DOCSLIB.ORG

MATH 480-01 (43128): Topics in History of Mathematics JB-387, Tuth 6-7:50PM SYLLABUS Spring 2013

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
MATH 480-01 (43128): Topics in History of Mathematics JB-387, Tuth 6-7:50PM SYLLABUS Spring 2013 480a.htm MATH 480-01 (43128): Topics in History of Mathematics JB-387, TuTh 6-7:50PM SYLLABUS Spring 2013 John Sarli JB-326 (909)537-5374 [email protected] TuTh 11AM-1PM, or by appointment Text: V.S. Varadarajan, Algebra in Ancient and Modern Times (AMS Mathematical World Vol. 12, 1998) ISBN 0-8218-0989-X Prerequisites: MATH 252, MATH 329, MATH 345, MATH 355 This is a mathematics course structured around historical developments that produced our current understanding of algebraic equations. Rather than being comprehensive, we will focus on a few ideas dating from antiquity that will help explain the interpretation of solutions to algebraic equations in terms of roots of polynomials. This modern interpretation required the systematic development of numbers from their early representation as geometric quantities to their formalization, more than two thousand years later, as structured algebraic systems. One of our objectives is to come to an understanding of why we teach algebra the way we do. The above text will be used as a guide. We will not cover all of it but you should read as much of it as possible. I will supplement its topics with notes that will appear on my website www.math.csusb.edu/faculty/sarli/ along with this syllabus. In order to maintain a seminar approach to this course (active participation through discussion) the grading will be based on just four components, 25% each: 1) First Written Project; 2) First Exam; 3) Second Written Project; 4) Final exam. As the course progresses I will make suggestions for suitable project topics, some of which will derive from exercises in the text. The exams, for which you may use your notes, will be require you to implement some of the basic mathematical techniques that we will develop in class. The date for the First Exam and the due date of the First Written Project will be announced in class and recorded on the website. Guidelines for project format will also be posted there. After assessing your performance on each of the four components, course grades will be assigned as follows: Some important dates: April 2, University closed April 12, Late add period ends April 19, Last day to drop w/o record 480a.htm[6/10/2013 4:14:11 PM] 480a.htm May 2, First Exam; First Project due May 31, University closed June 6, Last day of class (Second Project Due) Thursday, June 13, Final Exam Constructible Numbers Before the invention of the number line, real quantities were represented by geometric constructions, typically with straightedge and compass. More than an entire book of Euclid's Elements is devoted to geometric arithmetic consistent with his postulates for the development of plane geometry. For example, given a unit length one can construct a square whose side has this length. Then, by the Pythagorean Theorem, a diagonal of this figure has the property that the square of its length is . From our perspective we would say that is a constructible number. It is natural to ask just what numbers are constructible. This is made precise by stating axioms of constructibility consistent with the proof methods of Euclidean geometry. The purpose of these axioms is to determine which points in the plane are considered to be constructible. From these constructible points we can then define constructible numbers. For example, the distance between two constructible points is considered to be a constructible length (which we would associate with a non-negative real number). Any two distinct points may be chosen and designated constructible, and the distance between them taken as the unit length. The intersection of two constructible figures results in constructible points. The line or segment determined by two constructible points is a constructible figure. A circle with a constructible point as center and a constructible length as radius is a constructible figure. The following theorems are easily derived from these four axioms: The line parallel to a given constructible line and passing through a given constructible point not on the given line is a constructible figure. The perpendicular bisector of a constructible line segment is a constructible figure. The circle determined by three constructible points is a constructible figure. (If the three points are collinear then the resulting "circle" is clearly a constructible line.) These three theorems were all Euclid needed to do arithmetic with constructible numbers. By arithmetic we mean the operations of . Though Euclid did not have access to the coordinate plane, we can use that setting to describe the arithmetic of constructible numbers succinctly. In fact, we can take it further by interpreting the ordered pair as the complex number . This formalism was not fully developed before the time of Gauss, but we will see that the arithmetic of constructible complex numbers simplifies many of the historical discoveries we will study. To get started, let us take the points and as the two points in axiom . These correspond to the complex (real) numbers and . By axiom the line we call the real axis is constructible, and by axiom the circle we call the unit circle is also constructible. Then, by axiom the number is constructible (as is any integer), and by T the line we call the imaginary axis is constructible. Now 480a.htm[6/10/2013 4:14:11 PM] 480a.htm suppose that and are constructible real numbers, that is, they have been constructed on the real axis. Exercise. Show that is constructible, as are and . Now suppose and . The numbers and are clearly constructible, by axiom . By T the circle through , , and is constructible. From Euclid (III.35) we have where is the length of the segment from to the other intersection of the circle with the real axis. It follows that the product is a constructible number. Similarly, by constructing the circle through the constructible numbers , , and we see that is also a constructible number. We have shown: The collection of constructible real numbers is closed under the arithmetic operations. In other words, we can perform arithmetic within the set of constructible real numbers. A set of numbers with this property is called a field, to use modern terminology. Note also that the set of rational numbers is a field consisting entirely of constructible numbers. Exercise. Use T to show that the complex number is constructible if and only if the real numbers and are constructible. Deduce that the set of all constructible complex numbers is a field and develop formulas for the sum, difference, product and quotient of two constructible complex numbers. Geometers of Euclid's time did not have the concept of complex numbers but they discovered many constructions that had an impact on modern algebra. Here is one that allows us to find the reciprocal of any complex number although it was originally applied only to constructible points: Consider a constructible circle centered at with radius and let be a constructible point inside the circle, that is, . The line through and is constructible as is the line through perpendicular to line . Since the points and where this perpendicular intersects the circle are constructible, the segment between any two of these four points is constructible. Also, the tangents to the circle at and are constructible (why?), and these two tangents meet on the line , hence at a constructible point . In the early nineteenth century mathematicians began referring to as the inversion of in the given circle and interpreted this construction as the generalization of reflection in a line. Note that the right triangles , , and are similar to one another (and analogously with in place of ). This produces many relations among these constructible lengths, in particular Thus, the product of the distances from the center of the circle to two points related by inversion is the square of the radius of the circle. The symmetrical relationship between and suggests there is an analogous construction if the constructible point is given to be outside the circle, that is, (see suggested project 5, below). Perhaps because they did not have a theory of number systems as we understand it, the ancients were aware of some of the limitations of geometric arithmetic. In particular, they devoted a lot of mathematics to the attempt to resolve the following four questions regarding constructibility using only straightedge and compass: 480a.htm[6/10/2013 4:14:11 PM] 480a.htm Q Is it possible to trisect an arbitrary angle? Q Is it possible to construct any regular polygon? Q Is it possible to construct a square with area equal to that of a given circle? Q Is it possible to construct a cube with volume twice that of a given cube? Eventually it was proved that each of these questions has a negative answer, but the proofs required an understanding of roots of polynomials that was not available to the ancients. Questions of constructibility in general are answered by the following theorem, the result of work by Pierre Wantzel (1814-1848): If a complex number is constructible then it is a root of an irreducible polynomial with integer coefficients whose degree is a power of . So Q has a negative answer because, for example, constructing a cube with volume would require that be constructible. But is a factor of any polynomial that has as a root. For Q , consider the unit circle, whose area is . A square with side is not constructible because is transcendental, that is, not a root of any polynomial with integer coefficients. (This was proved by Ferdinand Lindemann (1852-1939) working from ideas that Charles Hermite (1822-1901) used to prove that the natural log base is transcendental.) As for Q , it can be shown that the above theorem has the following corollary: Let be the number of integers less than or equal to that are relatively prime to .
Load more

Recommended publications
  • EVARISTE GALOIS the Long Road to Galois CHAPTER 1 Babylon
    A radical life EVARISTE GALOIS The long road to Galois CHAPTER 1 Babylon How many miles to Babylon? Three score miles and ten. Can I get there by candle-light? Yes, and back again. If your heels are nimble and light, You may get there by candle-light.[ Babylon was the capital of Babylonia, an ancient kingdom occupying the area of modern Iraq. Babylonian algebra B.M. Tablet 13901-front (From: The Babylonian Quadratic Equation, by A.E. Berryman, Math. Gazette, 40 (1956), 185-192) B.M. Tablet 13901-back Time Passes . Centuries and then millennia pass. In those years empires rose and fell. The Greeks invented mathematics as we know it, and in Alexandria produced the first scientific revolution. The Roman empire forgot almost all that the Greeks had done in math and science. Germanic tribes put an end to the Roman empire, Arabic tribes invaded Europe, and the Ottoman empire began forming in the east. Time passes . Wars, and wars, and wars. Christians against Arabs. Christians against Turks. Christians against Christians. The Roman empire crumbled, the Holy Roman Germanic empire appeared. Nations as we know them today started to form. And we approach the year 1500, and the Renaissance; but I want to mention two events preceding it. Al-Khwarismi (~790-850) Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was born during the reign of the most famous of all Caliphs of the Arabic empire with capital in Baghdad: Harun al Rashid; the one mentioned in the 1001 Nights. He wrote a book that was to become very influential Hisab al-jabr w'al-muqabala in which he studies quadratic (and linear) equations.
    [Show full text]
  • The Assault on the Quintic Niels Henrik Abel
    The Assault on the Quintic Niels Henrik Abel • Niels Henrick Abel was born in 1802 to a Luther Minister and the daughter of a shipping merchant. • He came from a long line of pastors; she was a beautiful woman with a passion for the finer things. Niels Henrick Abel • Poverty and alcoholism haunted the family; at the same time, famine haunted Norway. • Abel attended Cathedral school is Oslo and along with many other students was beaten by the mathematics teacher. Abel • Being with his friends and going to the theater became Abel’s salvation. • Bernt Michael Holmboe replaced the sadistic math teacher and recognized Abel’s talent. They remained friends throughout Abel’s life. Abel • During these high school years he thought he’s solved the general quintic. He submitted the proof and was asked to better explain it. In trying to do so, he found his mistake. Abel • His father died in 1820, making even worse the poverty that was to remain with him all his life. Somehow, in spite of this poverty, he entered the university in 1821. • During this time, two professors supported him, and even helped him obtain funds for travel to Denmark to meet other mathematicians. • During this trip he met his future fiancée Crelly Kemp; they were engaged in 1824. Abel • He wrote a proof that the quintic was not solvable by radicals in 1823. Understanding its importance, he wrote a very brief version of the proof and used it as a sort of “business card” to send to mathematicians. • The one he sent to Gauss was never opened, and was found among Gauss’s papers after his death.
    [Show full text]
  • View This Volume's Front and Back Matter
    i i “IrvingBook” — 2013/5/22 — 15:39 — page i — #1 i i 10.1090/clrm/043 Beyond the Quadratic Formula i i i i i i “IrvingBook” — 2013/5/22 — 15:39 — page ii — #2 i i c 2013 by the Mathematical Association of America, Inc. Library of Congress Catalog Card Number 2013940989 Print edition ISBN 978-0-88385-783-0 Electronic edition ISBN 978-1-61444-112-0 Printed in the United States of America Current Printing (last digit): 10987654321 i i i i i i “IrvingBook” — 2013/5/22 — 15:39 — page iii — #3 i i Beyond the Quadratic Formula Ron Irving University of Washington Published and Distributed by The Mathematical Association of America i i i i i i “IrvingBook” — 2013/5/22 — 15:39 — page iv — #4 i i Council on Publications and Communications Frank Farris, Chair Committee on Books Gerald M. Bryce, Chair Classroom Resource Materials Editorial Board Gerald M. Bryce, Editor Michael Bardzell Jennifer Bergner Diane L. Herrmann Paul R. Klingsberg Mary Morley Philip P. Mummert Mark Parker Barbara E. Reynolds Susan G. Staples Philip D. Straffin Cynthia J Woodburn i i i i i i “IrvingBook” — 2013/5/22 — 15:39 — page v — #5 i i CLASSROOM RESOURCE MATERIALS Classroom Resource Materials is intended to provide supplementary class- room material for students—laboratory exercises, projects, historical in- formation, textbooks with unusual approaches for presenting mathematical ideas, career information, etc. 101 Careers in Mathematics, 2nd edition edited by Andrew Sterrett Archimedes: What Did He Do Besides Cry Eureka?, Sherman Stein Beyond the Quadratic Formula, Ronald S.
    [Show full text]
  • History of Algebra
    History of Algebra The term algebra usually denotes various kinds of mathematical ideas and techniques, more or less directly associated with formal manipulation of abstract symbols and/or with finding the solutions of an equation. The notion that in mathematics there is such a sepa- rate sub-discipline, as well as the very use of the term “algebra” to denote it, are them- selves the outcome of historical evolution of ideas. The ideas to be discussed in this article are sometimes put under the same heading due to historical circumstances no less than to any “essential” mathematical reason. Part I. The long way towards the idea of “equation” Simple and natural as the notion of “equation” may appear now, it involves a great amount of mutually interacting, individual mathematical notions, each of which was the outcome of a long and intricate historical process. Not before the work of Viète, in the late sixteenth century, do we actually find a fully consolidated idea of an equation in the sense of a sin- gle mathematical entity comprising two sides on which operations can be simultaneously performed. By performing such operations the equation itself remains unchanged, but we are led to discovering the value of the unknown quantities appearing in it. Three main threads in the process leading to this consolidation deserve special attention here: (1) attempts to deal with problems devoted to finding the values of one or more unknown quantities. In Part I, the word “equation” is used in this context as a short-hand to denote all such problems,
    [Show full text]
  • PAOLO RUFFINI (September 22, 1765 – May 10, 1822) by HEINZ KLAUS
    PAOLO RUFFINI (September 22, 1765 – May 10, 1822) by HEINZ KLAUS STRICK, Germany Born in the small town of Valentano, halfway between Rome and Siena, PAOLO RUFFINI grew up as the son of a doctor. Later the family moved to Modena (Emilia-Romagna), where PAOLO began studying mathematics, medicine, philosophy and literature at the university at the age of 18. When his calculus professor was appointed administrator of the princely estates by the Duke of Modena and Reggio, the student RUFFINI was assigned to give the calculus lectures. In the following year (1788), he finished his studies with degrees in philosophy, medicine and mathematics and was appointed Professor of the Fundamentals of Calculus. (drawings © Andreas Strick) And when three years later his former geometry professor had to give up teaching for health reasons, RUFFINI's appointment as Professor of the Foundations of Mathematics followed. In the same year he was also licensed to practise medicine. In 1795, the French revolutionary troops began the conquest of northern Italy, and finally, in June 1797, NAPOLEON proclaimed the Cisalpine Republic as a French "daughter republic" with Milan as its capital. Against his will, RUFFINI was appointed as a delegate to one of the chambers of the newly founded state. He soon succeeded in relinquishing this unloved office and resumed his university activities. This was short-lived, however, as he was obliged to take an oath to the constitution of the republic, which he refused to do for religious reasons. RUFFINI bore his dismissal from the university service with great equanimity, because it gave him more time to treat his patients, to whom he devoted himself with great dedication.
    [Show full text]
  • Mathematics in Ancient China
    Mathematics in Ancient China Chapter 7 Timeline Archaic Old Kingdom Int Middle Kingdom Int New Kingdom EGYPT 3000 BCE 2500 BCE 2000 BCE 1500 BCE 1000 BCE Sumaria Akkadia Int Old Babylon Assyria MESOPOTAM IA 3000 BCE 2500 BCE 2000 BCE 1500 BCE 1000 BCE 500 BCE 0 CE 500 CE Classical Minoan Mycenaean Dark Archaic Christian Hellenistic Roman GREECE 3000 BCE 2500 BCE 2000 BCE 1500 BCE 1000 BCE 500 BCE 0 CE 500 CE 1000 CE 1500 CE Warring CHINA Shang Zhou Han Warring States Tang Yuan / Ming States Song Gnomon, Liu Hui Nine Chapters Zu Chongzhi Li Zhi Qin Jiushao Yang Hui Zhu Shijie Early Timeline • Shang Dynasty: Excavations near Huang River, dating to 1600 BC, showed “oracle bones” –tortoise shells with inscriptions used for divination. This is the source of what we know about early Chinese number systems. Early Timeline Han Dynasty ( 206 BC –220 AD) • System of Education especially for civil servants, i.e. scribes. • Two important books*: • Zhou Bi Suan Jing (Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) • Jiu Zhang Suan Shu (Nine Chapters on the Mathematical Art) *unless of course we’re off by a millennium or so. Nine Chapters • This second book, Nine Chapters, became central to mathematical work in China for centuries. It is by far the most important mathematical work of ancient China. Later scholars wrote commentaries on it in the same way that commentaries were written on The Elements. Chapters in … uh, the Nine Chapters 1. Field measurements, areas, fractions 2. Percentages and proportions 3.
    [Show full text]
  • An Historical
    International Letters of Social and Humanistic Sciences Submitted: 2016-01-21 ISSN: 2300-2697, Vol. 66, pp 154-161 Accepted: 2016-02-03 doi:10.18052/www.scipress.com/ILSHS.66.154 Online: 2016-02-03 CC BY 4.0. Published by SciPress Ltd, Switzerland, 2016 An historical - didactic introduction to algebra Paolo Di Sia1,2,3 1University of Verona, Lungadige Porta Vittoria 17, I-37129 Verona (Italy) 2Higher Institute of Religious Science, Via Alto Adige 28, I-39100 Bolzano (Italy) 3ISEM, Institute for Scientific Methodology, I-90146 Palermo (Italy) E-mail address: [email protected] Web-page: www.paolodisia.com Keywords: Mathematics; Algebra; Didactics; Pedagogy; History of Science; Philosophy of Science. ABSTRACT. In this paper we consider a teaching educational introduction to ideas and concepts of algebra. We follow a historical path, starting by the Egyptians and the Babylonians, passing through the Greeks, the Arabs, and the figure of Omar Khayyām, for coming to the Middle Age, the Renaissance, and the nineteenth century. Interesting and peculiar characteristics related to the different geographical areas in which algebra has developed are taken into account. The scientific rigorous followed treatment allows the use of the paper also as a pedagogical introduction to this fundamental branch of current mathematics. 1. INTRODUCTION It can be said that algebra is the use of analytical methods applied to arithmetics. In this context, the adjective “analytic” has a different connotation from that which is normally understood in mathematics; it refers rather to the philosophical positions of Descartes, who as first explicitly introduced the dichotomy “analysis - synthesis”.
    [Show full text]
  • Mathematics, Faith and Politics During the Italian Risorgimento Snapshot Two – Mutual Goals and Collaboration
    Mathematics, Faith and Politics during the Italian Risorgimento Snapshot Two – Mutual Goals and Collaboration Introduction In the previous snapshot from early nineteenth century Naples we examined controversies between the Fergola’s synthetic school of the geometry and that of analytics who focused on the mathematization of science. While the debate was framed in terms of the right way to do geometry, in actuality these disagreements were a direct result of changes occurring in Neapolitan society during the French occupation and subsequent Restoration period, in which the Bourbon monarchy was returned to power. Our second snapshot looks at mid-nineteenth century Italy and the collaborative efforts of Italian mathematicians from different religious and political persuasions to establish an Italian school of mathematics, which would rival those of France, Germany and England. Snapshot Two: Mutual Goals and Collaboration The early to mid-nineteenth century in Italy is often referred to as the Risorgimento, a national rebirth of Italy with broad cultural, social, and economic revival. Politically its themes were independence from foreign rulers, unification of the Italian peninsula and liberty for its citizens. It was also a time of a rebirth of Italian mathematics. While many reforms enacted by the French were put on hold with the Congress of Vienna’s establishment of Restoration governments, movements within the scientific community, including annual scientific congresses, a proliferation of general disciplinary journals and a gathering of statistical information, all helped develop a sense of an Italian scientific community. The scientific congresses were especially significant as they provided one of the first opportunities for scientists from across the different Italian regions to meet each other, to exchange ideas, and to debate both scientific and political ideas.
    [Show full text]
  • Abel–Ruffini Theorem - Wikipedia, the Free Encyclopedia
    Abel–Ruffini theorem - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Abel–Ruffini_theorem Abel–Ruffini theorem From Wikipedia, the free encyclopedia In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no general algebraic solution—that is, solution in radicals— to polynomial equations of degree five or higher.[1] The theorem is named after Paolo Ruffini, who made an incomplete proof in 1799, and Niels Henrik Abel, who provided a proof in 1823. Évariste Galois independently proved the theorem in a work that was posthumously published in 1846.[2] Contents 1 Interpretation 2 Lower-degree polynomials 3 Quintics and higher 4 Proof 5 History 6 See also 7 Notes 8 References 9 External links Interpretation The content of this theorem is frequently misunderstood. It does not assert that higher-degree polynomial equations are unsolvable. In fact, the opposite is true: every non-constant polynomial equation in one unknown, with real or complex coefficients, has at least one complex number as solution; this is the fundamental theorem of algebra. Although the solutions cannot always be expressed exactly with radicals, they can be computed to any desired degree of accuracy using numerical methods such as the Newton–Raphson method or Laguerre method, and in this way they are no different from solutions to polynomial equations of the second, third, or fourth degrees. The theorem only concerns the form that such a solution must take. The theorem says that not all solutions of higher-degree equations can be obtained by starting with the equation's coefficients and rational constants, and repeatedly forming sums, differences, products, quotients, and radicals (n-th roots, for some integer n) of previously obtained numbers.
    [Show full text]
  • Paolo Ruffini
    PAOLO RUFFINI (September 22, 1765 – May 10, 1822) by HEINZ KLAUS STRICK, Germany Born in the small town of Valentano, halfway between Rome and Siena, PAOLO RUFFINI grew up as the son of a doctor. Later the family moved to Modena (Emilia-Romagna), where PAOLO began studying mathematics, medicine, philosophy and literature at the university at the age of 18. When his calculus professor was appointed administrator of the princely estates by the Duke of Modena and Reggio, the student RUFFINI was assigned to give the calculus lectures. In the following year (1788), he finished his studies with degrees in philosophy, medicine and mathematics and was appointed Professor of the Fundamentals of Calculus. (drawings © Andreas Strick) And when three years later his former geometry professor had to give up teaching for health reasons, RUFFINI's appointment as Professor of the Foundations of Mathematics followed. In the same year he was also licensed to practise medicine. In 1795, the French revolutionary troops began the conquest of northern Italy, and finally, in June 1797, NAPOLEON proclaimed the Cisalpine Republic as a French "daughter republic" with Milan as its capital. Against his will, RUFFINI was appointed as a delegate to one of the chambers of the newly founded state. He soon succeeded in relinquishing this unloved office and resumed his university activities. This was short-lived, however, as he was obliged to take an oath to the constitution of the republic, which he refused to do for religious reasons. RUFFINI bore his dismissal from the university service with great equanimity, because it gave him more time to treat his patients, to whom he devoted himself with great dedication.
    [Show full text]
  • Arnold's Proof of Abel-Ruffini
    ARNOLD’S ELEMENTARY PROOF OF THE INSOLVABILITY OF THE QUINTIC LEO GOLDMAKHER ABSTRACT. We give a proof (due to Arnold) that there is no quintic formula. Somewhat more precisely, we show that any finite combination of the four field operations (+; −; ×; ÷), radicals, the trigonometric functions, and the exponential function will never produce a formula for producing a root of a general quintic polynomial. The proof is elementary, requiring no knowledge of abstract group theory or Galois theory. 1. PREREQUISITE IDEAS AND NOTATIONS To understand the arguments in this essay you don’t need to know Galois theory. You also don’t need to know abstract algebra or group theory. However, you do need to know about complex numbers and the complex plane C. Let’s begin with a basic Question. What is the definition of the imaginary number i? We all know the answer: it’s the square-root of −1. There’s only one problem. There are two square roots of −1! Thus, our definition defines two numbers ±i but doesn’t give a way to distinguish between them. So how can we define i without simultaneously defining −i? It turns out that this is impossible to do.1 Of course, we can arbitrarily label one of the two square-roots as i, and then this forces the other to be −i. But this choice is arbitrary, and demonstrates that there’s a fundamental symmetry between the two numbers ±i; the two are yoked together and are algebraically indistinguishable. This observation lies at the heart of Galois theory, which studies other symmetries between numbers (not just pairs of numbers, but also triples and quadruples etc.) and, using group theory to extract properties of the symmetries, deduces properties that such numbers must have.2 These types of ideas will play a major role in our discussion below, as well.
    [Show full text]
  • Witold Więsław (Wrocław)
    Witold Więsław (Wrocław) Matematyka Hoene-Wrońskiego i za jego czasów 0. Wstęp. Na wstępie należy zadać pytanie: czy Hoene-Wroński był polskim matematykiem? Odpowiedź jest raczej jednoznaczna: nie był. Ale uważał się za Polaka. Jego ojciec, Antoni Hoene, przybył z Czech. Podobnie, jak Mikołaj Łobaczewski, choć syn Polaka, nie był polskim matematykiem1. Łatwość, z jaką Hoene-Wroński przeszedł na służbę rosyjską pozwala domniemywać, że bardziej kierowały nim pobudki osobiste, aniżeli patriotyczne. Nie studiował w Polsce, tylko za granicą. Niektórzy biografowie podejrzewają2, że uczył się w Korpusie Kadetów w Warszawie. Jednak przypuszczenie to nie znajduje potwierdzenia w faktach3. Nie miał więc Wroński żadnych związków z nauką w Polsce. A nauczanie na uniwersytetach w Krakowie i w Wilnie nie odbiegało od ówczesnych standardów europejskich4. Zostanie to przedstawione w ustępie 3. Po studiach Wroński przebywał we Francji, tam publikował i to wyłącznie w języku francuskim. W opracowaniach poświęconych polskim uczonym wymieniany jest zapewne tylko z powodu polskiego pochodzenia. Swoje dzieło Wstęp do filozofii matematyki dedykował cesarzowi Rosji, Aleksandrowi I.5 Ale już rok później pracę o rozwiązywaniu równań algebraicznych dedykował Polsce6. Nie on jedyny wykazywał serwilizm w stosunku do cara Aleksandra I. Podobną dedykację znajdujemy w tłumaczeniu Józefa Czecha Elementów Euklidesa (Wilno, 1807). Jan Śniadecki, niewątpliwie polski patriota, w wielu swoich drukowanych wystąpieniach pisał peany na cześć tego cara. Wynikało to nie tylko z istniejącej sytuacji politycznej, lecz także z niewątpliwych zasług cara dla rozwoju Uniwersytetu Wileńskiego i Wileńskiego Okręgu Szkolnego. Zarówno na Uniwersytecie, jak i w szkołach, językiem wykładowym pozostawał, jak w czasach Komisji Edukacji Narodowej nadal język polski. Hoene-Wroński nie był znany ówczesnym uczonym polskim.
    [Show full text]