mathematics

Zhu Xiping

Zhu Xiping 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 Zhu Xiping rather than just read about it. In short: Zhu Xiping (born 1962 in Shixing, Guangdong) is a Chinese mathematician. He is a professor of Mathematics at Sun Yat-sen University, China.

Key takeaways

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

Reference excerpt

Zhu Xiping (born 1962 in Shixing, Guangdong) is a Chinese mathematician. He is a professor of Mathematics at Sun Yat-sen University, China.

Poincaré conjecture In 2002 and 2003, Grigori Perelman posted three preprints to the arXiv claiming a resolution of the renowned Poincaré conjecture, along with the more general geometrization conjecture. His work contained a number of notable new results on the Ricci flow, although many proofs were only sketched and a number of details were unaddressed. Zhu collaborated with Huai-Dong Cao of Lehigh University in filling in the details of Perelman's work, along with reworking various elements. Their work, containing expositions of Perelman's work along with the foundational work of Richard Hamilton, was published in the June 2006 issue of the Asian Journal of Mathematics. Other notable expositions were released around the same time, one by John Morgan of Columbia University and Gang Tian of Princeton University, and the other by Bruce Kleiner of Yale University and John Lott of University of Michigan. Cao and Zhu later posted a version with revised wording to the arxiv, following criticism alleging that their original version claimed too much credit for themselves. They also published an erratum, as it had been found that one of the pages of their work was essentially identical to a page from a publicly available draft of Kleiner and Lott from 2003. They explained that they had taken down some notes from Kleiner and Lott's paper. When writing their exposition, they had failed to realize these particular notes' original source.

Morningside Medal In December 2004, Zhu won the Morningside Medal of Mathematics at the Third International Congress of Chinese Mathematicians (ICCM), a triennial congress hosted by institutions in Mainland China, Taiwan, and Hong Kong on a rotating basis. According to ICCM, "Awardees (of the Morningside Medal) are selected by a panel of international renowned mathematicians with the aim to encourage outstanding mathematicians of Chinese descent in their pursuit of mathematical truth."

Major publications Cao, Huai-Dong; Zhu, Xi-Ping (2006). "A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton–Perelman theory of the Ricci flow". Asian Journal of Mathematics. 10 (2): 165–492. doi:10.4310/ajm.2006.v10.n2.a2. MR 2233789. Zbl 1200.53057.– – (2006). "Erratum". Asian Journal of Mathematics. 10 (4): 663–664. doi:10.4310/AJM.2006.v10.n4.e2. MR 2282358.– – (2006). "Hamilton–Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture". arXiv:math/0612069.

References

Worked examples

Example 1 — a first encounter with Zhu Xiping

Start with the simplest possible case. Write down what Zhu Xiping 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 Zhu Xiping 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 Zhu Xiping 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 Zhu Xiping

In research: Zhu Xiping 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 Zhu Xiping 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: Zhu Xiping is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1962 births, 21st-century Chinese mathematicians, 21st-century Chinese science writers, so understanding it makes those chapters shorter.
In everyday life: Look for Zhu Xiping 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 Zhu Xiping in 20 minutes

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

Frequently asked questions

What is Zhu Xiping in simple terms?

Zhu Xiping (born 1962 in Shixing, Guangdong) is a Chinese mathematician. He is a professor of Mathematics at Sun Yat-sen University, China.

Why does Zhu Xiping 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 Zhu Xiping?

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 Zhu Xiping.