Archive for April, 2009

30
Apr
09

Peter Abelard (2 of 4)

There he taught openly but was also given  as a private pupil the young Heloise, niece of one of the clergy of the cathedral of Paris, Canon Fulbert.  Abelard and Heloise fell in love and had a son whom they called Astralabe.  They then married secretly.  To escape her uncle’s wrath Heloise withdrew into the convent of Argenteuil outside Paris.  Abelard suffered castration at Fulbert’s instigation. 

In shame he embraced the monastic life at the royal abbey of Saint-Denis near Paris and made the unwilling Heloise become a nun at Argenteuil. At Saint-Denis Abelard extended his reading in theology and tirelessly criticized the way of life followed by his fellow monks.  His reading of the Bible and of the Fathers of the Church led him to make a collection of quotations that seemed to represent inconsistencies of teaching by the Christian Church. 

He arranged his findings in a compilation entitled Sic et Non (“Yes and No”); and for it be wrote a preface in which, as a logician and as a keen student of language, he formulated basic rules with which students might reconcile apparent contradictions of meaning and distinguish the various senses in which words had been used over the course of many centuries.  He also wrote the first version of his book called Theologia, which was formally condemned as heretical and burned by a council held at Soissons in 1121.

Abelard’s dialectical analysis of the mystery of God and the Trinity was held to be erroneous, and he himself was placed for a while in the abbey of Saint-Medard under house arrest.  When he returned to Saint-Denis he applied his Sic et Non methods to the subject of the abbey’s patron saint; he argued that St. Denis of Paris, the martyred apostle of Gaul, was not identical with Denis of Athens (also known as Dionysius the Areopagile), the convert of St. Paul.  (D.E.L)

29
Apr
09

Peter Abelard (1 of 4)

peter-abelard1

Peter Abelard, the most famous and the most controversial teacher of his age, was a logician, moral philosopher, and theologian.  He was also a gifted and original poet, the founder of a famous convent for women, and the tragic lover of Heloise.  He was twice condemned for heresy by ecclesiastical councils in France.

The outline of Abelard’s career is well-known, largely because he described so much of it in his famous Historia calamitatum (“History of  Troubles”)  he was born the son of a knight in 1079 at Le Pallet in Brittany south of the Loire River.  He sacrificed his rights of inheritance and the prospect of a military career in order to study philosophy, particularly logic, in France.  He provoked bitter quarrels with two of his masters, Roscelin of Compiegne and William of Champeaux. 

The two men represented opposite poles of philosophy.  Roscelin was a Nominalist who asserted that universals are nothing more than mere words;  William in Paris upheld a form of Platonic Realism according to which universals exists.  Abelard in his own logical writings brilliantly elaborated an independent philosophy of language.  While showing how words could be used significantly, he stressed that language itself is not able to demonstrate the truth of things (res) that lie in the domain of physics.

Abelard was a peripatetic both in the manner in which he wandered from school to school at Paris, Lelun, Corbell and elsewhere and as one of the exponents of Aristotelian logic who were called the Peripatetics.  In 1113 or 1114 he went north to Laon to study theology under Anselm of Laon, the leading biblical scholar of the day.  He quickly developed a strong contempt for Anselm’s teaching, which he found vacuous, and returned to Paris.  – (D.E.L)

Photo courtesy:  records.viu

16
Apr
09

Niels Henrik Abel (3 of 3)

This theorem forms the basis for the later theory of Abelian integrals and Abelian functions.  Abel was accepted with restrained civility in Paris, for his work was still unknown.  He submitted his memoir for presentation to the Academy of Sciences, hoping that it would establish his reputation; but he waited in vain.  Before leaving Paris thinking he had a persistent cold, Abel consulted a physician, who informed him he had tuberculosis.

Abel returned to Norway heavily in debt.  He subsisted by tutoring, by receiving a small grant from the university, and in 1828, by accepting a substitute teaching position.  His poverty and ill health did not decrease his production; he wrote a great number of papers, principally on equation theory and elliptic functions.  Among them are the theory of the Abelian equations with Abelian groups.  He rapidly developed the theory of elliptic functions in competition with Karl Gustav Jacobi.

By this time Abel’s fame had spread to all mathematical centers, and strong efforts were made to secure a suitable position for him by a group from the French academy, who addressed Bernadotte, the king of Norway-Sweden; Crelle worked to secure a professorship for him in Berlin.  

In the fall of 1828, Abel became seriously ill, and his condition deteriorated on a sled trip at Christmas time to visit his fiancée at Froland, where he died on April 6, 1829.  The French Academy of Science published this memoirs in 1841.

15
Apr
09

Niels Henrik Abel (2 of 3)

While waiting for the royal decree to be issued, in 1824 the published at his own expense his proof of the impossibility of solving algebraically the general equation of the fifth degree, which he hoped would bring him recognition.  He sent the pamphlet to Gauss, who dismissed it, failing to recognize that the famous problem had indeed been settled.

Abel spent the winter of 1825-26 with Norwegian friends in Berlin, where he met August Leopold Crelle, civil engineer and self-taught enthusiast of mathematics, who became his close friend and mentor.  With Abel’s warm encouragement, Crelle founded the Journal fűr die reine und angewandte Mathematik (“Journal for Pure and Applied Mathematics”), the first volume of which (1826) contains papers by Abel, including a more elaborate version of his work on the quintic equation.  Other papers dealt with equation theory, functional equations, integration in finite forms, and problems from theoretical mechanics.

Abel’s early mathematical training had been in the formal school typified by Euler.  In Berlin new directions in mathematics stimulated him to do further independent work.  Soon distracted socially, however, Abel travelled throughout Europe.

Arriving in Paris in the summer of 1826, he called on the foremost mathematicians and completed a memoir on transcendental functions.  In this major work he presented a theory of integrals of algebraic functions, in particular the result know as Abel’s theorem: there is a finite number, or genus, of independent integrals of this nature. 

14
Apr
09

Niels Henrik Abel ( 1 of 3)

28742-004-eb928cc2

Niels Henrik Abel was a Norwegian mathematician, recognized only after his death as a pioneer in the development of modern mathematics.

Abel was born on August 5, 1802, on the island of Finnǿy, near Stavanger, Norway, where his father was a poor Protestant minister.  The family soon moved to the parish of Gjerstad, near the town of Risǿr (southeast Norway), where the boy grew up.  In 1815, when he entered the cathedral school in Oslo, his mathematical talent was recognized by a teacher who introduced him to the classics in mathematical literature and proposed original problems for solution.  Thoroughly challenged, Abel studied the works of the 17th-century English mathematician and physicist Isaac Newton and the contemporary mathematicians Leonhard Euler (German), Joseph-Louis Lagrange (French), and Carl Friedrich Gauss (German) and learned to detect gaps in their mathematical reasoning.

Although when Abel’s father died in 1820 the family was left in straightened circumstances, the boy was able to enter the University of Christiania (Oslo) in 1821 because his teacher contributed and raised funds.

On graduation from the University in 1822, Abel continued his studies with further subsidies obtained by his teacher.  His first papers, published in 1823 in the new periodical Magazin for Naturvidenskaberne, were on functional equations and integrals, his solution of an integral equation being the first.  Abel’s friends urged the Norwegian government to grant him a fellowship for study in Germany and France. 

 

Photo courtesy:  media-2

 




April 2009
M T W T F S S
« Mar   May »
 12345
6789101112
13141516171819
20212223242526
27282930  

Enter your email address to subscribe to this blog and receive notifications of new posts by email.

Join 5 other followers

Active Researchers Actual Leader Advocate Home Gardening Aggrandize Power Aggressive Research Annual Ritual Remembrance Another Tradition Applications in Plant Breeding Appropriate Knowledge Architect Architecture Artificial Coral Reef Asian Champion Asian Country Background Knowledge Best Faculty Member Better man Better Quality Big Gumamela Flowers Bitter Quarrels Books of Old Testaments Building Groups Buildings Career Careful Thinking Caste Place Central Figure Champins in the Game Chiefly Remembered Cloaked Woman Close Friends Closest Friends Collection of Quotations Companion Volume Comparative Life Computerized Operations Conceptual Design Consent of Human Mind Contemplated Flight Contemporary French Influence Continous Emphasis Contrasting Figures Controlling Plant Shoot Formation Conventional Classic Imagery Conventional Copper Wires Creative Designs Crowd of Pupils Crucial Work Line Cultivation of Personal Friendship Cultured Atmosphere Cultured Elite Current Trend Dedicated Coordinator Deep Concern Deep Drainage Channel Deepest Man Deep Hostility Deep Impression Deep Interest Deep Sense of Morality Delicate Neoclassical Adam Style Designs Destructive Fishing Practices Deteriorated Community Development of Plants Dialectical Analysis Direct Influence Disrupted by War Domed hall Domestic Architecture Drastic Conclusion Early Career Early Mathematical Training Early National Period Efficient Transactions Elderly Beau Eldest Son Elegant Art Eminent Scientist Eventual Annexation Exceptional Ability Exemplary Scientific Innovation Exhibition Work Exploding World of Science and Technology Exterior Expression Famed People Fame Writer Famous Convent for Women Famous Historia calamitatum Faster Data Transmission Faster Transactions Field of Huan Nutrition Final Version of Orechestra Fine City Firm Hand First Community-based Program First Important Work Fluent German Speaker Foremost mathematician Foremost Scottish Architect Forest Setting Former Admirer Formidable Cash Crop Formulated Basic Rules Fuller Understanding Functional Equations and integrals Future Frame Golden Calf Good Acquaintance Good Degree Good Life Good Professor Good Reputation Grand Tour of Europe Great Deal Greater in Umber Greatest British Architect Great Hour of Vicotry Great Ideas Great Liberal Sage Great Monasery Great Occasion Great Tragedies Great Variety of Letters Growing power of Economic Monpolies Hard Corals Hard Work Haunting Fear of Senility Heaviliy Critize Highest Advisory Highest Award Highest Priesthood House Completion House Redecoration Immediate Success Importance of Intellectual Work Important Assignment Important Figures Important Position important Professional Influence Independent Philosophy of Language Indigenous Medicinal Plants Influential Supporter Informal Warmth Inspired Men Inteior Style of Slip-pilasters International Consultations Ironic Literary Style Jewish Community Keen Student Kernel of Truth Kid's favorite game Laminated Wood Large Populations Largest Hospital Latest Fashion Layers of Traditions Leading Biblical Scholar Leading Journals Levi Tribe Library Lifelong Friendship Lifetime Study Literary Activity Literary Figure Living Proof Local Consultations Logical Writing Main Responsibility Main Support Foundation Major Viral Disease Many Countries Many Domestic Commissions Many Fundamental Aspect Marine REserves Significant Role Marital Unhappiness Martyred Apostle Materials Mathematical Reasoning Mathematical Talent Mature Style Merit Attention Meticulous Attention Midieval History Milston Moblized Team Modern Egalitarian Modernize Farming Methods Modern Mathematics Modified Foods Monumental Hall More Dominant Position More Effective Marine Sanctuaries More Powerful Whig Most Distinguised Most Distinguised Autobiographies Most Influenc=tial Figure Most Influential Master Most Sacred Part of Tabernacle Most Universally Admired Multilevel Room Narrative Told National Invitation New Architectural Style New Breed New Community New Foundation New Freedom New Light New Lightness New Lord Lieutenant New Monarch Notable Training Numerous Essays Nutritional Acceptability of Cluny Old-fashioned Country Squire Old Center Court Oldest One Oldest Simplest Greek Style Old Patron Opposing Side Opposite Poles of Philosophy Original Unwillingness Oustanding Biographies Out of Place Outstanding Educator Outstanding Pediatrician Award Outstanding Physician Award Own Love Letters Own Religious Correspondence Partially Paralyzed Partial Success Passionate Cares Peace Loving Perfect Building Perpetual Statue Personal Mission Physical Organic Chemistry Point of Dispute Popular Italia Opera Potential Flash Flood Probing Plants Prominent Whig Leader Proper Utilization of Science Public Buildings Purpose of Christ's Life Quiet Force Raised Funds Real Potential Rectangular Building Rectangular Column Resolute Defender of Liberty Resounding Cndemnation Ribbonlike Forms Rich Souce Romantic Figure Romantic Neo-Gothic Castles Sanatorium Scholarly Work Schools Seasonal Changes Second Highest Position Secretly Married Self Taught Enthusiast Seminar Method Seriously Ill Several International Publications Several Prestigious Awards Several Sources Several Studies Several Terraces of Houses Severity Shor Time Short Life Short Masterpiece Short Story Significant Contribution Significant Neo-classical Interiors Significant Researches Similar Fisheries Development Program Simple Things Six-storey Serpentine Wall Skillful Mediation Sled Trip Some Esegetes Source of Supplementary Vitamins Specific Plant Development Pathways Strong Contempt Strong Effort Strong Priesthood Style Style of Decoration Substantial Tory Victory Successful Exterior Successful Forecasts Suitable Position Superior Data Transmission Sustainale Development Sweeping Victory Swollen Volcanic Lake Sympthetic Commentators Tactful Hand Talented Young French Architect Teaching of Philisophy Timid Natures Tirelessly Criticize Top of Mt. Hor Towering Figure Town Hall Traditional Materials Traditional Reaching Typical Patrician Fashion Unbendable Perseverance Undergraduate Degree Undoubted Success Unfavorable Story Unified Scheme Unique Semiconductor Unique Semiconductor Materials University Small Grant Unmarked Grave Unobtrusive Decoration Unofficial Title Unofficial World Singles Champion Unquestionable Love for Country Unusual Area Upper Section of Wall Useful Art Valuable Contribution to Pediatrics Variety of Rice Various Achievement Various Senses Varius Line of Development Very ASctive Part Very Obscure Field Very Popular Music Virtually Collaborated Warm Encouragement Wealthiest Families Wedge-shaped rooms Widely Known Wiltshire Wolly Blameless Wood Structure Work Focus Worse Man Younger Brother James Young Scientist Young Scientists