Category: Mathematics


A good year for Robert Langlands

I just saw that Robert Langlands has won this year’s Abel Prize in mathematics. A month back I had noted that two University of Chicago mathematicians –Sasha Beilinson and Vladimir Drinfeld — had received the Wolf prize for work that builds upon Langlands’ ideas.

What are those ideas? Langlands has spent his life looking for connections between number theory and real analysis. The featured image is a rendering of an automorphic form, one of the kinds of functions that Langlands has been interested in. As far as I could understand, Beilinson and Drinfeld found ways of connecting this work to modern physics. Maybe a deeper understanding is my goal for 2018. This Quartz article is a good quick read as is this short piece on the fundamental lemma.

Or, you can let the distinguished Dr Langlands explain it himself.

Whether or not you have a liking for numbers, seeing an 81 year old still in the thick of things is infectiously inspiring. Perhaps you’ll allow him to re-acquaint you with Pythagorus?

I feel such a blessing to have the optimistic spirit of my 80-something mother still present to bring uplift, laughter, and fresh greens from the garden to us — all served with divinely channeled love.  I think of the many 70+ year olds who passionately hold the world accountable,  try to make a difference with their material success, fathom prime numbers like Langlands, weave saxophone melodies, and make the world a beautiful place with their wisdom and selflessness. Spring persists in the garden of the ageless mind. I’ll leave you with some Sonny Rollins


The geometrical beauty of Doha

As we passed through Doha on the way to Gaborone, I was amazed by the architectural beauty of so many Islamic inspired structures. It was truly a feast for the eyes and mind.

Though we did not have time to visit many of the older architectural treasures, I discovered that a lot of the buildings have received prestigious architectural awards over the last decade. The investment of Qatar in its country is amazing, and Al Jazeera is a gift to humanity.

There is even wonder in the Qatar airways “air sickness” bags!



The Wolf prize mathematicians outside my nook

Yesterday  I came across a photo of two gentlemen sitting outside of my old grad-school student lounge. They are Sasha Beilinson and Vladimir Drinfeld, two mathematicians from my alma mater who were awarded this year’s Wolf Prize in Mathematics.

The CS department at the University of Chicago shared space with Mathematics and Statistics in my day, so it was not unusual to encounter mathematicians while having lunch (or a nap) in the lounge. There have been many useful collaborations and intersections between these departments.

I have no idea what Sasha or Vladimir do. I tried to understand. I glanced at their ground breaking work, a book called Chiral algebras. They state in the introduction “Chiral algebras have their origin in mathematical physics;” and “Chiral algebras are “quantum” objects.” Ok.

Drinfeld and Beilinson still run the Geometric Langlands Seminar that of course captures the essence of what they care about most. As best I can figure, Langlands, himself a 1996 Wolf prize recipient, is a mathematician who envisioned building links between algebra and modern physics. Drinfeld and Beilinson have extended that work. Maybe the best explanation of this undertaking is provided by Edward Frenkel.

He seems to be a celebrity in his own right. I enjoyed how he connects Solaris to universals of number theory!

If Frenkel is still too abstract for you, then Mitya Boyarchenko suggests that this poem that I include below might be of use in understanding the Langlands talks


A man called Pakhomych, shaking as he rode on the carriage footboards,

Carried a bunch of forget-me-nots.

He got corn on his heels,

And treated them at home with camphor.

Reader! Having discarded the fable’s forget-me-nots,

Which were put here as a joke,

You can arrive at only a single conclusion:

If you get corns

And you want to rid yourself of the pain,

You, like our friend Pakhomych,

Should treat them with camphor.


MathematicsPoliticsSocial Justice

Mathematicians, rock the vote!

Can the resistance inspire a new generation of mathematicians?

Samuel Hansen thinks so. In his recent post on The Aperiodical, he describes how the recent avalanche of math-informed court decisions on gerrymandering in Pennsylvania and elsewhere are putting mathematics in the spotlight.

It is really heartening that discrete geometry and other branches of advanced mathematics can be use to preserve democracy — much in the spirit of the 1964 voting rights act (being signed in the featured image).

Tufts University mathematician Moon Duchin has done a lot of work in this area, leading the effort to train mathematicians to be expert witnesses in gerrymandering cases. Duchin’s Metric Geometry and Gerrymandering Group page has a lot of useful resources.

Consider registering for one of the gerrymandering trainings if you’re a mathematician, statistician, or data scientist based in the Bay Area!


HistoryinclusionMathematicsPoliticsSocial Justice

Black history month is Black mathematicians month — in the UK

In the US, the African American scholar (and February 1st Google doodle subjectCarter G Woodson began working in 1926 to establish “Negro History Week“, for in Woodson’s day the contributions of Black people were  “overlooked, ignored, and even suppressed by the writers of history textbooks and the teachers who use them.” Woodson’s Negro History week evolved into today’s US Black History Month thanks to the efforts of student activists of the 1970s.

My partner, Dr Gayatri Sethi, reminds me that the aspiration of marginalized and minoritized peoples to be heard, to enter into equity in whatever place they call home is universal.

With that in mind, it is no surprise then that Black History month has been celebrated in the UK for the last 30 years in October. This October a group of mathematicians at University College London — and  — decided to make October Black Mathematicians month.

During the month they presented interviews with UK mathematicians starting with Dr Nazar Miheisi who does research in Analysis at King’s College. The Aperiodical blog also ran pieces highlighting Black mathematicians, among them Dr Caleb Ashley who gives this Numberphile segment on the fifth postulate.

Building an equitable mathematics community, or better yet an equitable world, should not be confined to a single month — it is an undertaking that will require continuous and deliberate effort. But it is encouraging and inspiring to see many hopeful signs on a global scale.

Do you know of similar efforts in other countries to encourage the participation of marginalized peoples in science and mathematics? If so, please leave a comment or drop an email!