History of Mathematics Seminar

The History of Mathematics Seminar aims to provide a forum to discuss investigations into both the mathematics produced by various cultures and eras through history as well as the history of particular mathematical concepts of disciplines.

The seminar meets on Tuesdays during Period 9 (4:05pm – 4:55pm) in LIT368.

Below is  schedule of talks along with the speaker, title, and abstract. If you, or anyone you know, are interested in giving a talk, please feel free to email me: d.pfeffer@ufl.edu.

Date Speaker Title/Abstract Slides
August 27th, 2018 Douglas Pfeffer Title: Origins and Ancient Egypt

Abstract: It is nearly impossible to pinpoint the origin of mathematics. It is generally agreed that the concept of number existed before the development of written languages. In this talk we will begin by taking a look at ancient artifacts circa 30,000 BCE and investigate what conclusions we can draw about the extent these cultures knew of numbers. Turning the clock forward, we will then take a look at Ancient Egypt circa 2000 BCE. Thanks to the Rosetta Stone, our understanding of hieroglyphics grants us a window into Egyptian mathematics. In the second half of this talk, we will take a look at sources that suggest their knowledge of arithmetic, algebra, and geometry.

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September 11th, 2018 Douglas Pfeffer Title: Mesopotamian Mathematics

Abstract: In this talk we will discuss the mathematics conducted by the cultures in the Mesopotamian Valley. Starting with a look at cuneiform writing, we will then investigate their use of the sexagesimal numbering system (Base 60) and their ingenious introduction of a positional notation! We will then take a look at their use of arithmetic, algebra, and geometry — for example, their knowledge of staples like quadratic equations and Pythagorean triples.

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September 18th, 2018 Douglas Pfeffer Title: Greek Mathematics I: Thales and Pythagoras

Abstract: The mathematics of ancient Greece is rich with philosophy and geometry. In this talk we take a look at mathematics conducted in Greece during the the sixth century BCE and discuss the work done by Thales of Miletus and Pythagoras of Samos. In particular we will discuss what little sources we have of their work and investigate what we can infer of their achievements. Of interest are their works in geometry, proportions, and number theory. Finally we will take a look at the various ancient Greek numeration systems that common traders would have used to tabulate goods.

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September 25th, 2018 Douglas Pfeffer Title: Greek Mathematics II: The Heroic Age

Abstract: By the time just after Thales and Pythagoras, Athens had become the intellectual capital of Greece. It attracted scholars from all over and mathematicians were no exception. By 400 BCE, individuals like Anaxagoras, Hippasus, Hippias, Archytas, Hippocrates, and Zeno had made incredible advancements. Tackling mathematical problems like incommensurability and the Greek problems of antiquity, these mathematicians made significant progress while having such little machinery at their disposal. It is for these heroes that the age is named and it is their mathematics that we will take a look at in this talk.

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October 2nd, 2018 Douglas Pfeffer Title: Greek Mathematics III: The Academy

Abstract: Picking up where we left off last time, we will continue our tour of early Greek mathematics by delving into the fourth century BCE. With the death of Socrates in 399 BCE, his student Plato fostered intellectual development in Athens through his Academy. We will discuss some of the work conducted by his students and their impact on proportions, geometry, and the Greek problems of antiquity. This talk will end with the death of Alexander the Great in 323 BCE where the intellectual capital shifted from Athens to the city of Alexandria and the Golden Age of Greek mathematics began.

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October 9th, 2018 Andrew Kriehn Title: Euclid

Abstract: Euclid’s Elements served as the foundation of a mathematical education for more than 2000 years. While we know little about the man himself, we’ll talk about Elements, as well as some of the other books that Euclid wrote, and give some indication of the impact of his work.

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October 16th, 2018 Douglas Pfeffer Title: Archimedes of Syracuse

Abstract: By 264 BCE, the Mediterranean sea was primed for war. Carthage and Rome would spend the next century warring with one another in what we now call the Punic Wars. In 214 BCE, amidst the Second Punic War, Rome laid siege to the Kingdom of Syracuse. Defending his native city, Archimedes invented incredible war machines and other devices to fend off the invaders. Ultimately, Syracuse fell and Archimedes with it, but his work remained. While sometimes hailed as the Father of Mathematical Physics, his contributions to solely mathematics were both broad and deep. Throughout this talk we will investigate some of the work he conducted on levers, numeration, estimates for pi, attempts at trisecting the angle, and the quadrature of conic sections. This talk will, by no means, be an exhaustive one. We will simply attempt to gain a greater appreciation for his work and discuss what we know about him.

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October 23rd, 2018 Andrew Kriehn Title: Apollonius of Perga

Abstract: If Euclid was the last mathematician to develop synthetic geometry until Lobachevsky, then Apollonius was the last to develop analytic geometry until Descartes. Except for the progress made by the 11th century Persian mathematician Omar Khayyám, the state of analytic geometry up until Descartes was almost unchanged since Apollonius’ work. Yet despite being a prolific mathematician, very few of Apollonius’ works survive. Some have been reconstructed and/or translated from Arabic, but most were lost. Only half of one work can claim a direct descent from Apollonius’ original writings: Conics. We will take a look at his life and his works and try as far as we can to give an overview of his work on conic sections. In particular, time permitting, I’d like to explore the three- and four-line locus problems and their central role in the development of analytic geometry.

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October 30th, 2018 Dave Wilson Title: Linear Algebra from Pythagoras to Peano
Abstract: The goal of this talk is to trace the complicated history and development of linear algebra from ancient to modern times. While Pythagoras and Apollonius of Perga knew little algebra, their geometric ideas appear everywhere in the subject. In 1640 Rene Descartes began the modern transition to algebra when he developed the discriminant to distinguish solution sets of the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 as an ellipse, a parabola, or a hyperbola. The ideas of eigenvalues and eigenvectors are embedded in his proofs. While the initial efforts were focused on the particular vector space Rn, in the 19th Century Hermann Grassmann, James Joseph Sylvester, Arthur Cayley, Carl Jacobi, and Giuseppe Peano moved the subject from coordinates in Rn to abstract axioms. The advantage is that Fourier Series, partial differential equations, splines, coding theory, and linear statistics all live under the same umbrella.
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November 6th, 2018 Andrew Kriehn Title: Geometry in the 19th century

Abstract: The 19th century saw an explosive rebirth of pure geometry. The state of modern mathematics and physics is largely a product of this revival. We’ll take a look at what led up to it and try to trace the development of some of the branches, including analytic geometry, differential geometry, projective geometry, and algebraic geometry.

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November 13th, 2018 No Seminar
November 20th, 2018 No Seminar
November 27th, 2018 Douglas Pfeffer Title: The Ancient and Medieval: China and India

Abstract: In this talk we move away from discussing Greek mathematics and consider Chinese and Indian mathematics. With almost no Western influence, much of their mathematical discoveries were both novel and independent. In China, we will take a look at a few classic texts such as The Nine Chapters on the Mathematical Art where we see instances of magic squares and systems of equations. Additionally we will take a look at their numeration systems and various attempts to approximate the value of pi. Culminating in the 13th and 14th century, we will investigate the mathematics of Li Zhi, Yang Hui, and Zhu Shiji and their early work on series and binomial coefficients. In India, we will take a look at the mathematics found in early works like the Sulbasutras as well as the contributions made by individuals like Aryabhata, Brahmagupta, Bhaskara, and Madhava. Their collective work on indeterminate equations represents a strong advancement in mathematics.

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December 4th, 2018 Douglas Pfeffer Title: Arabian Mathematics

Abstract: In this talk we will investigate Arabian mathematics from the 7th to the 14th centuries. By 750 CE, Baghdad had become the new Alexandria and with it came the the creation of the House of Wisdom and the translation of Euclid’s Elements and Ptolemy’s Almagest into Arabic. We will investigate the work done by Al-Khwarizmi (from whom we receive the word `algorithm’), and his text Hisob Al-jabr Wa’l Muquabalah (from which we receive the word `algebra’). From here we will take a look at his contemporaries and the Arabic numeral system (rather, the Hindu-Arabic numeral system). We will continue by investigating the 10th and 11th century mathematicians Abu’l-Wefa and Omar Khayyam, before ending on the 14th century mathematician Jamshid Al-Kashi.

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