mathematics

Tian Gang

Tian Gang 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 Tian Gang rather than just read about it. In short: Tian Gang (Chinese: 田刚; pinyin: Tián Gāng; born November 24, 1958) is a Chinese mathematician known for his contributions to the mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis. He is a professor of mathematics at Peking University and the Higgins Professor Emeritus at Princeton University.

Key takeaways

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

Reference excerpt

Tian Gang (Chinese: 田刚; pinyin: Tián Gāng; born November 24, 1958) is a Chinese mathematician known for his contributions to the mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis. He is a professor of mathematics at Peking University and the Higgins Professor Emeritus at Princeton University. As of 2020, he is the Vice Chairman of the China Democratic League and the President of the Chinese Mathematical Society. From 2017 to 2019 he served as the Vice President of Peking University.

Biography Tian was born in Nanjing, Jiangsu, China, on November 24, 1958. In 1978, after the Cultural Revolution, he qualified in the second Gaokao exam. He graduated from Nanjing University with a Bachelor of Science in mathematics in 1982, earned a Master of Science in mathematics from Peking University in 1984, and earned his Ph.D. in mathematics from Harvard University in 1988 under the supervision of Shing-Tung Yau. In 1998, he was appointed as a Cheung Kong Scholar professor at Peking University. Later his appointment was changed to Cheung Kong Scholar chair professorship. He was a professor of mathematics at the Massachusetts Institute of Technology from 1995 to 2006 (holding the chair of Simons Professor of Mathematics from 1996). His employment at Princeton started from 2003, and was later appointed the Higgins Professor of Mathematics. Starting 2005, he has been the director of the Beijing International Center for Mathematical Research (BICMR); from 2013 to 2017 he was the Dean of School of Mathematical Sciences at Peking University. He and John Milnor are Senior Scholars of the Clay Mathematics Institute (CMI). In 2011, Tian became director of the Sino-French Research Program in Mathematics at the Centre national de la recherche scientifique (CNRS) in Paris. In 2010, he became scientific consultant for the International Center for Theoretical Physics in Trieste, Italy. Tian has served on many committees, including for the Abel Prize and the Leroy P. Steele Prize. He is a member of the editorial boards of many journals, including Advances in Mathematics and the Journal of Geometric Analysis. In the past he has been on the editorial boards of the Annals of Mathematics and the Journal of the American Mathematical Society. Among his awards and honors:

Sloan Research Fellowship (1991-1993) Alan T. Waterman Award (1994) Oswald Veblen Prize in Geometry (1996) Elected to the Chinese Academy of Sciences (2001) Elected to the American Academy of Arts and Sciences (2004) Since at least 2013 he has been heavily involved in Chinese politics, serving as the Vice Chairman of the China Democratic League, the second most populous political party in China.

Mathematical contributions

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Tian Gang

Start with the simplest possible case. Write down what Tian Gang 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 Tian Gang 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 Tian Gang 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 Tian Gang

In research: Tian Gang 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 Tian Gang 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: Tian Gang is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1958 births, 20th-century Chinese mathematicians, 21st-century Chinese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Tian Gang 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 Tian Gang in 20 minutes

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

Frequently asked questions

What is Tian Gang in simple terms?

Why does Tian Gang 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 Tian Gang?

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 Tian Gang.