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Former NFL Player Proves a Maths Conjecture — episode cover art
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NFL球员不打球了,去解数学难题

Former NFL Player Proves a Maths Conjecture

About this story

HSK 5 Chinese listening. Former NFL player John Urschel becomes a mathematician and proves a longstanding conjecture about random matrices.

This is an HSK 5-6 Chinese listening episode that runs about 2 minutes. The full Mandarin script is shown with tap-for-pinyin and a line-by-line English translation, so you can listen and read at once — comprehensible input in the sense of Stephen Krashen's i+1 theory. It teaches 12 key vocabulary words such as 已经、方法、数字 and walks through 4 grammar patterns, each explained in English with examples. The same news story is retold at 4 difficulty levels — use the level selector above to find the version that is challenging but still understandable for you.

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原文

Read the complete story in Chinese. Reveal pinyin and English only when you need them.

John Urschel曾经打职业橄榄球,现在在MIT做数学研究,最近证明了一个几十年的猜想。
他在Baltimore Ravens打了三年球,不过数学,在他的职业体育生涯之前,就已经很重要。
在二〇一四年被选进NFL时,John Urschel已经拿到数学硕士学位。
在二〇一六年,他一边打球,一边去MIT学习,却几乎没有时间陪女朋友。
后来,他觉得这样的安排不好,两个事业,都需要时间。
在二〇一七年,John Urschel退役,决定全身心学习数学。
四年后,他拿到博士学位,又过两年,回到MIT成为助理教授。
最近的论文,研究的是随机矩阵,矩阵就是把数字排成几行几列的表。
高斯消元法,是一种解方程组的方法,计算机也经常使用,计算过程中,表里的数字会改变。
增长因子衡量的是,消元过程中,数字能变得多大,这关系到计算的稳定性。
John Urschel证明,对于高斯随机矩阵,在采用部分选主元的消元方法时,增长因子很少远大于矩阵维数的平方根。
这解决了数学家特雷费森,早年提出的猜想,范围是一类随机矩阵,和特定的计算方法。
它不等于,所有电脑计算的误差问题,都已经解决。
论文公开在预印本网站,致谢也提到,OpenAI模型给过帮助。
John Urschel说,他想理解事情背后的原因,人工智能不会破坏,这种做数学的兴趣。
就像电脑下棋很强,人仍然喜欢自己找下一步,数学对他,也有这样的乐趣。
如果你有一份很好的工作,可是心里想做别的事,你会在什么情况下,决定换一条路?
English transcript reference

John Urschel used to play professional football, and now does mathematics research at MIT, and recently proved a conjecture that had stood for decades.

He played football for the Baltimore Ravens for three years, but mathematics was already very important before his professional sports career.

When he was selected into the NFL in 2014, John Urschel had already earned a master's degree in mathematics.

In 2016, he was playing football while also studying at MIT, yet he had almost no time to spend with his girlfriend.

Later, he felt that this arrangement was not good, because two careers both need time.

In 2017, John Urschel retired and decided to devote himself entirely to studying mathematics.

Four years later, he received his doctorate, and two years after that, he returned to MIT to become an assistant professor.

His recent paper studies random matrices; a matrix is a table that arranges numbers into rows and columns.

Gaussian elimination is a method for solving systems of equations, and computers also often use it; during the calculation, the numbers in the table change.

The growth factor measures how large the numbers can become during the elimination process, and this relates to the stability of the computation.

John Urschel proved that for Gaussian random matrices, when using elimination with partial pivoting, the growth factor is rarely much larger than the square root of the matrix dimension.

This solved a conjecture proposed early on by the mathematician Trefethen, covering a class of random matrices and a specific computational method.

It does not mean that all error problems in computer calculations have already been solved.

The paper is publicly available on a preprint website, and the acknowledgements also mention that an OpenAI model provided help.

John Urschel says he wants to understand the reasons behind things, and artificial intelligence will not destroy this interest in doing mathematics.

Just as computers are very strong at chess, people still like to find the next move themselves; mathematics also gives him this kind of pleasure.

If you have a very good job, but in your heart you want to do something else, under what circumstances would you decide to change to a different path?

Listen again

Try it without the transcript and notice what sounds clearer.

What vocabulary does this episode teach?

词汇
yǐjīngalready

HSK 2. Used before a verb or adjective to indicate that an action or state has already happened. In the script: 已经拿到数学硕士学位.

fāngfǎmethod; way

HSK 3. A common noun for a way of doing something. In the script: 一种解方程组的方法.

shùzìnumber; digit

HSK 3. Refers to numerals or numerical data. In the script: 表里的数字会改变.

diànnǎocomputer

HSK 3. Common word for computer. In the script: 计算机也经常使用 and 电脑下棋很强.

xuéxíto study; to learn

HSK 1. To gain knowledge or skill through study. In the script: 决定全身心学习数学.

jiějuéto solve; to resolve

HSK 3. To find a solution to a problem. In the script: 这解决了数学家特雷费森早年提出的猜想.

yánjiūto research; research

HSK 3. To study something carefully to discover facts. In the script: 现在在MIT做数学研究.

juédìngto decide; decision

HSK 3. To make a choice after consideration. In the script: 决定全身心学习数学.

zhèngmíngto prove; proof

HSK 4. To show that something is true with evidence or logic. In the script: 最近证明了一个几十年的猜想.

guòchéngprocess; course

HSK 4. The series of steps taken to achieve something. In the script: 计算过程中,表里的数字会改变.

jǔzhènmatrix

Beyond HSK. A rectangular array of numbers or symbols. In the script: 研究的是随机矩阵.

Gāosī xiāoyuánfǎGaussian elimination

Beyond HSK. An algorithm for solving systems of linear equations. In the script: 高斯消元法,是一种解方程组的方法.

* beyond level超纲词

What grammar patterns appear in this episode?

语法

一边……一边……

Expresses two actions happening at the same time. It links two verb phrases.

在二〇一六年,他一边打球,一边去MIT学习,却几乎没有时间陪女朋友。

在……时

Marks a specific time or occasion when something happens. It is equivalent to 'when...' or 'at the time of...'.

在二〇一四年被选进NFL时,John Urschel已经拿到数学硕士学位。

对于……

Introduces the object or topic being discussed, meaning 'regarding' or 'for'.

John Urschel证明,对于高斯随机矩阵,在采用部分选主元的消元方法时,增长因子很少远大于矩阵维数的平方根。

如果……,会……

A conditional pattern: 'if..., then (one) will...'. It sets up a hypothetical situation and its consequence.

如果你有一份很好的工作,可是心里想做别的事,你会在什么情况下,决定换一条路?

Proper nouns

专有名词
John UrschelJohn UrschelJohn UrschelMITMITMITBaltimore RavensBaltimore RavensBaltimore RavensNFLNFLNFL特雷费森TèléifèisēnTrefethenOpenAIOpenAIOpenAI

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