead, Leonardo ‘draws’ his explanations. For instance, Leonardo is credited with having proved Pythagoras’ theory, a proof that he illustrated by adding triangles and squares on an original triangle to provide the proof of the theory. Leonardo was very keen on studying available Greek manuscripts on various mathematical principles, and he proved the Pythagorean Theorem in his unique way, before delving into Archimedes’ principles (Nelsen and Alsina 28). The Renaissance period did not only involve a passive study of the Greek texts, but also active analysis and development of such texts.
Having studied Archimedes’ principles, Leonardo focused on the Greek’s work on the lever and pulley system. He drew shapes and diagrams that illustrated the functioning of the lever and pulley system from a painter’s point of view and contributed significantly to the concept of balance of forces in such a system. His force analysis that contributes to the balance of the system and the accompanying concept behind it led to a better understanding of the lever and pulley system. Additionally, Leonardo had a keen interest in objects and their stability insofar as it concerned the center of gravity. He made a significant contribution to the analysis of an object’s center of gravity. Concerning his pet subject of geometry, Leonardo was able to offer a more dynamic understanding of the relationship between solids and their projected area and heights.
Furthermore, Leonardo developed an interest in various diverse fields of mathematics and mechanics. According to Ball, Leonardo had an interest in the mechanics of hydraulics and optics, and scholars accredit him with offering insights into this field, although the extent of his contribution is subject to debate and controversy (213). A significant contribution by Leonardo was in the development of the concept of the mechanism of friction. Leonardo first worked on the premise that different materials are subject to different levels of friction, and realizing the significance of friction on the functioning of different machine devices, theorized that a smoother material would contribute to less friction. One of his laws on friction states that doubling the load of an object doubles its friction, a law that scientists have proved correct. His second law stated that the surfaces’/material in contact do not affect friction, an idea that was not prevalent then. The modern world accredits him as the first person to have studied friction in a systematic and calculative manner. Significantly, Leonardo did not receive much credit from contemporary mathematicians and engineers for his ideas and contributions. Having not gone to formal schooling like most of the recognized mathematicians and engineers of his time, he was continuously overlooked by his contemporaries (Veltman 383). Therefore, his status as an illegitimate child continued to haunt him even in adulthood, and his ability to outsmart his contemporaries who had received better education is proof of his extraordinary talents.
In conclusion, Leonardo da Vinci as a mathematician made significant contributions to the subject and its early development, especially during the vibrant Renaissance era and beyond. His works on geometry and the projection of heights, his analysis of the balance of forces in the lever and pulley system by Archimedes, his proof of the Pythagorean Theorem, and his works on the mechanics of friction were all a breath of fresh intellectual air in mathematics. Famed primarily as a painter extraordinaire, then secondly as an inventor, his significant interest in mathematics, and his subsequent contribution to its development portray a Leonardo da Vinci worthy of all the admiration and recognition as a genius born well ahead of his time.
Works Cited
Ball, Rouse. A Short Account of the History of Mathematics. New York: Macmillan, 1893. Print.
Capps, Donald. “The Mother Relationship and Artistic Inhibition in the Lives of Leonardo da Vinci and Erik H. Erikson.” Journal of Religion & Health 47.4 (2008): 560-576.
Dauben, Joseph, and Christopher Scriba. Writing the History of Mathematics: It’s Historical Development. Basel, Switzerland: Birkhäuser Verlag, 2002. Print.
Frere, Jean-Claude. Leonardo: Painter, inventor, visionary, mathematician, philosopher, engineer. New York: Konecky & Konecky, 1995. Print.
Moon, Francis. The Machines of Leonardo Da Vinci and Franz Reuleaux: Kinematics of Machines from The Renaissance to the 20th Century. Dordrecht: Springer, 2007.
Nelsen, Roger, and Claudi Alsina. Math Made Visual: Creating Images for Understanding Mathematics. The Mathematical Association of America, 2006.
O’Connor, Barbara. Leonardo Da Vinci: Renaissance Genius. Minneapolis: Lerner publishing group, 2003. Print.
Petto, Sarah, and Andrew Petto. “The Potential Da Vinci in All of Us.” Science Teacher 76.2 (2009): 49-53.
Romei, Francesca. Leonardo Da Vinci. New York: Peter Bedrick Books, 1994. Print.
Stakhov, Alexey, and Scott Olsen. The Mathematics of Harmony: From Euclid To Contemporary Mathematics and Computer Science. World Scientific, 2008. Print.
Veltman, Kim H. “Leonardo Da Vinci: A Review.” Leonardo 41.4 (2008): 381-388. Wilson, Robin J. Stamping Through Mathematics. Dordrecht: Springer, 2001. Print.