Nour Chalhoub Shanyu Ji MATH 4388 October 14, 2017

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1 Nour Chalhoub Shanyu Ji MATH 4388 October 14, 2017 Rebirth Claimed to be the bridge between the middle ages and modern history, the Renaissance produced many masters, whether it be in the visual arts, in science, or in mathematics. Stretching from the 14th to the 17th century, this period s most famous accomplishments included the Copernican Revolution, inventions of discovery such as the mariner s compass, and most importantly, a reintroduction to classical learning. Simply put, it was a cultural and intellectual movement. A certain mode of thinking was more prevalent back then in comparison to today - the idea that science and the arts were related - and some of the greatest minds were epitomes of this connection, not the least of which are Leonardo da Vinci and Isaac Newton. Many mathematicians lived through this time, and to cram them and all of their respective accomplishments into a three-page paper would do them a great dishonor. Arguing in defense of this mode of thought, in hopes of its revival, a chronological approach is more appropriate, with emphasis on the 16th and 17th centuries. The Renaissance would not have become what it was if not for a few geniuses who were born before their time. By the end of the 13th century, after the famous medieval mathematician Fibonacci made the Hindu-Arabic system more commonplace, the Roman numeral system became irrelevant and inefficient. In combination with the rise of humanism and the increasing failure of the Roman Catholic Church, the Age of Reason was born. Humanism, the belief system prioritizing human matters over the supernatural and emphasizing the potential value and goodness of humanity, prided itself in its most important axiom - to seek purely rational solutions to human problems. One could argue that without Dante and other prominent figures as its predecessor, the Renaissance would not have yielded the fruits we enjoy today. Without humanists easing the path into the Renaissance, the mathematical, astronomical, physical, and artistic works of pure genius would have been more prone to rejection; this could have ultimately

2 resulted in a stagnation of intellect and authenticity. The slow move away from basing every academic result in religion was crucial to the mathematicians, scientists, and artists that were to come. Beginning with the French, Nicole Oresme was born in 1320 and attended the University of Paris; Oresme became known for...using a system of rectangular coordinates centuries before his countryman René Descartes popularized the idea, as well as...the first time-speed-distance graph. Also, leading from his research into musicology, he was the first to use fractional exponents, and also worked on infinite series, being the first to prove that the harmonic series is a divergent infinite series ( The Story of Mathematics ). His mathematical discoveries speak to the historical and structural co-dependence that exists between math and art. Luca Pacioli, born about a century later, introduced the present day, universally understood mathematical symbols for addition (+) and subtraction (-) in one of his books, Summa de Arithmetica, Geometria, Proportioni et proportionalita. This compilation summarized the arithmetic, geometric, and algebraic knowledge of the time. Summa contained multiple ways to perform multiplication, quadratic equations, and a section on bookkeeping. Pacioli was also known to be a pioneer in accounting and is remembered for his sprawling interests; De viribus quantitatis, written around the start of the 16th century, connects two unlikely subjects - mathematics and magic. Described as the foundation of modern magic and numerical puzzles, it contains mathematical games, as well as steps on how to eat fire and juggle. Another one of Pacioli s books, De divina proportione,... discusses mathematical and artistic proportion, referencing the calculations behind the golden ratio, its relation to architecture, and its recurrence in nature. Leonardo da Vinci drew the illustrations of the regular solids in De divina proportione while he lived with and took mathematics lessons from Pacioli...The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano (Royster ). There is no need to defend the idea that Leonardo da Vinci was a genius - both as an artist and an engineer. The connection between mathematics and art is strong in the work of Leonardo da Vinci...and Albrecht Durer, one of da Vinci s contemporaries (Boyer). At the peak of the Renaissance,... Art came to be seen as a branch of knowledge, valuable in its

3 own right and capable of providing man with images of God and his creations as well as..insights into man s position in the universe. [To] Leonardo da Vinci it was even a science, a means for exploring nature...art was based on the observation of the visible world and practiced according to mathematical principles of balance, harmony, and perspective ( Encyclopædia Britannica ). In Leonardo s Mona Lisa, Luca Pacioli s studies of the golden ratio are expressed in multiple yet subtle ways. The Vitruvian Man, another one of da Vinci s timeless pieces, exudes mathematics more obviously. All of his works exhibit mathematical concepts, such as linear perspective and geometry. Albrecht Durer, another prominent figure of the High Renaissance, was a painter more than anything else, but also wrote multiple books, including Four Books on Measurement and Four Books on Human Proportion, which discuss, respectively, geometry and the fractional properties that human figures exhibit. Four Books on Measurement discusses mastering the technique of perspective for painting; this book turned out to be a significant contribution to mathematics (Durer: The Mathematical Artist ). Nicolaus Copernicus, the father of modern astronomy, had a well-rounded early education, focusing on painting and math. Later on, he proved the entire world wrong about the Earth being the center of the universe using mathematics. Around the same time, Rene Descartes, a French philosopher and mathematician, studied analytical geometry and its link to algebra. This specific focus, along with giving us the Cartesian plane, is why we refer to him as The Father of Analytic Geometry. He is also known as the only philosopher to use mathematical methods to fulfill the philosophical goal of finding the true meaning of knowledge. Descartes was a firm believer in providing visuals or geometric representations that accompany numerical algebraic proofs. Born in 1642, Isaac Newton brings the era of Renaissance mathematics to an elegant close. Newton and his colleague (and occassionally rival), Gottfried Leibniz, worked on problems involving derivatives, integrals, infinite sums, and limits for years. The discovery of

4 calculus gave us more questions than answers. It revolutionized the way we view the universe, and its relevance with biology, chemistry, physics, meteorology, economics, and engineering pushes humanity to the cutting edge in almost every field. Newton s accomplishments with gravity and his three laws of motion govern the physical universe up until today, and his discovery of the color spectrum resulting from his experiments with natural light give him recognition in the field of optics. Newton s brilliance was so distinct that he was the first scientist to be knighted. The relationship that has existed between the arts and the sciences is best represented in some of the most incredible minds that have lived in human history, and the Renaissance provided the most tolerant environment for intellectual correspondence. The one thing all the aforementioned mathematicians have in common is their interest in the arts. One could argue that to truly thrive in the field of mathematics, a creative mind is crucial. Exercising both halves of the human brain, rather than just one, can yield only positive results. Mathematics and the arts never lost their connection; however, it is doubtful that we will ever see a revival of such all-inclusive intellectual indulgence. While conversing, bringing up the link between these two subjects has unfailingly caused people to look at me with either confusion or irritation; only when this once-popular school of thought becomes prevalent in today s mathematical and artistics realms will this reaction become non-existent. Until then, dwell on this: Albert Einstein once said, After a certain high level of technical skill is achieved, science and art tend to coalesce in esthetics, plasticity, and form. The greatest scientists are artists as well.

5 Works Cited Medieval Mathematics. The Story of Mathematics, 10 Oct. 2017, Royster, D. The Divine Proportion. 2011, Lecture 20: Topics in Geometry, Slide 62 The Editors of Encyclopædia Britannica. Renaissance. Encyclopædia Britannica, Encyclopædia Britannica, Inc., 19 July 2017, Boyer, Carl Benjamin, and Uta C. Merzbach. A History of Mathematics. 2nd ed., Wiley, International, Parkstone. Dürer: the Mathematical Artist. Parkstone International, 9 Sept parkstone.international/2012/05/17/durer-the-mathematical-artist