Resources for a new term from our vantage point

 Crop from Broad Institute src

Eric Lander has been appointed director of the US Office of Science and Technology Policy, a post newly elevated to Cabinet status. He is thus the top science advisor in Joe Biden’s cabinet.

Today we congratulate Eric, whom we both have known personally, and survey some sources of science advice at his career’s roots.

Peter Cameron, who was Eric’s doctoral advisor at Oxford University, says in his blog that:

I have had so many congratulatory emails that it almost seems as if I have done something good myself ${\dots}$

I found out about Eric’s appointment while working on this post. Eric is a longtime friend, who while not close is someone that I have always been impressed with. He is a mathematician who turned molecular biologist—we interacted when I worked on DNA computing. Eric previously worked closely with Biden during the Barack Obama presidency.

 Obama archives source (note Biden next to Obama at left, Lander across from Obama)

Ken found out first from reading his Princeton Class of 1981 news on Facebook. He says:

Eric was my Resident Advisor in Foulke Hall my freshman year, 1977–78. I originally had the ground-floor double room next to his, but I swapped roommates one door further down with another lover of mathematics and Broadway musicals. His RA group of 16 in the staircase included now-Justice Elena Kagan. Eric brought all of us down for meetings in the early weeks; blessing the roommate swap and discussing compatibility aspects in general was a subject of one of them. I got to Oxford just as Eric was leaving, and my first interaction with Peter Neumann was actually Neumann saying Eric had neglected to do something and could I get him in touch before he returned to the US? Kagan also came to Oxford along with three other ’81-ers whom I associated with more.

## A Wellspring of Advice

Eric did a swap himself his first weeks in Oxford. As Cameron relates in a followup post:

He arrived in Oxford on a Rhodes Scholarship to do research in algebraic topology. But before the term started, he had changed his mind and decided to do coding theory instead. By chance, it happened that I was the only person in Oxford at the time who claimed to know anything about coding theory. ${\dots}$ So I got to supervise Eric.

Peter had a good problem ready about how to combine two strands of applying design theory to codes.

Eric, with a good background in algebraic number theory, took to it immediately. The coding theorists had taken an integer matrix and considered its row space over the finite field with ${p}$ elements. Eric observed that, if instead you took the row space over the ${p}$-adic numbers, then you could reduce it modulo arbitrary powers of ${p}$, and get a chain of codes, with the property that duality reversed the order in the chain (so if the power of ${p}$ involved was odd then the code in the middle was self-dual).

Eric’s thesis took off from there, and at the end he turned it into a book with the title Symmetric Designs: An Algebraic Approach.

Of course, coding theory and “stringology” feed into genomics, and from there into the broad reach of science. Eric has no shortage of sources across the spectrum. But the wellspring of his career was our general area, not to mention that both of us followed him in several geographic and academic respects.

Many of our peer bloggers step out to give general advice on science. Some conspicuously often take their advice and recommendations on natural sciences openly national. Others address it within smaller communities, but their ideas can be equally valuable. All may be worthy of consultation.

## Blogs

The one rule we’re setting out now is that in order to be advising the advisor, the blogs must stay current. There are tons of terrific blogs that have stopped publishing altogether, or whose last new post is many moons ago. As for those who try to be reasonably current, Ken and I know how hard it is to do. So we took a three-week horizon—that is, who has posted something this year, 2021. That said, here are some of our favorite blogs on math and CS theory—after the first they are alphabetical by writer(s).

${\bullet }$ What’s New Terence Tao
The best math blog of all time. If you must read one, then this is the one. If you read two or more math blogs, then this is still the one. If you read two or more posts on this blog, then you qualify as a mathematician.

${\bullet }$ Shtetl Optimized Scott Aaronson
Wonderful blog. A brilliant combination of results, comments, and opinions. We have “encoded” his name in the previous section—see if you can spot where and how.

${\bullet }$ Machine Learning Research Blog Francis Bach
Focused on connections between optimization and learning. I conjecture that the key to solving some of our deep questions—P${<}$NP—could be resolved by machine-learning technology. I recall a year ago while talking with learning experts at Chicago that they said: We think SAT should have an algorithm that runs in ${2^{c\sqrt n}}$ time for some ${c}$.

${\bullet }$ Azimuth John Carlos Baez
Often goes into physics and policy, such as today’s third post in a series on environmental policy and climate change. But two recent posts were on Petri nets and higher abstractions of them.

${\bullet}$ Windows on Theory Boaz Barak
This was originally a joint blog by researchers at the Microsoft Silicon Valley Research Center before it closed in 2014. Last week’s post is also on machine learning and theory.

${\bullet }$ Mathematics under the Microscope Alexandre Borovik
See his book with Tony Gardiner, The Essence of Mathematics. The spirit of the book is seen in this quote from George Pólya: It is better to solve one problem in five different ways than to solve five problems in one way.

${\bullet }$ Turing’s Invisible Hand Felix Brandt, Michal Feldman, Jason Hartline, Bobby Kleinberg, Kevin Leyton-Brown, Noam Nisan, Vijay Vazirani
They have an annotated version of John Nash’s 1955 letter to the NSA about the complexity of crypto, which beat Kurt Gödel’s “lost letter” by a whole year. As we joked on 4/1/12, if we had known about it, GLL would have been NLL.

${\bullet }$ Peter Cameron’ Blog Peter Cameron
This is where I found out about the appointment of Lander to Biden’s cabinet. Peter is at St. Andrews and emeritus from Queen Mary University of London. Ken wrote about him in his memorial for Peter Neumann.

${\bullet }$ Quomodocumque Jordan Ellenberg
He asks: Am I Supposed To Say Something About The Invasion Of The United States Capitol? He does. We haven’t. (We are mulling a post on quantitative matters from the pandemic and election that have become political footballs.)

${\bullet }$ 11011110 David Eppstein—the blog name is his initials DE in hexadecimal and his surname has a double-p.
Right now he has a wonderful list of open questions and known results. For example there is a discussion of USA flag arrangements, and also the recent claimed solution of an almost 50 year old conjecture: A proof of the Erdős-Faber-Lóvasz conjecture by Dong Yeap Kang, Tom Kelly, Daniela Kuhn, Abhishek Methuku, Deryk Osthus.

${\bullet }$ Explaining mathematics Joel Feinstein
He asks: When proving there exists statements, is it enough to give just one example or do you have to prove it using the definitions, and so on? Read on for more.

${\bullet }$ Computational Complexity Lance Fortnow and Bill Gasarch
The CS theory blog that started it all. Continues to be one of the top blogs. Lance’s post on Tuesday says that “the way of most suggestions I make in my blog [is] a quick road to nowhere,” but the one in that post went somewhere.

${\bullet }$ logic and more Joel Hamkins
He discusses the math tea argument—one heard at an afternoon tea. I miss these very much, even though I do not drink tea. The argument is: There must be some real numbers that we cannot define, since there are uncountably many real numbers, but only countably many definitions. Is it correct? Read on about the talk he is giving tomorrow “in” Warsaw for an explanation.

${\bullet }$ Combinatorics and more Gil Kalai
Gil’s wonderful blog is a great place to see announcements of new results. He’s had a year-long series, “To cheer you up in difficult times”; its 18th installment links to a wonderful, thoughtful, entertaining, and provocative post by Igor Pak about conjectures. The 17th installment was about the Erdős-Faber-Lóvasz news.

${\bullet }$ M-Phi Many authors
All of the recent entries have been by Richard Pettigrew but they have a long list of previous contributors. The recent posts catch Ken’s eye because they employ the Brier score to reason philosophically about inaccuracy. Ken has employed his group’s novel adaptation of the Brier score in chess cheating cases all through the pandemic.

${\bullet }$ Short, Fat Matrices Dustin Mixon
He discusses a problem by Mario Krenn. The problem has consequences for quantum computation—and comes with cash prizes—one is €3,000.

${\bullet }$ Turing Machine VZN
Just nipped under with a New Year’s Day post on the Collatz ${3n+1}$ conjecture. Ken used to know VZN’s full name but can’t find it now.

${\bullet }$ Noncommutative Analysis Orr Shalit
The issues here are important to quantum computation, since for operators ${A}$ and ${B}$, ${AB = BA}$ is usually not true.

${\bullet }$ in theory Luca Trevisan
The only theory blog—I believe—that quotes Homer Simpson: “Marge, I agree with you—in theory. In theory, communism works. In theory.”

${\bullet }$ Not Even Wrong Peter Woit
Mathematical physics, for the most part, growing out from his 2005 book of that title critiquing string theory.

We also link to sites such as John Awbrey’s Inquiry Into Inquiry and Pink Iguana that grow in beehive style, and sites with higher-volume politics and culture content such as prior probability by Enrique Guerra-Pujol.

## Open Problems

We would be grateful for suggestions of additional mathematics and computing blogs that an advisor’s staff might consult.

[added Obama-era photo to intro]

10 Comments leave one →
January 22, 2021 6:13 am
• javaid aslam permalink
January 22, 2021 10:23 pm

2. January 22, 2021 6:15 pm

An interesting french website is « Les Mathématiques.net ».
You can find various note courses and visit the forum where you can have discussions with students and (active or retired) professors.
What makes this site so singular, even on the whole internet, is its geometry forum: very rich with numerous problems on plane, projective, constructive, analytic, synthetic, spherical, hyperbolic, symplectic, differential geometry with passionate stakeholders !
A precious ressource in our times where geometry is in sharp decline in higher education !

3. January 23, 2021 10:45 am

Re: Blogs

Vardi’s Insights

No posts yet this year but keeps the Comp Sci pot stirring on Facebook and elsewhere.

4. January 24, 2021 11:39 pm

“Some conspicuously often take their”. A peruvian reader :D.

• January 26, 2021 5:50 pm

Can others really recognize esta comunicación tal ofuscada? 🙂

January 25, 2021 11:00 am

perhaps more ‘programming’ blogs than ‘math’ blogs, but i have learned a lot of math from https://byorgey.wordpress.com/ and https://bartoszmilewski.com/