Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

August 4, 2023

Hoàng Xuân Sính’s Thesis

Posted by John Baez

During the Vietnam war, Grothendieck taught math to the Hanoi University mathematics department staff, out in the countryside. Hoàng Xuân Sính took notes and later did a PhD with him — by correspondence, under very difficult conditions!

I wrote about this here a while back, and on that basis got invited to contribute a paper to a volume in honor of her 90th birthday. Here’s a draft:

I’d love corrections or suggestions.

I’m trying to minimize the technical details but still give a sense of what she actually did in her thesis. So, besides explaining some of the history, I’m also trying to give a gentle introduction to 2-groups. That’s why I’m not taking a very sophisticated point of view…. or at least that’s my excuse.

There are a lot of historical puzzles here, and I wish I had a time machine to investigate them, or at least a year or two to interview people.

Posted at August 4, 2023 5:36 PM UTC

TrackBack URL for this Entry:   https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/3483

3 Comments & 0 Trackbacks

Poem for Madame Hoang

As this is tangentially about Grothendieck, I thought it might be appropriate to share a poem I wrote as an eulogy for Grothendieck when he passed away. And then I had the brighter idea to write a poem for Madame Hoang’s birthday - it seemed much more appropriate.


Hoang’s Song


Avoid myth, avoid illusion

Seek the real, seek the authentic


Even in ruins

Even in fiery carnage


Where once bamboo groves swayed

In monsoon squalls

Where once bamboo villages filled

With the laughter of children


The sky, once a river of rain

Or a haze of quiet summer heat

Where dragon flies dream

Is now a river of fire, of flame


They aim to enslave us

But we will not be enslaved

They aim to starve us

But we will not be swayed


A drop of rain can chisel a cliff

And a small chisel in the right place

Can crack open a mountain

And the stars are cracks in heavens night

That let the far distant light in

Such splendid light that enchanted

Those watchers of the skies above

And the skies within and without


I read by the light of a kerosene lamp

Sometimes sooty black the light by which

The crystal realm is illuminated is inscribed

A spiral pirouettes on a pole and threads

An axis and dances the spheres

Hieroglyphs that reveal the crystal contours

The beat of a drum that tattoos the pattern


These are distant peaks that few see

But here, the water runs as natural

As water falls elsewhere


It cleans and it nourishes


Seek myth, and be a myth maker

Seek the real, and make new realities

A pebble dropped into a middle of an ocean

Can rock the whole ocean.


We are descendents of the dragon

And our swords are carved whole from jade

And do not fade even in the fading evening light


And I am dragon’s daughter

And my dragon’s eyes

Sees into the depths of all things

Posted by: Mozibur Rahman Ullah on August 10, 2023 7:26 AM | Permalink | Reply to this

Re: Hoàng Xuân Sính’s Thesis

Great article! What a cool story on the human side, and involving some very nice math too!

Isn’t your definition of symmetric monoidal category on page 12 missing S x,yS y,x=1S_{x,y} \circ S_{y,x} = 1?

… and that reminds me of a question I don’t know the answer to: the definition I’ve seen of braided monoidal category has two hexagons, do you need both? In other words, is the definition on page 12 a definition of braided monoidal category?

Posted by: Omar Antolín-Camarena on August 11, 2023 11:46 PM | Permalink | Reply to this

Re: Hoàng Xuân Sính’s Thesis

Oh-oh! The definition of symmetric monoidal category definitely needs S x,yS y,x=1S_{x,y} \circ S_{y,x} = 1. If I left that out, I need to put it in.

The definition of braided monoidal category needs two hexagon equations, but the definition of symmetric monoidal category only needs one, since S x,yS y,x=1S_{x,y} \circ S_{y,x} = 1 lets you get either hexagon from the other one. That’s why I put in only one hexagon—I wasn’t trying to get into braided monoidal categories, since those came historically later.

Posted by: John Baez on August 12, 2023 10:09 AM | Permalink | Reply to this

Post a New Comment