mathematics

Noam Elkies

Noam Elkies 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 Noam Elkies rather than just read about it. In short: Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At age 26, he became the youngest professor to receive tenure at Harvard.

Key takeaways

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

Reference excerpt

Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At age 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist, chess national master, and chess composer.

Early life and education Elkies was born to an engineer father and a piano teacher mother. He attended Stuyvesant High School in New York City for three years before graduating in 1982 at age 15. A child prodigy, in 1981, at age 14, Elkies was awarded a gold medal at the 22nd International Mathematical Olympiad, receiving a perfect score of 42, one of the youngest to ever do so. He went on to Columbia University, where he won the Putnam competition at age 16 and four months, making him one of the youngest Putnam Fellows in history. Elkies was a Putnam Fellow twice more during his undergraduate years. He graduated valedictorian of his class in 1985. He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harvard University. From 1987 to 1990, Elkies was a junior fellow of the Harvard Society of Fellows.

Work in mathematics In 1987, Elkies proved that an elliptic curve over the rational numbers is supersingular at infinitely many primes. In 1988, he found a counterexample to Euler's sum of powers conjecture for fourth powers. His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990. In 1993, Elkies was made a full, tenured professor at age 26. This made him the youngest full professor in Harvard's history. He and A. O. L. Atkin extended Schoof's algorithm to create the Schoof–Elkies–Atkin algorithm. Elkies also studies the connections between music and mathematics; he is on the advisory board of the Journal of Mathematics and Music. He has discovered many new patterns in Conway's Game of Life and has studied the mathematics of still life patterns in that cellular automaton rule. Elkies is an associate of Harvard's Lowell House. Elkies is one of the principal investigators of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a large multi-university collaboration involving Boston University, Brown, Dartmouth, Harvard, and MIT. Elkies is the discoverer (or joint-discoverer) of many current and past record-holding elliptic curves, including the curve with the highest-known lower bound (≥28) on its rank, and the curve with the highest-known exact rank (=20). In August 2024, he posted to a number theory listserv that he and Zev Klagsbrun had found an elliptic curve of rank at least 29 by methods similar to those used to find the rank 28 example.

Music Elkies is a bass-baritone and formerly played the piano for the Harvard Glee Club. Jameson N. Marvin, former director of the Glee Club, compared him to "a Bach or a Mozart", citing his "gifted musicality, superior musicianship and sight-reading ability". He rings the bells of Lowell House.

Chess Elkies is a composer and solver of chess problems (winning the 1996 World Chess Solving Championship). One of his problems appears in the chess trainer Mark Dvoretsky's book Dvoretsky's Endgame Manual. Elkies holds the title of National Master from the United States Chess Federation, but no longer plays competitively.

Awards and honors In 1994, Elkies was an invited speaker at the International Congress of Mathematicians in Zürich. In 2004, he received a Lester R. Ford Award and the Levi L. Conant Prize. In 2017, Elkies was elected to the National Academy of Sciences.

References

External links

Personal site of Noam Elkies at Harvard University Endgame Explorations – an 11-part series of articles by Noam Elkies in Chess Horizons

Illustrations

Worked examples

Example 1 — a first encounter with Noam Elkies

Start with the simplest possible case. Write down what Noam Elkies 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 Noam Elkies 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 Noam Elkies 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 Noam Elkies

In research: Noam Elkies 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 Noam Elkies 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: Noam Elkies is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1966 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Noam Elkies 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 Noam Elkies in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Noam Elkies 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 Noam Elkies out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Noam Elkies in simple terms?

Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At age 26, he became the youngest professor to receive tenure at Harvard.

Why does Noam Elkies 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 Noam Elkies?

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 Noam Elkies.