mathematics

Peter Shor

Peter Shor is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Peter Shor rather than just read about it. In short: Peter Williston Shor (born August 14, 1959) is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer. He has been a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) since 2003.

Key takeaways

Peter Shor belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Peter Shor to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Peter Shor from memory before moving on to harder problems.

Reference excerpt

Peter Williston Shor (born August 14, 1959) is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer. He has been a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) since 2003.

Early life and education Shor was born on August 14, 1959, in New York City, to Joan Bopp Shor and S. W. Williston Shor. He grew up in Washington, D.C. and Mill Valley, California. While attending Tamalpais High School, he placed third in the 1977 USA Mathematical Olympiad. After graduation that year, he won a silver medal at the International Math Olympiad in Yugoslavia (the U.S. team achieved the most points per country that year). Shor graduated from the California Institute of Technology (Caltech) in 1981 with a B.S. in mathematics. He was a Putnam Fellow in 1978. He then did doctoral study in applied mathematics at MIT, receiving a Ph.D. in 1985. His doctoral advisor was F. Thomson Leighton, and his thesis was on probabilistic analysis of bin-packing algorithms.

Career After being awarded his PhD by MIT, he spent one year as a postdoctoral researcher at the University of California, Berkeley, and then accepted a position at Bell Labs in New Providence, New Jersey. It was there that he developed Shor's algorithm. This development was inspired by Simon's problem. Shor first found an efficient quantum algorithm for the discrete log problem (which relates point-finding on a hypercube to a torus) and,"Later that week, I was able to solve the factoring problem as well. There’s a strange relation between discrete log and factoring."Both of these problems are examples of the HSP. For his work discovering the efficient quantum algorithms for factoring and discrete logarithm he was awarded the Nevanlinna Prize at the 23rd International Congress of Mathematicians in 1998 and the Gödel Prize in 1999. In 1999, he was awarded a MacArthur Fellowship. In 2017, he received the Dirac Medal of the ICTP and for 2019 the BBVA Foundation Frontiers of Knowledge Award in Basic Sciences. Shor began his MIT position in 2003. Currently, he is the Henry Adams Morss and Henry Adams Morss, Jr. Professor of Applied Mathematics in the Department of Mathematics at MIT. He also is affiliated with CSAIL. He received a Distinguished Alumni Award from Caltech in 2007. On October 1, 2011, he was inducted into the American Academy of Arts and Sciences. He was elected as an ACM Fellow in 2019 "for contributions to quantum-computing, information theory, and randomized algorithms". He was elected as a member of the National Academy of Sciences in 2002. In 2020, he was elected a member of the National Academy of Engineering for pioneering contributions to quantum computation. In an interview published in Nature on October 30, 2020, Shor said that he considers post-quantum cryptography to be a solution to the quantum threat, although a lot of engineering effort is required to switch from vulnerable algorithms. Along with three others, Shor was awarded the 2023 Breakthrough Prize in Fundamental Physics for "foundational work in the field of quantum information."

Personal life Through his father, S. W. Williston Shor, he is a descendant of Samuel Wendell Williston.

See also Entanglement-assisted classical capacity Keller's conjecture Stabilizer code Quantum capacity

Notes

External links Peter W. Shor at DBLP Bibliography Server . Peter Shor's Home Page at MIT. Quantum Computing Expert Peter Shor Receives Carnegie Mellon's 1998 Dickson Prize in Science. Peter Williston Shor at the Mathematics Genealogy Project Peter Shor's results at International Mathematical Olympiad The story of Shor's algorithm — Youtube. Lectures and panels

Video of "Harnessing Quantum Physics", Peter Shor's panel discussion with Ignacio Cirac, Michele Mosca, Avi Wigderson, Daniel Gottesman and Dorit Aharonov, at the Quantum to Cosmos festival

Illustrations

Worked examples

Example 1 — a first encounter with Peter Shor

Start with the simplest possible case. Write down what Peter Shor claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Peter Shor before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Peter Shor ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Peter Shor

In research: Peter Shor appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Peter Shor in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Peter Shor is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 20th-century American engineers, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Shor outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Peter Shor in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Peter Shor means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Peter Shor out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Peter Shor in simple terms?

Why does Peter Shor matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Peter Shor?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Peter Shor.