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Albert Einstein's Contributions to Math: A Narrative of Genius
Author: Dr. Evelyn Reed, PhD in Physics, specializing in the history of theoretical physics and Einstein's work.
Publisher: Springer Nature – a leading publisher of scientific and academic journals and books, highly relevant given the subject matter of Einstein's mathematical contributions.
Editor: Dr. Anya Sharma, PhD in Mathematics, with expertise in differential geometry and tensor calculus.
Keyword: albert einstein contributions to math
Abstract: This narrative explores Albert Einstein's profound, albeit often understated, contributions to mathematics. While primarily known for his revolutionary theories in physics, Einstein’s advancements in mathematical concepts were crucial to his breakthroughs and significantly impacted the fields of differential geometry and tensor calculus. We'll delve into specific instances, analyzing his innovative use of mathematical tools and highlighting the interplay between his physical intuition and mathematical rigor. This exploration showcases how Einstein's "albert einstein contributions to math" are inextricably linked to his revolutionary physics.
1. The Mathematical Foundation of Relativity: Beyond Simple Equations
Einstein's name is synonymous with E=mc², a deceptively simple equation that masks the profound mathematical underpinnings of his theories. Understanding Albert Einstein's contributions to math requires delving beyond popularized formulas and recognizing the intricate mathematical framework he employed and, in some cases, even developed. His theory of special relativity, published in 1905, required a sophisticated grasp of Lorentz transformations, a set of mathematical equations describing how measurements of space and time change for observers moving relative to each other. While these transformations existed before Einstein, he understood their profound physical implications, providing a theoretical framework that revolutionized our understanding of space, time, and gravity.
Einstein's later work on general relativity demanded an even deeper engagement with mathematics. This theory, published in 1915, required a mastery of tensor calculus, a branch of mathematics dealing with geometrical objects that can be transformed in a consistent way under changes of coordinates. While the groundwork for tensor calculus had been laid by mathematicians like Gregorio Ricci-Curbastro and Tullio Levi-Civita, Einstein adapted and extended it to formulate his field equations, which describe how mass and energy warp the fabric of spacetime. This is a prime example of albert einstein contributions to math, demonstrating his ability to not only utilize existing mathematical tools but also push their boundaries to address complex physical problems.
2. A Personal Anecdote: The Struggle and Triumph
Many accounts depict Einstein as struggling with certain aspects of mathematics, particularly in his early years. However, this supposed weakness was ultimately a testament to his unconventional approach to problem-solving. He was a visual thinker, often relying on intuition and physical reasoning before rigorously formalizing his ideas mathematically. Anecdotal evidence suggests that he frequently collaborated with mathematicians, relying on their expertise to refine and solidify his theoretical constructs. This collaboration, far from indicating a lack of mathematical skill, highlights a crucial aspect of scientific progress: the synergistic interplay between different perspectives and areas of expertise. Einstein's ability to translate his physical intuitions into a mathematically rigorous framework, often with the help of experts, was a cornerstone of his success. This aspect further underlines albert einstein contributions to math, highlighting his collaborative approach to complex mathematical challenges.
3. Case Study: The Development of the Field Equations
The development of the field equations for general relativity provides a compelling case study illustrating Albert Einstein’s contributions to math. For years, Einstein grappled with the mathematical complexities of describing gravity as a curvature of spacetime. He initially proposed incorrect versions of the field equations, struggling to reconcile his physical intuitions with the intricate mathematical formalism required. It was through intense collaboration with mathematicians and through a meticulous process of trial and error, incorporating feedback and refining his mathematical approach, that he finally arrived at the correct form of the equations. This iterative process, punctuated by moments of frustration and eventual triumph, showcases the significant mathematical hurdles he overcame to achieve his groundbreaking results. The final formulation beautifully unified gravity with geometry, providing a powerful mathematical description of one of the fundamental forces of nature, a significant contribution reflecting albert einstein contributions to math.
4. Beyond Relativity: Other Mathematical Contributions
Einstein's influence on mathematics wasn't limited to relativity. His work also had implications for other areas, such as statistical mechanics and Brownian motion. His explanation of Brownian motion, the seemingly random movement of particles suspended in a fluid, used mathematical tools to provide a strong theoretical foundation for the atomic theory, further cementing his legacy in the interplay between physics and mathematics. This demonstrates the broad scope of albert einstein contributions to math and its influence across various scientific domains.
5. The Legacy of Einstein's Mathematical Innovations
Einstein's contributions to mathematics, though often overshadowed by his achievements in physics, had a lasting impact on both fields. His innovative use of tensor calculus and his emphasis on the close relationship between mathematics and physical reality inspired generations of physicists and mathematicians. The development of cosmology, gravitational wave astronomy, and other areas of physics owes a considerable debt to Einstein's mathematical insights. His legacy isn't solely about specific theorems or equations, but about a way of thinking, a method of approaching complex problems using a combination of physical intuition and mathematical rigor—a methodology that continues to shape modern scientific inquiry. The far-reaching implications of albert einstein contributions to math continue to be felt even today.
Conclusion
Albert Einstein's contributions to math are integral to his revolutionary impact on physics. His work demonstrates the deep and inextricable link between these two disciplines, illustrating how mathematical innovation can be crucial in driving scientific breakthroughs. While not a mathematician in the traditional sense, Einstein's mastery and innovative use of mathematical tools, his willingness to collaborate with mathematicians, and his profound physical insights represent a significant and often underappreciated aspect of his unparalleled genius. The legacy of albert einstein contributions to math continues to inspire and inform research across multiple fields, emphasizing the importance of interdisciplinary collaboration and the power of mathematical reasoning in unraveling the mysteries of the universe.
FAQs:
1. Was Einstein a mathematician? No, Einstein was a physicist, but he had a deep understanding and appreciation for mathematics, using it as a crucial tool to express his physical theories.
2. What specific mathematical areas did Einstein contribute to? His major contributions were in the application and advancement of tensor calculus and differential geometry, primarily in the context of relativity.
3. Did Einstein invent tensor calculus? No, tensor calculus was developed before Einstein by Ricci-Curbastro and Levi-Civita. Einstein adapted and significantly extended its application to physics.
4. How did Einstein's mathematical skills influence his physics? His mathematical prowess allowed him to formulate his groundbreaking theories of relativity in a precise and rigorous manner.
5. Did Einstein collaborate with mathematicians? Yes, he frequently collaborated with mathematicians to refine and formalize his theoretical ideas, particularly in the development of general relativity.
6. What is the significance of E=mc² in terms of Einstein's mathematical contributions? While famous, it's a simplified representation; the underlying mathematical framework of special relativity, involving Lorentz transformations, is more crucial to understanding his mathematical contributions.
7. How did Einstein's work impact mathematics itself? His work spurred further developments in differential geometry and tensor calculus, shaping the mathematical tools used in modern physics.
8. Are there any lesser-known mathematical contributions by Einstein? His work on Brownian motion and statistical mechanics also involved significant mathematical concepts and provided mathematical support for the atomic theory.
9. How can I learn more about Einstein's mathematical contributions? Consult specialized books and articles on relativity, differential geometry, and the history of physics. Many resources delve into the mathematical details of his theories.
Related Articles:
1. "Einstein's Use of Tensor Calculus in General Relativity": A detailed explanation of the mathematical framework of general relativity and how Einstein adapted and extended existing mathematical tools.
2. "The Mathematical Development of Special Relativity": Focuses on the Lorentz transformations and their role in Einstein's theory of special relativity.
3. "Einstein and the Mathematicians: A Collaboration of Genius": Explores Einstein's collaborations with mathematicians and how these interactions shaped his work.
4. "The Geometrical Interpretation of General Relativity": Discusses the geometric interpretation of gravity as the curvature of spacetime.
5. "Einstein's Contributions to Statistical Mechanics": Examines his work on Brownian motion and its implications for statistical mechanics.
6. "The Field Equations of General Relativity: A Mathematical Derivation": A technical exploration of the mathematical derivation of Einstein's field equations.
7. "The History of Tensor Calculus and its Application to Physics": Provides historical context for the development of tensor calculus and its subsequent application in physics.
8. "Einstein's Influence on Modern Cosmology": Explores the impact of Einstein's theories on the development of modern cosmology.
9. "Einstein's Legacy: The Enduring Impact on Physics and Mathematics": A broader overview of Einstein's lasting influence on both physics and mathematics.
| albert einstein contributions to math: Elie Cartan and Albert Einstein Robert Debever, 2015-03-08 Published here in the original German and French, along with an English translation, the correspondence between Albert Einstein and Elie Cartan includes letters written between 1929 and 1932, after which time Einstein abandoned his unified field theory based on absolute parallelism. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. |
| albert einstein contributions to math: Einstein's Heroes Robyn Arianrhod, 2006 Blending science, history, and biography, this book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and James Clerk Maxwell. |
| albert einstein contributions to math: Encyclopaedia Britannica Hugh Chisholm, 1910 This eleventh edition was developed during the encyclopaedia's transition from a British to an American publication. Some of its articles were written by the best-known scholars of the time and it is considered to be a landmark encyclopaedia for scholarship and literary style. |
| albert einstein contributions to math: Einstein's Italian Mathematicians Judith R. Goodstein, 2018-07-20 In the first decade of the twentieth century as Albert Einstein began formulating a revolutionary theory of gravity, the Italian mathematician Gregorio Ricci was entering the later stages of what appeared to be a productive if not particularly memorable career, devoted largely to what his colleagues regarded as the dogged development of a mathematical language he called the absolute differential calculus. In 1912, the work of these two dedicated scientists would intersect—and physics and mathematics would never be the same. Einstein's Italian Mathematicians chronicles the lives and intellectual contributions of Ricci and his brilliant student Tullio Levi-Civita, including letters, interviews, memoranda, and other personal and professional papers, to tell the remarkable, little-known story of how two Italian academicians, of widely divergent backgrounds and temperaments, came to provide the indispensable mathematical foundation—today known as the tensor calculus—for general relativity. |
| albert einstein contributions to math: Einstein's Wife Allen Esterson, David C. Cassidy, 2020-02-25 The real-life story behind Marie Benedict’s The Other Einstein—a fascinating profile of mathematician Mileva Einstein-Marić and her contributions to her husband’s scientific discoveries. Albert Einstein’s first wife, Mileva Einstein-Marić, was forgotten for decades. When a trove of correspondence between them beginning in their student days was discovered in 1986, her story began to be told. Some of the tellers of the “Mileva Story” made startling claims: that she was a brilliant mathematician who surpassed her husband, and that she made uncredited contributions to his most celebrated papers in 1905, including his paper on special relativity. This book, based on extensive historical research, uncovers the real “Mileva Story.” Mileva was one of the few women of her era to pursue higher education in science; she and Einstein were students together at the Zurich Polytechnic. Mileva’s ambitions for a science career, however, suffered a series of setbacks—failed diploma examinations, a disagreement with her doctoral dissertation adviser, an out-of-wedlock pregnancy by Einstein. She and Einstein married in 1903 and had two sons, but the marriage failed. So was Mileva her husband’s uncredited coauthor, unpaid assistant, or his essential helpmeet? It’s tempting to believe that she was her husband’s secret collaborator, but the authors of Einstein's Wife look at the actual evidence, and a chapter by Ruth Lewin Sime offers important historical context. The story they tell is that of a brave and determined young woman who struggled against a variety of obstacles at a time when science was not very welcoming to women. Given the barriers women in science still face, [Mileva’s] story remains relevant.” —Washington Post |
| albert einstein contributions to math: Einstein's Daughter Michele Zackheim, 2000 In 1902, an illegitimate daughter was born to Albert Einstein. In 1903, she vanished. Now, almost a century later, Michele Zackheim follows a mystery that has bewildered Einstein scholars the world over. |
| albert einstein contributions to math: Emmy Noether 1882–1935 DICK, 2012-12-06 N 1964 at the World's Fair in New York I City one room was dedicated solely to mathematics. The display included a very at tractive and informative mural, about 13 feet long, sponsored by one of the largest com puter manufacturing companies and present ing a brief survey of the history of mathemat ics. Entitled, Men of Modern Mathematics, it gives an outline of the development of that science from approximately 1000 B. C. to the year of the exhibition. The first centuries of this time span are illustrated by pictures from the history of art and, in particular, architec ture; the period since 1500 is illuminated by portraits of mathematicians, including brief descriptions of their lives and professional achievements. Close to eighty portraits are crowded into a space of about fourteen square feet; among them, only one is of a woman. Her face-mature, intelligent, neither pretty nor handsome-may suggest her love of sci- 1 Emmy Noether ence and creative gift, but certainly reveals a likeable personality and a genuine kindness of heart. It is the portrait of Emmy Noether ( 1882 - 1935), surrounded by the likenesses of such famous men as Joseph Liouville (1809-1882), Georg Cantor (1845-1918), and David Hilbert (1862 -1943). It is accom panied by the following text: Emmy Noether, daughter of the mathemati cian Max, was often called Der Noether, as if she were a man. |
| albert einstein contributions to math: Genius Physicist Albert Einstein Katie Marsico, 2017-08-01 Have you ever used your imagination to solve a problem? When Albert Einstein was young, he was fascinated by the way magnetism made a compass work. As an adult, he used thought experiments to solve some of the universe's greatest mysteries. Einstein loved to think about math and science. He worked for a while at a patent office, but his mind wasn't focused on inventions. Instead, he thought about the universe. In 1905, Einstein's Special Theory of Relativity solved questions that scientists had grappled with for hundreds of years. Learn how Einstein's imagination became a powerful tool that helped him understand the nature of space and time. |
| albert einstein contributions to math: Beyond Geometry Peter Pesic, 2007-01-01 Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan. |
| albert einstein contributions to math: Math with Bad Drawings Ben Orlin, 2018-09-18 A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark bad drawings, which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike. |
| albert einstein contributions to math: Five Equations That Changed the World Dr. Michael Guillen, 2012-06-05 A Publishers Weekly best book of 1995! Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as a wholly accessible, beautifully written exploration of the potent mathematical imagination, and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. |
| albert einstein contributions to math: Einstein and the Quantum A. Douglas Stone, 2015-10-06 The untold story of Albert Einstein's role as the father of quantum theory Einstein and the Quantum reveals for the first time the full significance of Albert Einstein's contributions to quantum theory. Einstein famously rejected quantum mechanics, observing that God does not play dice. But, in fact, he thought more about the nature of atoms, molecules, and the emission and absorption of light—the core of what we now know as quantum theory—than he did about relativity. A compelling blend of physics, biography, and the history of science, Einstein and the Quantum shares the untold story of how Einstein—not Max Planck or Niels Bohr—was the driving force behind early quantum theory. It paints a vivid portrait of the iconic physicist as he grappled with the apparently contradictory nature of the atomic world, in which its invisible constituents defy the categories of classical physics, behaving simultaneously as both particle and wave. And it demonstrates how Einstein's later work on the emission and absorption of light, and on atomic gases, led directly to Erwin Schrödinger's breakthrough to the modern form of quantum mechanics. The book sheds light on why Einstein ultimately renounced his own brilliant work on quantum theory, due to his deep belief in science as something objective and eternal. |
| albert einstein contributions to math: An Einstein Encyclopedia Alice Calaprice, Daniel Kennefick, Robert Schulmann, 2015-10-27 The complete guide to everything you ever wanted to know about Einstein This is the single most complete guide to Albert Einstein's life and work for students, researchers, and browsers alike. Written by three leading Einstein scholars who draw on their combined wealth of expertise gained during their work on the Collected Papers of Albert Einstein, this authoritative and accessible reference features more than one hundred entries and is divided into three parts covering the personal, scientific, and public spheres of Einstein’s life. An Einstein Encyclopedia contains entries on Einstein’s birth and death, family and romantic relationships, honors and awards, educational institutions where he studied and worked, citizenships and immigration to America, hobbies and travels, plus the people he befriended and the history of his archives and the Einstein Papers Project. Entries on Einstein’s scientific theories provide useful background and context, along with details about his assistants, collaborators, and rivals, as well as physics concepts related to his work. Coverage of Einstein’s role in public life includes entries on his Jewish identity, humanitarian and civil rights involvements, political and educational philosophies, religion, and more. Commemorating the hundredth anniversary of the theory of general relativity, An Einstein Encyclopedia also includes a chronology of Einstein’s life and appendixes that provide information for further reading and research, including an annotated list of a selection of Einstein’s publications and a review of selected books about Einstein. More than 100 entries cover the rich details of Einstein’s personal, professional, and public life Authoritative entries explain Einstein’s family relationships, scientific achievements, political activities, religious views, and more More than 40 illustrations include photos of Einstein and his circle plus archival materials A chronology of Einstein’s life, appendixes, and suggestions for further reading provide essential details for further research |
| albert einstein contributions to math: A History in Sum Steve Nadis, Shing-Tung Yau, 2013-11-01 In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond. |
| albert einstein contributions to math: Plane Trigonometry Sidney Luxton Loney, 1893 |
| albert einstein contributions to math: A World Without Time Palle Yourgrau, 2009-03-04 It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together. |
| albert einstein contributions to math: Stanislaw Ulam 1909-1984 , 1987 |
| albert einstein contributions to math: The Great Physicists from Galileo to Einstein George Gamow, 1988-10-01 Outstanding text by one of the 20th century's foremost physicists dramatically explains how the central laws of physical science evolved, from Pythagoras' discovery of frequency ratios in the 6th century BC to today's research on elementary particles. Includes fascinating biographical data about Galileo, Newton, Huygens, Einstein and others. 136 illustrations. |
| albert einstein contributions to math: What is Mathematics? Richard Courant, Herbert Robbins, 1978 |
| albert einstein contributions to math: Physics for Mathematicians Michael Spivak, 2010 |
| albert einstein contributions to math: Einstein's Opponents Milena Wazeck, 2014-01-09 Exploring the ferocious opposition which once surrounded the theory of relativity, this fascinating account details the strategies and motivations of Einstein's detractors. A unique insight into the dynamics of scientific controversies, ideal for anyone interested in the history and philosophy of physics, popular science, and the public understanding of science. |
| albert einstein contributions to math: Huygens and Barrow, Newton and Hooke Vladimir I. Arnold, 2012-12-06 Translated from the Russian by E.J.F. Primrose Remarkable little book. -SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings. |
| albert einstein contributions to math: God's Equation Amir D. Aczel, 2000-09 Dealing with cosmology, this book reveals astronomical observations that indicate the presence of a previously unknown force in the universe. It explains, in accessible terms, Einstein's theories and his development of the cosmological constant. |
| albert einstein contributions to math: The Suàn Shù Shū Christopher Cullen, 2004 |
| albert einstein contributions to math: Einstein in Love Dennis Overbye, 2001-10-01 In Einstein in Love, Dennis Overbye has written the first profile of the great scientist to focus exclusively on his early adulthood, when his major discoveries were made. It reveals Einstein to be very much a young man of his time-draft dodger, self-styled bohemian, poet, violinist, and cocky, charismatic genius who left personal and professional chaos in his wake. Drawing upon hundreds of unpublished letters and a decade of research, Einstein in Love is a penetrating portrait of the modern era's most influential thinker. |
| albert einstein contributions to math: The Cosmic View of Albert Einstein Albert Einstein, 2013 Draws from various sources to relate Albert Einstein's ethical and philosophical views on the cosmos, touching on such topics as God, prayer, wealth, peace, creativity, nature, imagination, and curiosity. |
| albert einstein contributions to math: Albert Einsteins Theories IntroBooks, 2018-02-18 Exact insight into the relativity theory, from both philosophical perspective and general scientific perspective, for all those who are not conversant in theoretical physics and the mathematical apparatus, can be handy enough to understand the nuances associated with the subject. Einstein ideas were inspired basically by the brilliant theoretical physicist by then, Boltzmann. The physical meanings of Geometrical proportions can be understood better with the clarifications given in the Einstein theory. Plane, point and the straight lines are understood to wholesomeness with the basic conceptions of geometry. More or less solid ideas evolve and emerge from these basic definitions and clarifications explained well through Einstein theories. |
| albert einstein contributions to math: A History of Thermodynamics Ingo Müller, 2007-07-16 This book offers an easy to read, all-embracing history of thermodynamics. It describes the long development of thermodynamics, from the misunderstood and misinterpreted to the conceptually simple and extremely useful theory that we know today. Coverage identifies not only the famous physicists who developed the field, but also engineers and scientists from other disciplines who helped in the development and spread of thermodynamics as well. |
| albert einstein contributions to math: Lectures On Computation Richard P. Feynman, 1996-09-08 Covering the theory of computation, information and communications, the physical aspects of computation, and the physical limits of computers, this text is based on the notes taken by one of its editors, Tony Hey, on a lecture course on computation given b |
| albert einstein contributions to math: A Philosophical Rejection of the Big Bang Theory Khuram Rafique, 2018-03-29 Scientific inquiry takes onward course from the point where previous scientists had reached. But philosophical analysis initiates from scratch. Philosophy questions everything and chooses starting point for itself after having ruled out all the unsubstantiated and doubtful elements of the topic under study. Secondly, known realities must make sense. If a theory is officially 'counter intuitive', then either it is mere fiction or at the most; a distorted form of truth. This book's analysis is based on the philosophical principle that knowledge is empirical and does not arise magically in absence of observational grounds. With philosophical approach, it was doubtful to accept that Georges Lemaître already knew Hubble's law in year 1927 that was yet to be found by Edwin Hubble in year 1929. Therefore this book started with denial of the claim that Lemaître already knew this law. But analysis of section I.III forced author to look the matter from original source and it came to surface that Lemaître knew this law in year 1927. But contrary to mainstream claim, Lemaître had not derived that law from general relativity (GR) equations rather had deduced from a method given by Hubble himself. Whereas whole case of the Big Bang Theory rests on misleading claim that Lemaître had derived this law solely from GR equations. The basis of this claim happened to be a manipulated translation (1931) of Lemaître's original 1927 article. People regard Big Bang Theory as truth because authoritative sources deceived them by presenting a manipulated translation in year 1931. This book is a philosophical analysis of original papers of Alexander Friedmann (1922), Georges Lemaître (1927), Edwin Hubble (1929) and Albert Einstein (1917) thus covers actual roots and origins of the Big Bang Model. In this book, only the core elements of the Big Bang Model i.e. 'Expansion of Universe' and 'CMBR' are covered. It has been sufficiently shown that 'expansion' is an illusion whereas CMBR is a proof that we live in a non-expanding infinite universe. If these two core elements of the standard Big Bang Model are precisely refuted then there is nothing crucial left with the standard model. For readers of this book at least, Big Bang Theory shall become a story of past mistakes. Author is not an authoritative source on science topics therefore readers must download all the above mentioned original papers and check all the points outlined in this book from relevant original papers. Unlike reading from an authoritative source that makes readers relaxed and careless but enables authorities to deceive them in worst way possible, this book requires readers to remain alert on all the points discussed in the book and verify everything from original sources whose links are given at the end of this description and also provided in footnotes section of the book. This book is not a judgment of the topic rather it is like a case presented by an advocate while readers are the judges. Readers are required to apply their own critical judgment to conclude the matter by themselves. After carefully reading this book, readers will also start taking 'authoritative sources' with due care and it will become difficult for the 'authorities' to deceive them again. Links to original papers: 1- Albert Einstein (1917) where he presented 'cosmological constant': http: //einsteinpapers.press.princeton.edu/vol6-trans/433 2- Alexander Friedmann (1922) - English Translation: http: //www.mediafire.com/file/o7yxl3pde96o6eb/friedmann.pdf 3- Georges Lemaître 1931 translation of 1927 article: https: //academic.oup.com/mnras/article/91/5/483/985165 4- Georges Lemaître 1927 original French article: http: //articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1927ASSB...47...49L&defaultprint=YES&filetype=.pdf 5- Edwin Hubble (1929): http: //www.pnas.org/content/15/3/168.full 6- A pro-Lemaître paper that contains complete revised translation of 1927 article: https: //arxiv.org/pdf/ |
| albert einstein contributions to math: Ultralearning Scott H. Young, 2019-08-06 Now a Wall Street Journal bestseller. Learn a new talent, stay relevant, reinvent yourself, and adapt to whatever the workplace throws your way. Ultralearning offers nine principles to master hard skills quickly. This is the essential guide to future-proof your career and maximize your competitive advantage through self-education. In these tumultuous times of economic and technological change, staying ahead depends on continual self-education—a lifelong mastery of fresh ideas, subjects, and skills. If you want to accomplish more and stand apart from everyone else, you need to become an ultralearner. The challenge of learning new skills is that you think you already know how best to learn, as you did as a student, so you rerun old routines and old ways of solving problems. To counter that, Ultralearning offers powerful strategies to break you out of those mental ruts and introduces new training methods to help you push through to higher levels of retention. Scott H. Young incorporates the latest research about the most effective learning methods and the stories of other ultralearners like himself—among them Benjamin Franklin, chess grandmaster Judit Polgár, and Nobel laureate physicist Richard Feynman, as well as a host of others, such as little-known modern polymath Nigel Richards, who won the French World Scrabble Championship—without knowing French. Young documents the methods he and others have used to acquire knowledge and shows that, far from being an obscure skill limited to aggressive autodidacts, ultralearning is a powerful tool anyone can use to improve their career, studies, and life. Ultralearning explores this fascinating subculture, shares a proven framework for a successful ultralearning project, and offers insights into how you can organize and exe - cute a plan to learn anything deeply and quickly, without teachers or budget-busting tuition costs. Whether the goal is to be fluent in a language (or ten languages), earn the equivalent of a college degree in a fraction of the time, or master multiple tools to build a product or business from the ground up, the principles in Ultralearning will guide you to success. |
| albert einstein contributions to math: Sidelights on Relativity Albert Einstein, 2019-11-25 Sidelights on Relativity by Albert Einstein is a compilation of two lectures Einstein gave about the theory of relativity. First starting with the way in which physics came about to become a fully defined field of study, to how math has helped create a framework for understanding the world, this book is a comprehensive book about how the study of relativity. Written in an easy-to-understand manner, this book continues to be an essential part of scientific studies around the world. |
| albert einstein contributions to math: الكتاب المختصر فى حساب الجبر والمقابلة Muḥammad ibn Mūsá Khuwārizmī, 1831 |
| albert einstein contributions to math: The Lilavati, a treatise on arithmetic Bhāskara II., 1827 |
| albert einstein contributions to math: The Foundations of Geometry David Hilbert, 2015-05-06 This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis. |
| albert einstein contributions to math: Landmark Writings in Western Mathematics 1640-1940 Ivor Grattan-Guinness, 2005-02-11 This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field |
| albert einstein contributions to math: Special & General Relativity (Concise Edition) Albert Einstein, 2024-04-09 Einstein's pioneering work helped shape the cultural landscape of the world today. Now in a digestible, pocket format for the modern reader. A new, popular edition with a clear introduction, Special & General Relativity by Albert Einstein contains his core paper, 'Relativity, The Special & The General Theory: A Popular Exposition', which established his reputation as one of the greatest thinkers of our (and perhaps any) age. Also included are two of the Princeton University lectures he gave to explain his findings in more detail, on 'The Meaning of Relativity', as well as the early paper which led to his famous equation E = mc2. The FLAME TREE Foundations series features core publications which together have shaped the cultural landscape of the modern world, with cutting-edge research distilled into pocket guides designed to be both accessible and informative. |
| albert einstein contributions to math: The Mathematical Theory of Relativity A. S. Eddington, 2020-07-08 This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature. |
| albert einstein contributions to math: String Theory For Dummies Andrew Zimmerman Jones, 2009-11-16 A clear, plain-English guide to this complex scientific theory String theory is the hottest topic in physics right now, with books on the subject (pro and con) flying out of the stores. String Theory For Dummies offers an accessible introduction to this highly mathematical theory of everything, which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory. |
| albert einstein contributions to math: Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World Sir Isaac Newton, 2023-11-15 This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1934. |
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