mathematics

Ruth Lawrence

Ruth Lawrence 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 Ruth Lawrence rather than just read about it. In short: Ruth Elke Lawrence-Neimark (Hebrew: רות אלקה לורנס-נאימרק; born 2 August 1971) is a British-Israeli mathematician and a professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. In the public eye, she is best known for having been a child prodigy in mathematics.

Key takeaways

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

Reference excerpt

Ruth Elke Lawrence-Neimark (Hebrew: רות אלקה לורנס-נאימרק; born 2 August 1971) is a British-Israeli mathematician and a professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. In the public eye, she is best known for having been a child prodigy in mathematics. In 2012, she became a fellow of the American Mathematical Society.

Early life Ruth Lawrence was born in Brighton, England, and raised in Huddersfield, West Yorkshire. Her parents, Harry Lawrence and Sylvia Greybourne, were both computer consultants. When Lawrence was five, her father gave up his job so that he could educate her at home. She is Jewish.

Education At the age of nine, Lawrence gained an O-level in mathematics, setting a new age record (later surpassed in 2001 when Arran Fernandez successfully sat GCSE mathematics aged five). Also at the age of nine she achieved a Grade A at A-level pure mathematics. In 1981, Lawrence passed the University of Oxford entrance examination in mathematics, joining St Hugh's College in 1983 at the age of 12. At Oxford, her father continued to be actively involved in her education, accompanying her to all lectures and some tutorials. Lawrence completed her bachelor's degree in two years, instead of the normal three, and graduated in 1985 at the age of 13 with a congratulatory first and special commendation. Attracting considerable press interest, she became the youngest British person to gain a first-class degree, and the youngest to graduate from the University of Oxford in modern times. Lawrence followed her first degree with a bachelor's degree in physics in 1986 and a Doctor of Philosophy (DPhil) degree in mathematics at Oxford in June 1989, at the age of 17. Her doctoral thesis title was Homology representations of braid groups and her thesis adviser was Sir Michael Atiyah.

Academic career Lawrence and her father moved to America for Lawrence's first academic post, which was at Harvard University, where she became a junior fellow in 1990 at the age of 19. In 1993, she moved to the University of Michigan, where she became an associate professor with tenure in 1997. In 1998, Lawrence married Ariyeh Neimark, a mathematician at the Hebrew University of Jerusalem, and adopted the name Ruth Lawrence-Neimark. The following year, she moved to Israel with him and took up the post of associate professor of mathematics at the Einstein Institute of Mathematics, a part of the Hebrew University of Jerusalem.

Research Lawrence's 1990 paper "Homological representations of the Hecke algebra", in Communications in Mathematical Physics, introduced, among other things, certain novel linear representations of the braid group – known as Lawrence–Krammer representations. In papers published in 2000 and 2001, Daan Krammer and Stephen Bigelow established the faithfulness of Lawrence's representation. This result goes by the phrase "braid groups are linear."

Awards and honours In 2012, she became a fellow of the American Mathematical Society.

Selected publications Griniasty, Itay; Lawrence, Ruth (2019). "An explicit symmetric DGLA model of a triangle". Higher Structures. 3 (1): 1–16. arXiv:1802.02795. doi:10.21136/HS.2019.01. MR 3939044. Lawrence, Ruth; Sullivan, Dennis (2014). "A formula for topology/deformations and its significance". Fundamenta Mathematicae. 225 (1): 229–242. arXiv:math/0610949. doi:10.4064/fm225-1-10. MR 3205571. Lawrence, R. J. (1990). "Homological representations of the Hecke algebra". Communications in Mathematical Physics. 135 (1): 141–191. Bibcode:1990CMaPh.135..141L. doi:10.1007/BF02097660. MR 1086755. Lawrence, Ruth; Zagier, Don (1999). "Modular forms and quantum invariants of 3-manifolds". Asian Journal of Mathematics. 3 (1): 93–107. doi:10.4310/AJM.1999.v3.n1.a5. MR 1701924. Lawrence, Ruth; Rozansky, Lev (1999). "Witten-Reshetikhin-Turaev invariants of Seifert manifolds". Communications in Mathematical Physics. 205 (2): 287–314. Bibcode:1999CMaPh.205..287L. doi:10.1007/s002200050678. hdl:2027.42/41998. MR 1712599.

References

External links Ruth Lawrence's home page at the Hebrew University of Jerusalem

Illustrations

Worked examples

Example 1 — a first encounter with Ruth Lawrence

Start with the simplest possible case. Write down what Ruth Lawrence 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 Ruth Lawrence 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 Ruth Lawrence 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 Ruth Lawrence

In research: Ruth Lawrence 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 Ruth Lawrence 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: Ruth Lawrence is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1971 births, 20th-century British mathematicians, 20th-century British women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ruth Lawrence 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 Ruth Lawrence in 20 minutes

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

Frequently asked questions

What is Ruth Lawrence in simple terms?

Why does Ruth Lawrence 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 Ruth Lawrence?

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 Ruth Lawrence.