TIMELINE: the history of mathematics

Journey Through Millennia: Unveiling the Mathematical Odyssey Across 2000 Years

Timeline of Mathematics

Scipione del Ferro (1465-1526)

Antonio Maria del Fiore(S. XV - S. XVI)

Niccolò Fontana Tartaglia (1499-1557)

Gerolamo Cardano (1501-1576)

Paolo Ruffini (1765-1822)

Andrei Kolmogorov (1903-1987)

René Descartes (1596-1650)

Made by: Nadia Hajji, Luca Viola, Victoria Gomez y Adriana Micu of the group 4ºD

Niccolò Fontana Tartaglia (1500-1557)

Antonio Maria del Fiore (15th century - 16th century), an Italian mathematician from the Bologna school, played a crucial role in disputes surrounding the solution of cubic equations. A student of Scipione Dal Ferro, he learned the formula to solve particular cubic equations. Boasting of being the only one capable of solving them, he challenged Niccolò Tartaglia, who, years later, independently discovered Dal Ferro's method. Tartaglia surpassed Del Fiore in a public mathematical challenge.In an intriguing turn of events, Del Fiore revealed to Gerolamo Cardano that the formula for solving cubic equations was discovered by Dal Ferro, not Tartaglia. This freed Cardano from his promise to keep the formula secret. With the assistance of Del Fiore and Ludovico Ferrari, Cardano expanded and generalized the formula, eliciting Tartaglia's anger.Ferrari challenged Tartaglia in Milan, winning with the help of biased judges and Tartaglia's stuttering. He thus obtained the rights to the formula. Although Tartaglia retired and passed away in 1557, Del Fiore, despite his contribution, was long forgotten in mathematical history.

Antonio Maria del Fiore

Andrei Kolmogorov, a prominent Russian mathematician, made significant contributions to various branches of mathematics during his career. One of his notable achievements was in the field of probability theory, where he introduced the concept of algorithmic randomness and developed the theory of probability in a constructive way.Kolmogorov's most famous discovery is known as Kolmogorov's axioms, which form the foundation of modern probability theory. These axioms provide a rigorous mathematical framework for studying and analyzing random events and their probabilities.

Andrei Kolmogorov

Furthermore, Kolmogorov made important contributions to ergodic theory, which deals with systems that evolve over time. He developed the concept of dynamical systems and studied their behavior through time, including the concept of entropy within these systems.Additionally, Kolmogorov worked on mathematical logic, topology, information theory, and computational complexity. His fundamental research and discoveries have had a profound impact on various branches of mathematics and have provided a solid mathematical basis for probability theory and related fields.

Tragically, Del Ferro passed away in Bologna in 1526 at the age of 61. Although his life was relatively short, his impact endures in the pages of mathematical history. His work was crucial to the development of equation theory and served as a foundation for the subsequent studies of notable mathematicians, including Gerolamo Cardano and Niccolò Fontana Tartaglia. The resolution of cubic equations, a pivotal achievement, set the stage for future advancements in mathematics, demonstrating that an individual's ingenuity and tenacity can illuminate the path to a deeper understanding of mathematical mysteries.

Scipione del Ferro, born in Bologna in 1465, was an Italian mathematician whose contributions marked a milestone in the history of algebra. Although his legacy is not as widely known as that of some of his contemporaries, his work was fundamental to the later development of the discipline.Del Ferro is primarily remembered for his solution to the general cubic equation, a mathematical problem that perplexed many scholars of his time. In 1515, during his tenure at the University of Bologna, he presented his method for solving cubic equations of the form x³ + mx = n. His approach, known as "Del Ferro's solution," paved the way for future advances in the field of algebra.

Scipione del Ferro

Italian mathematician Gerolamo Cardano made several important discoveries throughout his career. One of his most notable achievements was the solution of cubic equations, which he published in his work "Ars Magna" in 1545. In this work, Cardano presented a method for solving equations of the form ax^3 + bx^2 + cx + d = 0.In addition to his contributions to solving equations, Cardano also made advances in probability and statistics. In 1564, he published the book "Liber de Ludo Aleae" (Book on games of chance), where he introduced concepts of probability and presented problems related to games of cards and dice.Another notable discovery by Cardano was the invention of the pop-up business card. In the Renaissance era, calling cards were common, but Cardano added a mechanism so they could be displayed, revealing more information about the bearer.

Gerolamo Cardano

Likewise, Cardano was a pioneer in the application of mathematical methods to the study of human anatomy and medicine. He conducted research on the circulatory system and heart problems, contributing to the advancement of medicine at that time.In summary, Gerolamo Cardano made important discoveries in the field of cubic equations, as well as in probability, statistics and medicine. His legacy endures to this day, and his work continues to be studied and applied in various areas of mathematics and science.

Niccolò Fontana, better known as Tartaglia, was a prominent Italian mathematician of the 16th century who made significant contributions to the development of mathematics. Born in Brescia in 1499, Tartaglia acquired his nickname due to an accident in his youth that left him with a jaw injury, affecting his ability to speak. His most notable contribution was in the field of algebraic equations, where he solved the general problem of angle trisection. In 1535, Tartaglia discovered a formula for solving cubic equations and published his findings in 1545. Subsequently, the renowned Italian mathematician Gerolamo Cardano challenged him to a mathematical duel, during which Tartaglia revealed his method for solving cubic equations, known as the "Tartaglia formula." This method had a significant impact on the development of algebra and the solution of cubic equations. Thanks to his contributions, Tartaglia is considered one of the great mathematicians of the Renaissance, and his legacy endures to this day. Despite personal difficulties, his mathematical genius overcame all adversities, leaving an indelible mark on the history of mathematics. Tartaglia passed away in 1557, but his legacy continues to be studied and admired by mathematicians around the world.

Niccolò Fontana Tartaglia

René Descartes, born in France in 1596 and died in 1650, known today simply as Descartes, is one of the most famous intellectuals in France and Europe. Descartes was a 17th century French philosopher, mathematician and scientist, considered one of the fathers of modern philosophy. He is best known for his famous statement "I think, therefore I am", and for his contributions to analytical geometry and the philosophy of mind. His ideas about the scientific method and the mind have had a great impact on our thought.In 1637, this French philosopher and mathematician published his “Discours de la methodé” in which he explained his rationalist approach to the interpretation of nature. “La methodé” contained three appendices: “La dioptrique”, “Les météories”, and “La géométrie”. The last of these, “The Geometry”, was Descartes’ only published mathematical work.

René Descartes

When Descartes wrote his “Discourse on Method” in the 17th century, the scientist made some decisions that marked the direction of mathematics and, specifically, within the field of algebra. In particular, he expressed unknown values though letters or unknowns, as we would later know them. Although it seems quite normal to us today, at that time, letters were not intended for such use.In the field of mathematics, Descartes was remarkable for establishing a relationship between mathematical calculations and plane geometry, which is what he called analytical geometry. In this way, Descartes was the first to relate the expression of a geometric reality through an equation, the use of coordinates and graphic representation.

Paolo Ruffini, was an italian mathematician born in the XVIII century who contributed to development of algebra and number theory. He is known for his work on algebraic equations and was one of the first to try to solve the general fifth degree equation using radicals. His work in mathematics has left a lasting legacy in the mathematics. Paolo Ruffini is known as the discoverer of the famous Ruffini method, which allows us to find the coefficients of the polynomial that results from the division of any polynomial by the binomial x-a.Ruffini's rule is a method (algorithm) that allows us to obtain the roots of a polynomial. It is very useful since for degrees bigger than 2 we don’t have formulas, at least easy, to be able to obtain them.

PAOLO RUFFINI