Breakfast Notes #21 (Prodigies, China, Math Fights)

Good morning friends. This is my 21st Breakfast Notes.

Here is my 'fortune cookie' quote of the week from William Kingdon Clifford, the English mathematician and philosopher on justice in the public square.

However convinced you were of the justice of your cause and the truth of your convictions, you ought not to have made a public attack upon any man’s [or person’s] character until you had examined the evidence on both sides with the utmost patience and care.

Even Prodigies Fail

Terence Tao was a child prodigy who started attending university-level mathematics courses at 9. Tao has been the author or co-author of over three hundred fifty research papers and has achieved an Erdos number of 2.

He is widely regarded as one of the greatest living mathematicians.

Charles Fefferman, another prodigy who achieved a full professorship at the University of Chicago at the age of 22,  the youngest full professor ever appointed in the United States, said this of him,

If you're stuck on a problem, then one way out is to interest Terence Tao.

In this essay, Terence Tao candidly shares how his genius harmed him. Given how easy mathematics came to him, he did not cultivate good study habits nor take studying seriously. This came to cost Terence as he came to pass his exams by the skin of his teeth. He had performed poorly on an exam that he was genuinely interested in performing well in for the first time.

This failure to live up to his talent served as a wake-up call to get his act together, which, unsurprisingly, marked the first chapter of his rise to superstardom in Mathematics.

Terence is a genius; hence, the standard for people like him should be much higher. Imagine crushing it at nine years old in university-level math and struggling to pass your PhD general exams; this would be considered a failure for him.

My takeaway is that failures can act as an incredible object lesson to force us to confront our shortcomings.

China's Impressive Economy

People always talk about how impressive the Chinese economy is, but how big is it exactly? Here are three indicators.

• China's Singles Day (11/11) Gross Merchandise Value is close to $30 billion (USD) more than American sales for Prime Friday, Black Friday, Cyber Monday and Thanksgiving weekend combined.
• Despite having a zero-COVID policy, China's GDP grew by 8.1% in 2021. What makes it more impressive was China grew at 2.3% in 2020 and was the only major economy to report economic growth for 2020.
• As of 2021, China was home to the largest companies in the Fortune Global 500, and for the first time, there are more Fortune Global 500 companies based in Mainland China and Hong Kong than in the U.S.–124 vs 121.

Visualization Of The Day

The U.S., China, Japan, and Germany—constitute half of the world's GDP. US GDP comes in at close to one-quarter of the world GDP, and China comes in close at 18%.

The Math Fight of the 17th Century

When we think of the Enlightenment, we conjure images of scientists working harmoniously and co-operating to advance humans to the next frontier of human possibility. We imagine white gentlemen in their wigs and monocles, smoking pipes and scribbling mathematical equations furiously on parchments of papers together.

What if that's just our wishful thinking?

In the early 1700s, the calculus controversy broke out. The heated argument of the day was who invented calculus? Was it Isaac Newton or Gottfried Wilhelm Leibniz?

The German polymath Leibniz had first published his work on differential and integral calculus, but Newton's supporters accused Leibniz of plagiarizing Newton's unpublished ideas. However, Leibniz insisted his work was 100% original.

The prevailing opinion in the 18th century was against Leibniz, and in 1716, he died a downtrodden man. Falling out of favour with his patrons, neither King George I of Great Britain nor any fellow courtier attended the funeral.

Although he was a life member of the Royal Society and the Berlin Academy of Sciences, neither organization honoured his death. His body rested in an unmarked grave for fifty years. His grave went unmarked for more than 50 years.

Today's modern consensus is that Leibniz and Newton independently invented and described calculus in Europe.

Whenever I recall this story, I can't help but marvel at how often we re-imagine history for our convenience and how much time Leibniz wasted to prove to critics he was not a plagiarizer, and even yet, he failed.

May The Sun Shine Upon Your Face,

Keith