Richard Shore

Key takeaways

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

Reference excerpt

Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at Cornell University who works in recursion theory. He is particularly known for his work on D {\displaystyle {\mathcal {D}}} , the partial order of the Turing degrees.

Shore settled the Rogers homogeneity conjecture by showing that there are Turing degrees a {\displaystyle a} and b {\displaystyle b} such that D a {\displaystyle {\mathcal {D}}_{a}} and D b {\displaystyle {\mathcal {D}}_{b}} , the structures of the degrees above a {\displaystyle a} and b {\displaystyle b} respectively, are not isomorphic. In joint work with Theodore Slaman, Shore showed that the Turing jump is definable in D {\displaystyle {\mathcal {D}}} .

Career He was, in 1983, an invited speaker at the International Congress of Mathematicians in Warsaw and gave a talk The Degrees of Unsolvability: the Ordering of Functions by Relative Computability. In 2009, he was the Gödel Lecturer (Reverse mathematics: the playground of logic). He was an editor from 1984 to 1993 of the Journal of Symbolic Logic and from 1993 to 2000 of the Bulletin of Symbolic Logic. In 2012, he became a fellow of the American Mathematical Society.

References

External links Cornell Math - Richard A. Shore. Richard Shore at the Mathematics Genealogy Project MathSciNet - Richard A. Shore

Illustrations

Worked examples

Example 1 — a first encounter with Richard Shore

Start with the simplest possible case. Write down what Richard Shore 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 Richard Shore 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 Richard Shore 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 Richard Shore

In research: Richard Shore 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 Richard Shore 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: Richard Shore is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Shore 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.

How to study Richard Shore in 20 minutes

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

Frequently asked questions

What is Richard Shore in simple terms?

Richard Arnold Shore (born August 18, 1946) is a professor of mathematics at Cornell University who works in recursion theory. He is particularly known for his work on D {\displaystyle {\mathcal {D}}} , the partial order of the Turing degrees.

Why does Richard Shore 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 Richard Shore?

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 Richard Shore.