Category: Uncategorized

Vienna Diary, July 12th

The Vienna Globe Museum has the pleasing quality of delivering more or less everything of what it promises: globes. It is globes from start to finish, from all across the ages. I learned about celestial globes and then was reminded of lunar globes. My Dad had a lunar globe up on the shelf of his study that predated my arrival in the world. Quite likely it is still there. It was an impressive token of Dad-sophistication to my young eyes, suggesting some tenuous but valid connection in my mind between my father and the men involved in the moon program.

Globes are revealing of our ability to understand the world. There was a time when the globes themselves were used as sophisticated instruments of astronomical calculation, allowing the user to forecast the night sky, and at some point those calculations were done without such globes. There was also a period of time when the general understanding was that California was a peninsula. This understanding became a reality on the surface of many old globes I saw — north America with this additional isle appended to it. A shock to see, like realizing an abstract painting has been hung upside down.

Spotted on Craigslist:

To me, this is pure and uncut contemporary Americana:

Vienna Diary, July 8th

We took a tram out the the MuseumsQuartier to visit the MUMOK on the understanding we would be treated to some expressionism. Whatever expressionist works they have remained a tease since that day they remained in the vault. Instead we found ourselves walking around an Adam Pendleton exhibition Blackness, White, and Light. I have little to say about it, and having read some of the exhibition text I had to wonder if anyone anywhere had anything worth saying about it.

There was a room that formed part of the exhibition, that I did not enter, but have been reliably informed involved being bombarded with an upsetting and overwhelming stream of sound and images. Leaving the room so discombobulated gave the exhibition an entirely different hue, but I’m pretty certain you could have walked out into the Museum of Bad Art and found the effect similarly transformative.

There were also two floors showcasing the work of Elizabeth Wild, an Austrian collage artist who was at work throughout her life, but only received real art world recognition in her 90s. A lot of time passed between her studying at the Academy of Fine Arts Vienna and that eventual success. It was a life that involved fleeing unpleasant regimes and dictatorships at certain key junctures. The collages came late in her creative practice but she produced one a day, so there was an entire floor full of them. You might have already seen one of her collages on the London tube.

Elisabeth Wild, ‘Fantasías’, 2019. Commissioned by Art on the Underground. Courtesy of Karma International, Zurich; and Proyectos Ultravioleta, Guatemala City. Photo: Benedict Johnson, 2020 (see tfl)

Vienna Diary, July 7th

I finished Measuring the World by Daniel Kehlmann. The novel recounts (with certain liberties and license) the lives of the German mathematician Carl Friedrich Gauss and the similarly German, but much wealthier, geographer Alexander von Humboldt. We are to understand that the pair were not motivated as other men and women of their time nor thought like others thought, and the material of their lives is presented with understated black humour and pathos at the loneliness their dedication to science and mathematics cost them.

I was particularly struck by the presentation of Gauss, whose mathematical powers read on the page as supernatural. He doesn’t merely have prescient ideas about how science and technology, but sees the actual that future will arrive, informing those around him as we might explain a new metro-line will gentrify the neighborhood. Like superman, he has arrived on a planet that is not his own, granting him insights as powerful as a Kryptonian’s strength is magnified under Earth’s weaker gravity. By the end Gauss is having ecstatic visions of a 21st century city. It would seem silly, were I not more than half convinced that it is deliberate. Nevertheless, I couldn’t help but suspect that the author might well understand the mathematics better than he understood the mathematician.

The penultimate chapter is a modernist tour de force, carried along on the momentum accumulated over the previous chapters. Up until that point Humbert and Gauss alternated chapters, providing an ostensibly conventionally styled account of the men’s lives. But then the narratives merge as the perspectives of the men are shared and the prose moves back and forth without announcement. I want to say it is one of the more effective employments of the modernist style that I have read. But perhaps it is fairer to say it the most accessible and generous to the reader.

Not everyone has been so taken with the text, however:

Hard to argue against the chap’s position of authority on the matter.

Vienna Diary, July 6

The Strudlhofstiege sits at a bend in a road that abruptly dead ends. And if you ascending the stairway and proceed onward you arrive at the mottled metal gates that announce the American embassy. A pair of fountains, asymmetric design, and Art Nouveau stylings set the Strudlhofstiege apart in obvious ways that don’t even require knowing what Art Nouveau actually is. A poem by the fish-faced fountain alludes to the literary significance of the site: a prominent location in the Great Austrian Novel Die Strudlhofstiege oder Melzer und die Tiefe der Jahre (The Strudlhof Steps or Melzer and the Depth of the Years) by Heimito von Doderer. I visit the Shakespeare and Company bookstore, but it is not among local offerings. (I settle for some Thomas Bernhard instead). Almost predictably, this Great Work was only published in English by New York Review Books Classics in 2021.

Here is my burnt offering upon the unholy alter of quit-lit.

This spring I sat on a career advice panel in Montreal at the Geometry of Subgroups conference, offering my thoughts from the perspective of someone who recently jumped from academia to industry. As fine as the panel was, I am frustrated at how far short I fell of what I felt should be said. So here is my attempt at better expressing myself. If you have more questions, feel free to pass them on to me, and maybe I’ll do another round. The more impertinent the questions, the better.

Q: If I quit mathematics, can I really consider myself to be a mathematician. Like, really?

There is a rich historical tradition of mathematicians leaving academia and going out into the world to do other things.

  • Isaac Newton in his later years tired of his cushy Cambridge position and wanted an exciting job in the capital. He became Warden of the Royal Mint and oversaw the Great Recoinage of 1696 (there is a book about the whole story).
  • John von Neumann had an impact on the post war world that I cannot adequately describe in a few sentences. But his work consulting with the US defense department led one recent AMS review of a recent biography to spend time addressing the question of whether or not he was evil.
  • Jim Simons ran off and started one of the world’s most successful hedge funds. He was successful in large part by employing quants — phds from scientific rather than financial backgrounds. He made so much money doing this he created the Simons Foundation. If you’ve ever read a Quanta magazine article, he paid for that (it certainly isn’t a revenue generating enterprise).
  • Robert Zimmer ascended to administrative heights, becoming Chicago University president. He was so celebrated that after his passing the NYT columnist Bret Stephens gave an invited Class Day speech complaining about cancel culture in tribute.
  • Alexander Grothendieck founded a commune, and later became a reclusive shepherd.
  • John Meynard Keynes got drawn into economics, trying to prevent World War 2, and founding the welfare state. (The real takeaway of all this is that you should go and read The Price of Peace by Zachary D. Carter).
  • Richard Garfield did his PhD in combinatorics, but found his dreams really came true when a dinky card game he designed became the international sensation known as Magic: The Gathering. It is only a matter of time before MTG cards become accepted as international reserve currency.

Being an mathematician at an academic institution is a very narrow avenue of human experience, and plenty of successful mathematicians have had healthy appreciation of this.

Q : Why did you quit mathematics?

Principally to resolve a two body problem; I was separated from my partner by the UK travel ban to the US during the pandemic. I saw my chances of getting a suitable job as being so negligible that as soon as my visa was approved, I quit my job, the UK, and flew over the Atlantic to get married and pursue the American Dream. I had another year to my postdoc, but considered waiting another year to be abject foolishness. Being separated from my partner by the pandemic did dramatic things to my tolerance of that situation. I certainly wasn’t willing to protract it any further on the vague possibility that something might turn up for me on the job market. At least part of this intensity of feeling was Pandemic induced, but it was pretty consistent with my general thinking. I’m a lot more mellow about the way it all worked out now I’m on the other side of it.

Q : Why couldn’t you get a job?

There a number of reasons. My job search became progressively more restricted as efforts to resolve my two body problem restricted me geographically. I was applying into the US, a highly competitive market, with a real lack of suitable teaching experience. I also didn’t have any fancy grants, and although I had a very fancy Oxford postdoc, I don’t believe it would have moved the needle in the same way as having a NSF grant. (A grant which is very important in the US, and I have never been eligible to even apply for). My visibility in the US was pretty low due to giving almost no talks while doing my PhD in Canada, and then being out in Israel and the UK. I certainly invited myself to seminars when I was stateside, but I was never invited to give conference talks or present at AMS meetings, which would have done a lot more. I was interviewed, once for a postdoc position when I finished my PhD and that is the most interest the US job market has ever shown. My strongest research and fanciest papers were produced towards the end of my time in math — during the pandemic, in fact. My fortunes would have been significantly different if I had finished my PhD with such results. My best chance of getting a job was probably when my partner got a bunch of job offers, but none of them were willing/able to consider a spousal hire. That kind of thing seems to work out for other people.

Q: Do you think it represents an institutional failure that someone as talented as yourself cannot get a job?

I obviously like to hear that people appreciated the work that I did, and I am very proud of it. But it is worth considering what this question might mean. The math job market is zero sum in every meaningful sense.
If you want there to be more nice research jobs to be available, sure, that would be nice, but that is a very general complaint, and applies as much to everyone else as to me. (Pure mathematicians are the only people who feel this way. Most people want more doctors, nurses, and teachers). If you think I am better qualified than some of the people getting the jobs, then maybe or maybe not, but that is very hard to speak to. Generally, it is worth being humble about how limited your judgment is about all the mathematics being done, and how strong the other candidates out there are.

Q: Why do other people quit mathematics?

They can’t get the job they want. They don’t believe they can get the job they want. They get bored with mathematics (or at least they way it ultimately gets practiced). They get a job and realize they don’t like some aspect of it, and it’s very difficult to get another job. They become interested in doing something else. They become interested in the idea of making lots of money. They need to make more money. They become sickened by the scientific community’s connections to the military industrial complex.

Q: Why do so many mathematicians leave academia and then go into tech and finance?

The short answer is because that is where the money and opportunity is, but there is a far better, longer answer that makes such a decision look far more sympathetic. Getting an academic, tenure track job is an example of what I will call a prestige vocation. There are other examples, mostly creative pursuits, but the easiest identifier is whether you can imagine a MasterClass (TM) Video Series being taught by someone doing this job. These jobs tend to have limited opportunities, fought over by highly qualified, highly educated, frequently highly privileged individuals, who have to stick it out in subordinate positions for many years. At the same time the industry itself either isn’t particularly lucrative, or even profit driven at all, from a market perspective. In some of the worst examples, aspirants are often required to pay increasing amounts for the degrees and accreditation just to access the bottom rungs.

Often this was different, many generations ago, but not anymore. Frequently people in these fields are overworked and underappreciated, becoming a miserable and dispirited. So when a mathematician jumps ship they would be wise to avoid making the same mistake again, and if you are a mathematician then there are these two industries that are ready and happy to put you to work.

As prestige vocations go, mathematics is probably one of the best. You are paid to go to graduate school, and there are a lots of perks like getting to travel. Best of all, you get to do mathematics.
You actually get to do the thing. You aren’t an assistant or an extra on a film set waiting for your moment.
You aren’t an editorial assistant with no time to work on your own novel. You get to do your thing.
Frequently, people do get the kind of job they are after — and maybe you will too! And, when the opportunities run out, you have a kind of training and qualification that you can convert into a new career.

It is also worth saying something about the tech industry. Computers are fascinating engines of mathematics worthy of a little respect. I often think about Frank Nelson Cole. In 1903 he gave an AMS presentation entirely devoted to multiplying 193,707,721 and 761,838,257,287 to demonstrate he had factorized the Mersenne number 147,573,952,589,676,412,927. According to his own report, discovering the factors had taken three years of Sundays. Today, I can spend 5 minutes writing a program in python that will discover the prime factors in a couple of seconds.

Q: Do you spend all your time wishing you had a nice tenure track job at a research university?

Not really. Getting a tenure track job, even a nice one, would have been a considerable change of pace. Assuming that the set-up resolved my personal situation as conveniently as my current job, a lot would have changed: more teaching, more meetings, and more responsibilities. Do the right postdocs and you can avoid all that until you hit the tenure track, but risk possibly ruling yourself out from the running for many such jobs.

I feel like I had a lot to bring to the table as a teacher, that I never really had the opportunity to offer. It would have been a lot of fun to have clever graduate students to farm out all the problems I couldn’t solve. I think I would have been a good graduate student supervisor.

In terms of the research, I now have a solid appreciation the amount of work that is involved to make substantial contributions happen. I don’t rue what I wasn’t able to do. In my more reflective moments, I rue the fact I can’t go back and become a graduate student again with all that I now know. If I were really dead set on returning to academia, my best bet would be to change my name, choose a distant, unrelated, but similarly exciting field, lie about my age, and start all over. I’d fucking kill the second time around. Leave everyone else for dead. Be feted within that clique, crank out some collaborations with the top peeps, and then when I collect my Fields medal all the geometric group theorists would jump out their seats and exclaim “That’s Daniel. He’s an old man! Take that prize away from him, the fraud!”

Q: Should I become a data scientist?

I can’t tell you what you should do. You have to look into your heart. Data scientist is a popular option and you can probably discuss that career with people who have actually gone away and done it. There are many such careers you might think about. Software engineering, AI, actuarial science, consulting, options trader, teacher, project manager, life coach, technical writer, substacker, astronaut. I can’t tell you how realistic or suitable any of them are for you. I can’t tell you what positions to apply for. I can’t tell you what company to try and work for. Academia offered a very limited range of opportunities and people generally would apply for almost anything and take what they could get. When you make the jump you have to think more carefully and act more deliberately.

Where would you like to work?
Would you like to work remotely?
Do you want to work for a nonprofit?
Do you want to work for a large or small company?
A startup?
Do you want to travel?
Would you like to work with customers?
Would you like to go into management?
Do you want to work for a public or privately traded company?
What sectors do you want to work in?
The financial sector?
The arms industry?
You should have opinions on these and other questions and let them guide you.

I know someone who quit academia and went off cycling around South America until Covid put an end to that. You have to respect the ability to make such decisions.

Q: Can I get a job in the tech sector without programming experience?

Yes, but you should spend time learning to program. Enough that at least you can do the interview style problems you can find on leet code. It is then important to find a job opening where they are sympathetic to your case and will appreciate what you can offer. There are many companies that understand that the ability to program can be learned on the job, but many of the qualities you have — mathematical facility, for one — are not so easy to find. There are many jobs you will not be qualified for (at least not at first), so you should keep an open mind about what you can do.

Q: What advice would you give for getting a job?

  1. I don’t know how long the transition will take, but I psychologically prepared for six months. The good news is you can start investigating and preparing in small ways and big ways, even before actually quitting.
  2. Get in contact with people you know or knew who left for industry. They will generally be very willing to talk and help you out. There is a kind of camaraderie among former math/phds. And at many big companies there is a financial reward when someone you refer gets hired.
  3. Get in contact with people you don’t know in industry. There are all kinds of ways to do this. I haven’t investigated them all. But learn to write short, polite emails that get to the point and aren’t weird.
  4. Learn Python. This is worth doing even if you are remaining in academia. Even if you aren’t going into the tech sector. It’s widely used, allows you to script quickly, and there are lots of resources for learning. Having some appreciation of what can be done in code is a very useful skill to have. What constitutes “learning Python” is obviously unclear. But best of all, if you hate it, you have learned that much. All that said, like mathematics, if you don’t have the right kind of motivation, it might be worth not bothering at all.
  5. Write your CV. Get other people to read it.
  6. Don’t be discouraged when your applications are ignored. Probably you didn’t apply for the right position. Half the battle is finding the right position to apply for. You probably don’t even understand what the right position to apply for is. That is why being able to talk to someone like a recruiter is so useful. They might actually know where they can place you. (I had the fortune to talk to an internal recruiter. I hear that external recruiters can be playing a numbers game, and may be less useful.)
  7. Take/audit courses that might be relevant. If you are still in an academic institution, taking a course on the side during a semester is a great way to hedge against the possibility of leaving at a later date. MIT has a bunch of good lectures online.
  8. Trust your mathematical instincts.
  9. Communication skills are valuable, to the point that this is something of a cliche. When I did my technical interview I went into TA mode, explaining what I was doing, and being self-deprecating about saying what I was confused about. If I had to interview again, I’d be 300% better. At least. But I was good enough.
  10. Be interested in what companies do, what people’s jobs involve. Sometimes you just have to ask to learn something useful.

Q: Weren’t you afraid that once you abandoned academia all your accumulated mathematical powers would dissipate, leaving you an empty vessel?

I feel like I spent enough time into the game that the thinking has been inscribed into me in some permanent way. I’ve also concluded that mathematical knowledge and understanding is not some precarious tower built up over successive years that will collapse without careful maintenance.
I believed that when I was an undergraduate, and the cumulative effect of undergraduate education certainly gave that impression. While I think good undergraduate courses should have that satisfying effect, I also suspect it can be harmful when transitioning into research.

Q: Weren’t you afraid of losing all those friends you made in mathematics?

Friends have confessed to me that this has been a non-trivial consideration. What is definitely true is that after a while as a mathematician you know a lot of people attending conferences, and you do enjoy having these regular reunions with them. The important point is that you don’t have to organize the get together (unless you are actually the conference organizer). This is nice, but really you should proactively maintain relationships with friends. Email, whatsapp, or meet up. Postcards are cool.

Q: I feel like my sense of self worth is tied to the mathematics I do, and the mathematical success I aspire to have. Is this a good reason to stay in mathematics?

You should not tie your self worth to success in mathematics. Pick anything else:
Being a good cook.
Having a sick set of shiny OG Pokemon cards.
Reading the poems published in the New Yorker.
Having a super discerning taste in music.
Always doing the washing up immediately after you’ve finished cooking.
Having a article appear on an online humour site.
Raising your FIDE chess ranking.
Raising your ranking.
Maintaining your wordle averages.
Finishing Gravity’s Rainbow.
Having very tidy cursive handwriting.

Just not being successful in mathematics.

Q: It sounds like by leaving academia and going into industry you have become a little too comfortable with late capitalism.

If you are afraid that I am not a good communist, then you are probably right. But there is a serious point, that isn’t especially political, and might be helpful. You should distinguish between having principals about what kind of work you want to do and being generally squeamish about capitalism. The danger is that when you do start to feel the desperation of finding some kind of job, you will embrace a kind of nihilism and decide that since you can’t achieve the purity of tenured academia, then you might as well make money by whichever means is most lucrative, working for whoever is ready to pay you.

[A quick note: this article lives here, on my blog. If you liked it, please do share it. Otherwise, I can assure you, very few people will find and read it.]

debate me

Reading more of These Truths and I was struck by this piece of context to the Lincoln-Douglas debates

In the eighteenth century, debate was understood as the foundation of civil society. In 1787, delegates to the constitutional convention had agreed “to argue without asperity, and to endeavor to convince the judgement without hurting the feelings of each other.” Candidates for office debated face-to-face. With the expansion of the franchise, debating spread: beginning in the 1830s, debating classes were offered to ordinary citizens as a form of civic education. Debating societies popped up in cities and even the smallest of towns, where anyone who could vote was expected to know how to debate, although this meant, in turn, that anyone who couldn’t vote was expected not to debate.

These Truths, Jill Lepore p275

I am sympathetic to opinion, now common among certain commentators, that the debate format is tiresome and frequently stupefying. I can only think of one good debate, and really I mean I can think of one debater who ever impressed me. The fact that debate did little to remedy the impasse that the US was rapidly approaching in the nineteenth century demonstrates that even a citizenry singularly devoted to debate will do little resolve the deeper issue.

Citizens today are not expected to debate and we don’t teach that kind of rhetoric anymore. In its place I can identify two modes of discourse looming large in its place. The first being able to describe your personal identity and experience, and the other being able to articulate in the language and techniques of statistics. Each taken on their own seems deficient in obvious ways, but taken together, it almost feels like a kind of progress.


Yesterday, while reading of the build up to the US annexation of Texas, I found the following parenthetical comment about the newspaperman Horace Greeley.

(Greeley, who, with his slumped shoulders and flat face, looked rather like a frog, was the most widely read editorial writer of his generation.)

These Truths, Jill Lepore (pg 235)

Such an aside makes a man reach for his smartphone. Did the man really look like a frog?

I can’t say that I see it. I have questions about the hair, but I don’t see much of the frog in the man.

This certainly has more of the “forest creature” about it. It doesn’t even feel like the same person as the first photo. My questions about neck hair still stand. I can only presume that this was a distinguished style for men of a certain class, and I would like to hear more about it. Contemporaneous diary entries and private letters. That sort of thing.

Reading ahead on the Wikipedia, it turns out that Greeley would run for president against President Grant. He did not succeed, in no small part due to the cartoons of Thomas Nast. In the above example, we see Greeley depicted, not as a frog, but as some kind of lion. This seems much more appropriate and in line with his mane.

A reader should understand that they cannot assume rigorous fact checking in the non-fiction they find on the bookstore shelves. I have to wonder if the New Yorker would have let such a remark slide by so easily.

Of an average, inconspicuous human being.

Like a lot of pontificaters, professional and amateur alike, I’ve had recent AI developments on my mind. Scary stuff, in many ways, all depending on the sort of newsletters you subscribe to. I was also reading Vasily Grossman’s Life and Fate, the great Russian novel of World War 2, finished in 1960 and very far from science fiction. One chapter, short enough I can type it all out, jumped out at me for reasons that should be clear enough.

An electronic machine can carry out mathematical calculations, remember historical facts, play chess and translate books from one language to another. It is able to solve mathematical problems more quickly than man and its memory is faultless. Is there any limit to progress, to its ability to create machines in the image and likeness of man? It seems that the answer is no.

It is not impossible to imagine the machine of future ages and millennia. It will be able to listen to music and appreciate art; it will even be able to compose melodies, paint pictures and write poems. Is there a limit to its perfection? Can it be compared to man? Will it surpass him?

Childhood memories … tears of happiness … the bitterness of parting … love of freedom … feelings of pity for a sick puppy … nervousness … a mother’s tenderness … thoughts of death … sadness … friendship … love of the weak … sudden hope … a fortunate guess … melancholy … unreasoning joy … sudden embarrassment …

The machine will be able to recreate all of this! But the surface of the whole earth will be too small to accommodate this machine — this machine whose dimensions and weight will continually increase as it attempts to reproduce the peculiarities of mind and soul of an average, inconspicuous human being.

Fascism annihilated tens of millions of people.

Vasily Grossman, Life and Fate, chapter 51. Translation by Robert Chandler

This title will not subsidize another.

An interesting column from Dan Sinykin in the Times:

A career like Mr. McCarthy’s, with its long gestation before a blockbuster second act, would be nearly impossible to repeat now. An author without an agent or a track record of book sales would never gain a hearing at a major publishing house. And a state-school dropout in his early 30s would face slim odds of becoming a prizewinning author, as an M.F.A. from a prestigious writing program has often become the price of entry for splashy literary fiction debuts.

It’s impossible to know what kind of writer Mr. McCarthy would have developed into without decades in which to hone his singular voice. But contemporary success stories about novelists tend to have a very different aspect: They’re stories like that of Colson Whitehead, who followed up his well-received 1999 debut, “The Intuitionist” with novels that deftly navigated genres before reaching a new plateau by winning a Pulitzer Prize in 2017 for “The Underground Railroad.” Or Bonnie Garmus, the author of “Lessons in Chemistry,” whose very first book became a runaway hit in 2022.

Cormac McCarthy Had a Remarkable Literary Career. It Could Never Happen Now.

I’m very interested in how the publishing industry conditions shape the literature that is produced, but I feel like there is more to the story than corporate consolidation. The nature of the reading public has also changed. The generation of young men in the trenches of World War 2 who eagerly read the first mass produced paperback novels are gone. I was reading reporting from the Ukrainian front line only a few weeks ago that featured a young soldier on the front line posting to social media. All creative conditions are transient and the only constant is that artists are forever waiting for favorable winds to arrive.