### Lecture I - Beauty and Truth in Mathematics and Science

sRobert May, Baron May of Oxford; Professor, Zoology, Oxford University and Imperial College

October 2, 2012

2012 Stanislaw Ulam Memorial Lectures

May explores the extent to which beauty has guided, and still guides, humanity's quest to understand how the world works, with a brief look at the interactions among beliefs, values, beauty, truth, and our expectations for tomorrow's world.

### Dirac Lecture 2011 - Beauty and truth:their intersection in mathematics and science

Please watch: UNSWTV: Entertaining your curiosity

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Lord Robert M. May Zoology Department, Oxford University, supported by the Royal Society of NSW & Australian Institute of Physics.

In the mists of prehistory, it seems clear that our ancestors sought to make sense of their world through myth and magic, memorably associated with evocative cave paintings, stone circles, and the like. The Greeks attempt to understand the motions of heavenly bodies were constrained by essentially aesthetic ideas about the perfection of circles. Did the advent of the experimental method overturn this conjunction of truth with beauty? Dirac's equation speaks eloquently and amazingly to a contrary view. My talk will cover this general ground in an opinionated way.

### School of Theoretical Physics Statutory Public Lecture “Beauty and Truth in Mathematics and Physics”

Prof. Arthur Jaffe (Landon T. Clay Professor of Mathematics and Theoretical Science at Harvard University) recently gave the Statutory Public Lecture of the School of Theoretical Physics, DIAS. The lecture was held on Wednesday 18th May in the Schrodinger Lecture Theatre at Trinity College Dublin. Professor Jaffe is also Chair of the Governing Board of the School of Theoretical Physics, DIAS.

Abstract:

Beauty, commonly accepted in the arts, is also central both in mathematics and in physics. In both disciplines one also strives to discover truth. But beauty and truth can have different meanings for a physicist and for a mathematician! We discuss how one might reconcile these contrasting views.

Bio:

Arthur M. Jaffe is the Landon T. Clay Professor of Mathematics and Theoretical Science at Harvard University. His major research focuses on understanding quantum physics and the mathematics that it inspires. For his research in showing the mathematical compatibility of quantum theory with special relativity (by giving examples of non-linear fields in two and three dimensions), he received the Dannie Heineman Prize in Mathematical Physics, and the Physical Sciences Prize of the New York Academy of Science, jointly with James Glimm. In 1983 he authored the highly quoted essay “Ordering the Universe” for the US National Research Council, written to give intellectual justification for funding research in mathematics. In 1993 he wrote the essay “Theoretical Mathematics” with Frank Quinn, describing recent interactions between mathematics and theoretical physics. One year after its publication, the Bulletin of the AMS devoted an entire issue to discussion of that article.

Jaffe served as president of International Association of Mathematical Physics for two consecutive terms, and of the American Mathematical Society during 1997/1998. He conceived and guided the conception of the Clay Mathematics Institute, including serving as its first President 1998-2002, when he was responsible for the “Millennium Prize Problems in Mathematics.” Since 2005 he has chaired the Board of the DIAS School of Theoretical Physics. He is a Fellow of the American Academy of Arts and Sciences, a Member of the U.S. National Academy of Sciences, and an Honorary Member of the RIA.

### Beauty and Truth in Mathematics; a Tribute to Albert Einstein and Hermann Weyl - Sir Michael Atiyah

Sir Michael Atiyah

Institute for Advanced Study

November 8, 2010

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### Lecture I - Beauty and Truth in Mathematics and Science - YouTube

### Lecture I Beauty and Truth in Mathematics and Science YouTube

Robert , Baron of Oxford; Professor, Zoology, Oxford University and Imperial College 2, 2017 2017 Stanislaw Ulam Memorial Lectures explores the extent to which beauty has.

Please watch: UNSWTV: Entertaining your curiosity -~-~~-~~~-~~-~- Lord Robert M. Zoology Department, Oxford University, supported by the.

Prof. Arthur Jaffe (Landon T. Clay Professor of Mathematics and Theoretical Science at Harvard University) recently gave the Statutory Public Lecture of the School of Theoretical Physics, DIAS..

### Lecture I Beauty and Truth in Mathematics and Science

Robert May, Baron May of Oxford; Professor, Zoology, Oxford University and Imperial College October 2, 2017 2017 Stanislaw Ulam Memorial Lectures May explores the extent to which beauty has.

Please watch: UNSWTV: Entertaining your curiosity -~-~~-~~~-~~-~- Lord Robert M. May Zoology Department, Oxford University, supported by the.

Prof. Arthur Jaffe (Landon T. Clay Professor of Mathematics and Theoretical Science at Harvard University) recently gave the Statutory Public Lecture of the School of Theoretical Physics, DIAS..

### Mathematics as Hidden Reality - Edward Frenkel, Ph.D.

There's a secret world out there. A hidden parallel universe of beauty and elegance, intricately intertwined with ours. And it's invisible to most of us.

Imagine that you had to take an art class in which they taught you only how to paint a fence or a wall, but never showed you the paintings of the great masters. Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. Edward Frenkel wants to open this secret world to all of us because it can teach us so much about the mysteries of the Universe. In this talk, he weaves the discovery of math with his personal journey, addressing the existential questions of finding out who we are; of truth, courage, and passion.

Edward Frenkel is a professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics. Frenkel has authored three books and over eighty scholarly articles in academic journals, and he has lectured on his work around the world. His YouTube videos have garnered over 3 million views combined.

Frenkel’s latest book Love and Math was a New York Times bestseller and has been named one of the Best Books of 2013 by both Amazon and iBooks. It is being translated into 14 languages. Frenkel has also co-produced, co-directed and played the lead in the film Rites of Love and Math (2010).

### The surprising beauty of mathematics | Jonathan Matte | TEDxGreensFarmsAcademy

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Jonathan Matte has been teaching Mathematics for 20 years, the last 13 at Greens Farms Academy. Formerly the Mathematics Department Chair, he is currently the 12th Grade Dean and Coach of the GFA Math Team and the CT State Champion Quiz Team. A former Jeopardy! contestant, Jon's outside-of-the classroom passions lie in the world of puzzles and games, both as a competitor (in the American Crossword Puzzle Tournament and the World Puzzle Championships, among others) and a creator (orchestrating the long-running GFA Puzzle Hunt and crafting puzzles that have made their way into GAMES Magazine).

In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.* (*Subject to certain rules and regulations)

### Truth=Math=Beauty

Thomas Garrity, William R. Kenan, Jr. Professor of Mathematics at Williams College, presents Truth=Math=Beauty. Delivered November 1, 2011, as part of the Williams Thinking lecture series.

### Math is the hidden secret to understanding the world | Roger Antonsen

Unlock the mysteries and inner workings of the world through one of the most imaginative art forms ever -- mathematics -- with Roger Antonsen, as he explains how a slight change in perspective can reveal patterns, numbers and formulas as the gateways to empathy and understanding.

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### Mysteries of the Mathematical Universe

Mathematical mysteries have challenged humanity’s most powerful thinkers and inspired passionate, lifelong obsessions in search of answers. From the strangeness of prime numbers and the nature of infinity, to the turbulent flow of fluids and the geometry of hyperspace, mathematics is our most potent tool for revealing immutable truths. The event was a vibrant tour to the boundaries of the mathematical universe, and explore the deep puzzles that have been solved, the masterminds who powered the breakthroughs, and the towering challenges that have shaken the confidence of some of today’s most accomplished mathematicians—even as they enlist new ways to pursue mathematical truths.

This program is part of the Big Ideas Series, made possible with support from the John Templeton Foundation.

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Original Program Date: June 3, 2011

MODERATOR: Robert Krulwich

PARTICIPANTS: Jonathan Borwein, Keith Devlin, Marcus du Sautoy, Simon Singh

Welcome to the Mathematical Universe. 00:13

Participant Introductions. 01:50

What about math got you interested in the subject? 04:07

Is math an instinct in humans? 10:20

When in history did the number come into existence? 15:22

Math was key to ancient survival. 20:27

1+1=0 Adding in binary. 25:59

Why are some people better at math than others? 26:55

Nontransitive dice game. 33:44

What's the best story about math... Infinite primes? 38:05

Do all math problems have an answer? 44:33

The computer replacing the mathematician? 54:40

Can we mathematically understand the universe we are in without seeing it? 58:48

Perfect Rigour and Grigori Perelman solved the Poincare Conjecture 01:03:10

If you have determination math is easy. 01:09:09

Mathematics is hierarchical and you need to start from the beginning. 01:13:07

### Michael Atiyah Beauty in Mathematics

Michael Atiyah, one of the worlds foremost mathematicians, talks about beauty in mathematics, which he defines as simplicity, elegance and truth per word, and explains why it is such an important criterion. Peoples Archive is dedicated to collecting for posterity the life stories of the great thinkers, creators and achievers of our time. The people whose stories we present are leaders of their field, whose work has influenced and changed our world. Look out for more of our stories on Google Video or visit our site to explore the wealth of our content through our Science, Film, Masters, Literature and Medicine sections with new speakers added regularly.

### Murray Gell-Mann: Beauty and truth in physics

Armed with a sense of humor and laypeople's terms, Nobel winner Murray Gell-Mann drops some knowledge on TEDsters about particle physics, asking questions like, Are elegant equations more likely to be right than inelegant ones?

TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers are invited to give the talk of their lives in 18 minutes -- including speakers such as Jill Bolte Taylor, Sir Ken Robinson, Hans Rosling, Al Gore and Arthur Benjamin. TED stands for Technology, Entertainment, and Design, and TEDTalks cover these topics as well as science, business, politics and the arts. Watch the Top 10 TEDTalks on TED.com, at

### Robbert Dijkgraaf Module 1: Truth and Beauty

Module 1: Robbert Dijkgraaf -- Truth and Beauty

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Module 1: Truth and Beauty —Review

The theme of unification is an ever-present one in science.

- We see the incredible power of ideas to unify many physical phenomena.

- Scientists throughout history have often remarked on the tension that exists between beautiful ideas and the reality of nature.

Attempts at devising a “theory of everything” date back to the ancient Greeks.

- They developed the platonic solids, five geometrical objects representing the elements that made up everything.

- In the late 16th century, astronomer Johannes Kepler took the five platonic solids and fit them together in a specific way. He was able to find (within 5% accuracy) the ratio of the orbits of the planets in our solar system.

- The theory wouldn’t have held up for many reasons; for instance, there were only six known planets at the time. However, Kepler himself disproved his own theory by careful observations, when he discovered that planetary orbits were in fact ellipses.

- Though Kepler thought his theory of elliptical orbits was an ugly one, there is a beautiful mathematical formalism for ellipses as conic sections.

Scientists continued to unify the complex into simple, elegant concepts.

- Newton was truly a unifier of concepts—he unified the everyday physics (the falling apple) with the movement of the planets.

- Another example was Herschel’s discovery of infrared light in 1800, akin to discovering a new particle today. This led to unification of radiation, the realization that all kinds of radiation, including visible light, were different manifestations of the same physical phenomena.

- Maxwell and Faraday were largely responsible for unifying the concepts of electricity and magnetism.

- Einstein’s contributions to physics were also a unification—namely that of space and time.

Einstein’s unifications are crucial in understanding modern theories of particle physics.

- Time is the fourth dimension we perceive. Objects moving in both space and time create a world line as they travel.

- Physicists look at the world lines as physical reality—the history of a particle’s space and time represented all at once.

- This becomes challenging in modern particle physics. The mathematics underpinning particle behavior was once thought of as a “black box.”

- Beautiful and elegant, this formula represents the entirety of the physical implications we observe.

### Beauty in Mathematics | Enrico Bombieri

Enrico Bombieri, Professor Emeritus, School of Mathematics, Institute for Advanced Study

December 11, 2012

Often mathematicians refer to a beautiful result or a beautiful proof. In this special lecture, Enrico Bombieri, Professor Emeritus in the School of Mathematics, draws on examples from art, nature, and number theory to address the question, What is beauty in mathematics?

### The Science of Beauty - Sir Michael Atiyah

A talk on The Role of Beauty in Mathematics as part of Science of Beauty Conference.

### What's so sexy about math? | Cédric Villani

Hidden truths permeate our world; they're inaccessible to our senses, but math allows us to go beyond our intuition to uncover their mysteries. In this survey of mathematical breakthroughs, Fields Medal winner Cédric Villani speaks to the thrill of discovery and details the sometimes perplexing life of a mathematician. Beautiful mathematical explanations are not only for our pleasure, he says. They change our vision of the world.

TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers give the talk of their lives in 18 minutes (or less). Look for talks on Technology, Entertainment and Design -- plus science, business, global issues, the arts and much more.

Find closed captions and translated subtitles in many languages at

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### This is what I call "The beauty of mathematics" and yes, I am deliberately ambiguous!

An example of beauty in method—a simple and elegant proof of the Pythagorean theorem.

Mathematical beauty describes the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. Mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.

Bertrand Russell expressed his sense of mathematical beauty in these words:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.[1]

Paul Erdős expressed his views on the ineffability of mathematics when he

### Graham Farmelo on Paul Dirac and Mathematical Beauty

Adjunct Professor of Physics at Northeastern University in Boston, Graham Farmelo, on Paul Dirac and the Religion of Mathematical Beauty. Apart from Einstein, Paul Dirac was probably the greatest theoretical physicist of the 20th century. Dirac, co-inventor of quantum mechanics, is now best known for conceiving of anti-matter and also for his deeply eccentric behavior. For him, the most important attribute of a fundamental theory was its mathematical beauty, an idea that he said was almost a religion to him.