Math can be hard even for very smart people

50 McCosh Hall an autumn evening in 1956. The place was packed. Chen Ning Yang was speaking about parity violation. Most of the people there had little idea (including me) of what he did, but wanted to be eyewitnesses to history.. But we knew that what he did was important and likely to win him the Nobel (which happened the following year).

That’s not why Yang is remembered today (even though he’s apparently still alive at 98). Before that he and Robert Mills were trying to generalize Maxwell’s equations of electromagnetism so they would work in quantum mechanics and particle physics. Eventually this led Yang and Mills to develop the theory of nonAbelian gauge fields which pervade physics today.

Yang and James Simons (later the founder of Renaissance technologies and already a world class mathematician — Chern Simons theory) later wound up at Stony Brook. Simons, told him that gauge theory must be related to connections on fiber bundles and pointed him to Steenrod’s The Topology of Fibre Bundles. So he tried to read it and “learned nothing. The language of modern mathematics is too cold and abstract for a physicist.”

Another Yang quote “There are only two kinds of math books: Those you cannot read beyond the first sentence, and those you cannot read beyond the first page.”

So here we have a brilliant man who invented significant mathematics (gauge theory) along with Mills, unable to understand a math book written about the exact same subject (connections on fiber bundles).

Two Christmas Presents

Two Christmas presents for you.  Yes Christmas presents.  I refuse to be culturally castrated by the professionally aggrieved.

The first is a link to a great scientific website — https://www.quantamagazine.org. It’s primarily about math and physics, with some biology thrown in. Imagine the News and Views section of Nature or the Perspectives section of Science on steroids.

Quanta is an editorially independent division of the Simons Foundation. And what is that you enquire? It is the answer to “If you’re so smart, why ain’t you rich”. Jim Simons is both much smarter and much richer than you and I. You can read more about him in a book I’m about to review on the blog — “The Physics of Wall Street”

Simons was a very accomplished mathematician winning prizes with a friend James Ax in the 60’s and 70’s — not quite the Fields Medal but up there. The Simons Chern 3 form is part of string theory. The two founded Renaissance Technologies in the late 80’s a stock fund using mathematical techniques to beat the market. And beat it they did, averaging 40% a year (after fees which were hefty). Even in the most recent market blowout in 2008 they were up 80% for the year. The firm employs about 200 people, mostly mathematicians and physicists. It was described by an MIT math prof as ‘the best mathematics and physics department in the world”.

At any rate after becoming a multibillionaire, Simons established his foundation, of which Quanta is a small part. It’s very good, with some heavies writing for it — such as Ingrid Daubechies full prof of math at Princeton who did a good deal of the early work on wavelets.

I haven’t read it all but the math is incredible, mostly about the latest and greatest new results and why it is important placing it in context. Physics isn’t forgotten, and the lead article concerns the philosophy of science and how it’s a’changin’ a la string theory, which is light years away from an experimental test of any of it.

Your second Christmas present is a Joke

The pope visited Colorado 22 years ago. A little known fact about him is that he loved to drive. Although Colorado is famed for the Rockies, the eastern half is high plains, so flat that you can see Pike’s peak from 100 miles away across the plains. At any rate the pope was being driven by his chauffeur from Colorado Springs to Denver on the Interstate, when the pope asked if he could drive. “Only if we go out on the plains where no one will see you” said the chauffeur.

So they switched when they got about 30 miles out in the middle of nowhere with the pope driving and the chauffeur in the back seat both behind tinted opaque windows. The pope started driving, really enjoying it, going faster and faster. He got up to 85 when a state trooper pulled them over.

Where’s the fire saith the trooper. He blanched when the driver’s window came down and he saw who was driving, and called headquarters. Arrest him came the answer. The trooper said I’m not sure, this guy is very big. I don’t care how big he is, arrest him. Are you sure. Yes.

I dunno boss, this guy is so big he’s got the pope driving for him.

Merry Christmas and Happy New Year to all