5 Rules of Quantum Mechanics By Werner Heisenberg

German physicist Werner Heisenberg is well known as one of the founders of quantum mechanics. Heisenberg was only 25 years old when he arrived at the uncertainty principle, which became the basis of Bohr-Einstein debate on the nature of reality.

For his pioneering contributions, Heisenberg was recognized by the Nobel Prize committee in 1932. He was among the youngest recipients of the Nobel Prize. The following are five rules or lessons in quantum mechanics by one of its creators, Werner Heisenberg.

1. The more precise the measurement of position, the more imprecise the measurement of momentum - and vice versa.

This is how Heisenberg summarized uncertainty principle in one line. Niels Bohr proposed later on that "complementarity" is a fundamental feature of reality. In other words, particles have certain pairs of complementary properties which cannot be observed simultaneously.

Earlier, the words "position" and "velocity" of an electron seemed perfectly well defined as per the mathematical framework of Newtonian mechanics. But actually when we are going to such unimaginably small scales, they are not well defined in accordance with uncertainty equation.

2. Wave particle duality arises because of limitation in our language.

By nature, light and matter are single entities. However we cannot describe them as they are - hence the solution is to split their overall behavior into wave and particle like properties. Because that is the limitation of human language, says Heisenberg.

Our language was invented to study and describe the experiences of daily life consisting of processes and objects involving large numbers of atoms. The apparent duality at small scales is a result of this limitation.

3. All particles are made of the same substance: energy.

In quantum mechanics, the smallest units of matter are not physical objects in the ordinary sense - they are forms and ideas which can be expressed only by means of a mathematical language. This makes true what Pythagoras famously said: All things are numbers.

Moreover, particles are not eternal and indestructible - they can be transformed into each other. For example: if two particles moving with a very high kinetic energy collide, then many new elementary particles may be created from the available energy and the old particles will have disappeared in the collision.

4. What we observe is not nature herself, but nature exposed to our method of questioning.

According to Heisenberg, physics does not simply describe and explain nature; it is part of the interplay between nature and ourselves; it describes nature as exposed to our nature of questioning.

As a matter of fact, every experiment destroys some of the knowledge of the system which was obtained by previous experiments. Can nature possibly be so absurd? asked Heisenberg, as he struggled to make sense of the world.

5. If you're not shocked by quantum mechanics, you don't understand quantum mechanics.

The very foundations of physics were shaken up by the arrival of new quantum theory. Heisenberg has said: Whenever we proceed from the known into the unknown, we may have to learn a new meaning of the word "understanding." Much of everything that was known before became null and void overnight.

For example: The law of causality is no longer applied in quantum theory and the law of conservation of matter is no longer true for the elementary particles.

That is why, before studying quantum mechanics one must discard all pre-existing notions about the world and forget what was learned in large scale or Newtonian physics.

How did Heisenberg cope? Heisenberg admired Eastern philosophy and saw parallels between it and quantum mechanics. He stated that after having conversations with Rabindranath Tagore about Indian philosophy "some of the ideas that seemed so crazy suddenly made much more sense".

10 Interesting Facts About Chien-Shiung Wu

Chinese American physicist Chien Shiung Wu [1912-1997] is most well known for performing an experiment in 1956 which proved that parity or mirror image symmetry is not conserved - when it comes to the weak nuclear force.

The result was a shocker. Nobel laureate Wolfgang Pauli said on behalf of the physics community: "We are all rather shaken by the death of our beloved friend, parity."

Wu was an acclaimed experimental physicist and her expertise in the subject evoked comparisons to Marie Curie. She was nicknamed the Chinese Madame Curie, queen of nuclear research, as well as the first lady of physics.

Following are ten facts on physicist Chien Shiung Wu...

1. Wu was extremely close to her father, who was an engineer. He created an environment for children that encouraged curiosity, questioning and research from an early age. Wu's mother was a school teacher who valued gender equality.

2. Wu received her primary education at a school for girls that was founded by her father. At home, she was surrounded by books, magazines and newspapers. Her hand writing was considered outstanding by others as she was praised for her Chinese calligraphy.

3. As a high school student, Wu struggled in the subject of mathematics. Her father bought self study guides to trigonometry, algebra and geometry one summer to help. That experience created a life long habit of self learning and gave Wu sufficient confidence.

4. In 1936, Wu was accepted by the University of Michigan, but she was shocked at the sexism in the campus. She decided to study at the more liberal Berkely in California. Wu was a popular student and among the most talented. Her nick name at Berkeley was Gee Gee.

5. Wu worked closely with Robert Oppenheimer on the Manhattan project in 1944 where she helped develop the process for separating uranium into isotopes by gaseous diffusion. Years later, Wu recommended the Taiwanese president not to build a nuclear weapon due to its destructive outcome.

6. In 1949, Wu was the first to conduct a successful experiment on quantum entanglement or as Einstein called it - spooky action at a distance. Her work was the first important confirmation of quantum results relevant to a pair of entangled photons.

7. When the communists came to power in China the following year, Wu's father wrote urging her never to return. Since her passport was issued by the former government, it became invalid to travel abroad. Wu became an American citizen in 1954.

8. Physicists Lee and Yang's theoretical studies showed that parity would be violated for the weak force. Wu was an expert on beta decay experiment, which is a consequence of the weak force. In 1956, she proved that beta particles from Cobalt were emitted asymmetrically and hence parity was not conserved.

9. Tsung-Dao Lee and Chen-Ning Yang won the Nobel Prize in 1957. However, Wu was not honored until 1978 when she won the inaugural Wolf Prize - the criteria for this award is those scientists who were thought deserving to win a Nobel Prize but did not win.

10. She spent her final years promoting STEM education for girls. Wu's dying wish was to be buried in the courtyard of the Ming De school that her father had founded and that she had attended as a little girl.

How Max Planck Discovered Quantum Theory

German physicist Max Planck (1858-1947) was born in a traditional, intellectual family. Religion played a big part in the Planck household as both his great grandfather and grandfather were theology professors.

In 1867, Planck was enrolled in the Maximilians gymnasium school, where he came under the guidance of Hermann Müller, a mathematician who immediately recognized Planck's genius.

It was from Müller that Planck first learned the principle of conservation of energy as a 10 year old - that energy can neither be created nor destroyed. This is how Planck first came in contact with the field of physics.

Planck's big problem

When Planck expressed desire to pursue a career in physics, a professor Philipp von Jolly advised him against it, saying: "In physics, almost everything is already discovered."

Planck did not intend to make a discovery of new kind... he simply wanted to study physics deeply. In 1877, aged 19, Planck came under the mentorship of such renowned German scientists as Hermann von Helmholtz and Gustav Kirchhoff.

Max Planck, 1878

Planck was a devoted student with a knack for solving problems. By 1880, he had earned two of the highest degrees offered in Europe - a PhD degree and a qualification for professorship in Universities.

In 1894, Planck started working on the problem of black body radiation as classical theory of light had failed to explain what all was happening.

What is a black body?

A hypothetical black body can absorb all the energy that comes in contact with it, and then because of the laws of thermodynamics, this ideal body must also re-emit as much light as it absorbs.

Spectrum of a near perfect black body at an arbitrary constant temperature is shown below:

All objects actually emit radiation if their temperature is greater than absolute zero. An iron horseshoe, a ceramic cup and even people. The blackbody spectrum tells what is the peak wavelength emitted by that object at that temperature.

Very hot objects will glow - like Tungsten filament in a light bulb at 3300 Kelvin. Human body would emit invisible infrared radiation at 310 Kelvin.

It is important to note that all black body distributions look alike, except that they "peak" in different wavelength regions of the electromagnetic spectrum.

Classical VS quantum

In 1893, Wilhelm Wien had introduced Wien's law, which correctly predicted the behavior of black body at high frequencies - smaller wavelengths, but failed at low frequencies.

The Rayleigh–Jeans law of 1900 agreed with experimental results at low frequencies (below 100 THz), but created an "ultraviolet catastrophe" at higher frequencies.

There was no single law or theory that agreed with experimental data at all the values of frequency. Planck was determined to find a solution and at the turn of the century - he did.

In 1901, by assuming that radiation cannot be emitted continuously, as taught by classical physics, but in discrete packets or quanta.

Thus, energy is quantized according to Planck's law.

Planck considered quantization as being purely a mathematical trick and didn't really believe it to be anything more - it just fit the data at hand. In Planck's own words, energy quantum was "purely a formal assumption".

After all, physics is not really about "why" something is true but more about "how" does it work part. Ultimately, by moving away from classical theory Planck was able to explain the shape of black body spectrum to a high degree of accuracy.

Few years later, when Einstein solved another phenomenon where classical theory failed - the photoelectric effect - he gave physical meaning to Planck's energy quantum. The term "photon" was coined and a whole new quantum revolution began.

5 Physicists Who Started Their Own Business

It is said that anyone can start a business - and scientists too have delved into entrepreneurship from time to time. As physics and technology are closely related, most companies by physicists are technological - but there is one exception of a fast food chain!

1. Peter Buck

Peter Buck was an American physicist who co-founded the Subway fast food chain of restaurants. He earned master's and doctoral degrees in physics at Columbia University. Buck specialized in nuclear physics and worked for General Electric company for a while.

In 1965, Buck loaned $1000 to family friend Fred DeLuca and advised him to open a sandwich shop. Initially, the company was named Pete's Super Submarines. In 1974, they started franchising out the restaurant and renamed it to Subway sandwiches.

As of June 2021, Subway sandwiches had 37,540 locations in more than 100 countries and territories. It was also the fastest growing fast food chain in 2015.

2. Akio Morita

Akio Morita was a Japanese physicist and entrepreneur who co-founded the Sony corporation - initially named Tokyo Telecommunications Engineering Corporation - with physicist Masaru Ibuka.

Morita was born into a business family and was trained to one day overtake the operations. However, Morita found his true calling in mathematics and physics. He graduated from Osaka Imperial University with a degree in physics in 1944.

Sony sold the first tape recorder in Japan in 1950. In 1957, Sony also launched pocket sized radio - a precursor to Walkman which was introduced in 1979. It is believed that Steve Jobs, founder of Apple, wanted his company to create products that Akio would love.

3. Robert Noyce

Nicknamed the "mayor" of Silicon valley, Robert Noyce was an American physicist and inventor who co-founded the Intel corporation in 1968.

As a child, Noyce would build remote controlled aircraft and radio from scratch. He was a multi-talented person who not only exhibited a talent for mathematics in high school, but also sang at college and was part of the swimming team.

He graduated with a BA in physics and mathematics in 1949 and received his doctorate in physics from MIT in 1953. Noyce was hooked when his physics professor showed in one class the very first transistors invented at Bell labs.

In 1959, Noyce invented a new type of integrated circuit made of Silicon, that triggered a personal computing revolution later on, and gave Silicon valley its name. Today, the company Intel is inseparably linked to the business of personal computers.

4. Cecil Howard Green

Cecil Howard Green was a British-born American geophysicist, electrical engineer and entrepreneur who co-founded Texas Instruments in 1951. He also set up the University of Texas at Dallas in 1969.

Green was employed at Geophysical Service Incorporated, a petroleum exploration company. He purchased the entire business with colleagues in 1941 and they started manufacturing electrical instruments during the World War.

Today, Texas Instruments company holds over 45,000 patents worldwide! The growth of his company made Green an enormously wealthy man and he turned to philanthropy, giving away $200 million to educational and medical causes.

5. Ray Dolby

Ray Dolby was an American physicist, engineer and entrepreneur who invented a noise reduction system for use in audio tape recording in 1965 - the same year he also founded his company, Dolby laboratories in London.

Dolby received a bachelor degree in electrical engineering from Stanford University (1957). He went on to complete a PhD in physics from the University of Cambridge in 1961 by winning the Marshall scholarship.

Dolby left in his will a sum of £35 million to Pembroke College of University of Cambridge. His family also donated a further £85m to the University's Cavendish Laboratory. Today, Dolby is a leading developer of audio technologies for cinema, home theatres and mobile phones.

10 Albert Einstein Quotes To Inspire Students

Albert Einstein was not only one of the greatest physicists of all time, but also famous for his words of wisdom. Students often approached Einstein with their problems and he would be more than willing to help.

The following are just a few of Einstein's wise sayings that will encourage and inspire you to be all that you can be.

1. Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. (In a letter to high school student Barbara Lee Wilson in 1943).

2. I do not carry such information in my mind since it is readily available in books. (In response to not knowing the speed of sound).

Einstein also similarly said, "The value of a college education is not the learning of many facts but the training of the mind to think".

3. Life is like riding a bicycle. To keep your balance you must keep moving. Einstein wrote this gem of an advice in a letter to his son - Eduard, dated 5 February 1930.

4. If A is success in life, then A = x + y + z. Work is x, play is y and z is keeping your mouth shut. (Said to Samuel J Woolf in 1929).

5. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world. (1929)

Einstein's imagination led him to discover new theories in physics. For example, once when he was sitting in his office, Einstein thought: If a person falls freely, he will not feel his own weight. This thought pushed Einstein to a new theory of gravitation.

6. Everyone sits in the prison of his own ideas; he must burst it open, and that in his youth, and so try to test his ideas on reality.

7. I have only two rules which I regard as principles of conduct. The first is: Have no rules. The second is: Be independent of the opinion of others. 1930

8. Never lose a holy curiosity. It is enough if one tries merely to comprehend a little bit of mystery each day. Don't stop to marvel.

9. Try not to become a man of success. Rather become a man of value.

10. I never think of the future. It comes soon enough.

Clearly, Nobel prize winning scientist Albert Einstein had a knack for solving problems - be it in physics or in life in general. He continues to inspire millions of people every day.

7 Physicists Who Were Also Great Musicians

Physics and music - two wildly separate fields, both make life joyous and beautiful in their own ways. Without the laws of physics, there would be no sunset, rainbow or internet, and without music, the living couldn’t so eloquently express feelings such as, say a heartbreak.

Following is a list of 7 physicists who also played music:

Brian May:

English musician and astrophysicist Brian May is the co-founder of one of the greatest rock bands in history - Queen. He was the lead guitarist and songwriter while being the member of immensely successful musical group.

Brian graduated with a BSc (hons) degree in physics from Imperial College in London. In 1974, when he was a doctoral student, Queen became so popular that Brian abandoned his studies to focus on the band.

In 2006, Brian May re-registered for his doctorate degree and completed his thesis within a year. His revised thesis was approved and he got his PhD in 2007 from Imperial College London after over 30 years of wait.

Albert Einstein:

Einstein’s interest in music developed as a child thanks to his mother, who was a reasonably decent piano player. She wanted her son to also learn the violin and help him assimilate into the German musical culture.

Einstein began learning both the instruments from the young age of 5. By 16, he had mastered Mozart’s and Beethoven’s violin sonatas. Einstein displayed a deep love and appreciation of classical music - a quality that was and remains in short supply.

Einstein said years later, “If I were not a physicist, I would be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music… I get most joy in life out of music.”

Max Planck:

The founding father of quantum theory was gifted when it came to music. Max Planck played various musical instruments including piano, organ and cello. Moreover, he also composed his own songs and operas. Einstein and Planck played together, finding not only a shared love for physics but also music.

Brian Cox:

Popular English particle physicist Brian Cox started his career as a piano and keyboard player in the rock band Dare. They released two studio albums with Cox in 1988 and 1991 respectively. Brian then joined another group - D:Ream, with whom he had several hits including the number one song, ‘Things can only get better’ that was also used as a New Labour election song.

Richard Feynman:

Feynman took Bongo, a relatively obscure musical instrument and made it mainstream. Feynman used to organize mini concerts for his students and played along with his friend Ralph Leighton - they even sang together, while drumming. Feynman is most easily recognized by a black and white picture in the Caltech archives, donning an ordinary white shirt and tailored pants, with a big smile on his face - playing his favorite percussive instrument.

Satyendra Nath Bose:

Well known Indian physicist in whose honor Bosons are named, was a person of varied interests. Bose was well versed in several languages such as Bengali, English, French, German and Sanskrit. He played an Indian stringed musical instrument similar to violin, called the Esraj, like a master. He was trained in Indian classical music and occasionally sang poems of Rabindranath Tagore and Kalidasa.

Werner Heisenberg:

Heisenberg is famous for laying the foundations of quantum mechanics. But very few are aware of his other interest - music. Like Einstein, Werner Heisenberg too came in contact with music from an early age.

Heisenberg could read sheet music when only 4 years old, so it is said that he was a prodigy. Heisenberg’s parents wanted him to become a concert pianist - however - his love of physics outgrew his love of music. Heisenberg's work in physics irked Einstein to such an extent that he commented, “God does not play dice with the Universe”.

Who Proposed The Idea of Black Hole?

The black hole is a great source of mystery and inspiration for scientists and writers alike. These are abnormalities in space where the gravity is so strong that not even light, traveling at an enormous speed of 300,000 km/sec, can escape.

How did the idea of black hole come about?

In 1915, more than a hundred years ago, Albert Einstein published a theory of space and time or "spacetime" in which one of the crucial predictions was the bending of light as it approached a massy body, like the sun or a black hole.

That light bent in the presence of mass was confirmed in an experiment led by English astronomer Arthur Eddington in 1919. After this observation, Einstein's general relativity was taken more seriously, as it resurrected the original idea of black hole – which was published way back in 1784!

It was English astronomer John Michell who suggested the existence of a body so big that even light could not escape. As a result, such an object could not be seen directly but its gravitational effects on nearby bodies could be measured.

At that time, the term black hole did not exist. Astronomers instead used the term "dark stars" which is a pretty cool name to describe a stellar body hiding in plain sight.

In 1916, Karl Schwarzschild used Einstein's field equations of general relativity to calculate the radius up to which any object of mass must be "cramped" to make it a black hole. This is called the Schwarzschild radius.

For example: Earth crushed to the size of a pea would turn into a black hole.

Although the theory of general relativity implied the existence of a monstrous space object capable of trapping light in its grasp, Einstein wrote in a paper that a star would "never shrink" to zero size.

When will black hole form

A new development occurred in 1930. Indian physicist Subrahmanyan Chandrasekhar calculated how a star could actually shrink or collapse if it "ran out of hydrogen" or other nuclear fuels to burn.

Consequently, there come various stages in the star's life cycle. Upon collapse, the star may become a white dwarf - like our sun will - too feeble to burn bright in our skies.

Chandrasekhar predicted that a white dwarf with mass greater than "a limit" will be subject to further gravitational collapse, evolving into a different type of stellar remnant - a denser neutron star.

What would it take to form a black hole then? In 1939, American physicist Robert Oppenheimer produced a paper titled, "On Continued Gravitational Attraction" and in it calculated that a star would have to be at least three times as massive as the sun to become black hole.

Birth of black hole

The paper by Oppenheimer was the key factor in the rejuvenation of astrophysical research in the United States in the 1950s - mainly by John Archibald Wheeler.

In fact, the term black hole was coined in 1967 by Wheeler during a talk he gave at the NASA Goddard Institute of Space Studies. Not even light could escape from it, it was undetectable - hence, "black" hole.

One also could not tell from the outside what was inside the black hole. This means that the black hole contains a lot of information which is hidden from the outside world and Wheeler called this, "A Black Hole Has No Hair".

But in 1971, English mathematical physicist Roger Penrose described a way for information to be transferred from rotating black hole to an outside particle. Three years later, another method for the same was provided by cosmologist Stephen Hawking, as in Hawking radiation.

At around the same time in America, physicist Kip Thorne, one of Wheeler's doctoral students, developed the general relativistic theory of thin accretion disks around black holes, a flattened band of spinning matter around the event horizon.

Something you may have already seen in artist's impressions of the black hole:

Thorne compiled many theoretical results about the black holes in a 1994 book for non-scientists, titled Black Holes and Time Warps. It was a widely recognized book on the subject and translated into six languages.

Cut to present

The phenomenon of black hole captured the attention of some of the greatest minds in history and continues to surprise us even more in mainstream media.

Most recently, in the 2014 film "Interstellar" by director Christopher Nolan. Physicist Kip Thorne was also closely involved in the making and acted as executive producer.

Interstellar was a huge success - the science fiction movie project not only generated a fortune at the box office but also a new public interest regarding the black holes.

In 2019, the first picture of a black hole in Messier 87 was released based on data from 2017. It was compiled by the event horizon telescope - a collective effort of scientists from over 20 countries made it possible to see the distant space object by converting the entire planet Earth into a giant virtual telescope!

The image of black hole confirmed how lucky we are as a species at this particular time, with the capacity of the human mind to comprehend the universe, to have built all the science and technology to see it in glorious action.

On a fun ending note, black holes have come a long way - from gigantic mass eating monsters in space to the shape of a doughnut!

10 differences between astrology and astronomy

1. Every newspaper in the world has a daily column on astrology. How many papers carry even a weekly column on astronomy? – this is a major, disappointing difference between the two fields, as pointed out by Carl Sagan.

2. Astronomy is a practical science built upon technical skills such as in observation, mathematics and computer programming. Astrology does not demand such complicated knowledge.

3. If you delete all of human history, astronomy will come up again in exactly the same manner since it is based upon facts and figures. Whereas, astrology is a product of the human imagination and will acquire different shapes and forms.

4. There is a Nobel Prize for astronomers who make great advances to our understanding of the universe – astronomy being a branch of physics. In astrology, there is no such honor.

5. According to astrology, the position of a planet such as Saturn can trigger a life changing influence on an individual located on some corner of the Earth. Astronomy denies this claim.

6. After decades of research, astronomy has reached to the conclusion that life on earth is made from elements that were forged in the core of dying stars – a poetically beautiful truth. Astrology could not have reached to this sophisticated result.

7. Historians say that astrology is 2,500 years old. On the contrary, astronomy is vastly older. The first human beings depended on astronomical events for various activities, such as in agriculture and navigation. This developed into questions like, "What's out there?" and into inventions like the telescope.

8. Hence, astronomy is a natural tendency (aka curiosity) whereas astrology is derived, from observations and results in astronomy. Astrology is something that people turn to thinking it would have answers to life's problems.

9. Astronomy is a healthy activity for kids to get involved in. Astrophotography is one way to get started. Whereas, a sincere belief in astrology puts children inside boxes and they grow up asking dumb questions like, "What's your star sign?" to measure compatibility.

10. Reading astrology may be comforting to some people, but at only a superficial level. On the contrary, astronomy appeals to the very core of a person and may inspire them to paint a timeless piece like the "starry night".

Five Quotes By Freeman Dyson On Religion

Freeman Dyson (1923-2020) was no ordinary physicist. In a letter of recommendation to Robert Oppenheimer, Nobel laureate Hans Bethe wrote in praise of Dyson: "He is the best student I have ever had or observed."

Dyson was unusual in that he won the Templeton Prize in 2000, which is given annually in the field of spirituality, recognizing achievements at the intersection of science and religion. Dyson was pleasantly surprised by this honor.

Yes, Dyson was openly religious.

But his God was a kind of meta-scientific, collective consciousness. As someone who regarded the universe as a manifestation of God, Dyson said: The many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the Universe must in some sense have known that we were coming.

Dyson partially disagreed with fellow physicist Steven Weinberg's view that "with or without religion, good people can behave well and bad people can do evil; but for good people to do evil – that takes religion" and added: "For bad people to do good things – that also takes religion."

Following are 5 quotes by Freeman Dyson on science, religion and life:

1. Both as a scientist and as a religious person, I am accustomed to living with uncertainty. Science is exciting because it is full of unsolved mysteries, and religion is exciting for the same reason. The greatest unsolved mysteries are the mysteries of our existence as conscious beings in a small corner of a vast universe.

2. To talk about the end of science is just as foolish as to talk about the end of religion. Science and religion are both still close to their beginnings, with no ends in sight. Science and religion are both destined to grow and change in the millennia that lie ahead of us, perhaps solving some old mysteries, certainly discovering new mysteries of which we yet have no inkling.

3. Science and religion are two windows that people look through, trying to understand the big universe outside, trying to understand why we are here. The two windows give different views, but they look out at the same universe. Both views are one-sided, neither is complete.

4. Without discipline there can be no greatness. Without diversity there can be no freedom. Greatness for the enterprise, freedom for the individual — these are the two themes, contrasting but not incompatible, that make up the history of science and the history of religion.

5. Over periods of 10,000 years the distinctions between Western and Eastern and African cultures lose all meaning. Over a time span of 100,000 years we are all Africans. And over a time span of 300 million years we are all amphibians, waddling uncertainly out of dried-up ponds onto the alien and hostile land.

As a scientist, Dyson made several important contributions to the field of astrophysics that also bear his name, including concepts like Dyson tree and Dyson eternal intelligence, which find repetitive use in the realm of science fiction.

Dyson was Professor Emeritus in the Institute for Advanced Study in Princeton, remembered by friends and colleagues as shy and polite, with a refreshing view of the world. Physicist Geoffrey Ingram Taylor described Dyson as "the best mathematician in England."