One thing I learned: he did his work while at Warwick. Warwick is kind of under-estimated among UK universities. It's reasonably well-run (which makes it almost unique), regularly hires smart people, and doesn't have the Brideshead Revisited hangover of Oxbridge.

Basically since Warwick was founded, it had a reputation for being the place people went to when they were rejected from oxbridge. This sounds bad but one subtlety with the U.K. system is that almost all students may apply to at most one of Oxford and Cambridge in any given year and those universities tend to get more sufficiently good applicants than they take in. If one of Oxford or Cambridge is commonly considered better than the other by applicants then Warwick the distribution of the abilities of the rejects is higher than if they had all applied to a single top university equal in size to the sum of Oxford and Cambridge. Therefore Warwick gets to take in lots of very good undergraduates.

The university was founded in the 60s out of what used to be a research retreat for mathematicians. At its inception a large portion of its mathematics department (at least the topologies) came directly from Cambridge (I believe the story is that Christopher Zeeman went around his colleagues telling them that all the others were going to Warwick). And in the mathematics department in particular has been strong ever since.

I believe the course structure is also different there than from oxbridge (or many other U.K. universities) in that it is meant to be more like an American university with more choice to pursue courses from different subjects or with wide varieties of specialisation.

Don't a number of universities belong to that category? I've certainly heard it about Durham:

https://en.wikipedia.org/wiki/Oxbridge_reject

Yeah it's definitely Durham. I've never heard it said about Warwick.

Imperial suffers from that too. We'd joke (perhaps in slight pain) about it as freshers - 'so, Oxford or Cambridge?' or 'which college?', etc.

I did my undergrad, Masters, and PhD at Warwick. I was originally aiming for a Cambridge, for a conditional offer, and failed to make the grades in the exams.

No regrets. Warwick is a fantastic university.

I actually met Martin Hairer a few times, as my doctorate was between maths, physics, and computer science departments. We didn't overlap much in interests ( or ability... ) but he seemed nice.

Britain has a whole clutch of universities which are global research powerhouses but are scorned as boring redbricks (or whatever) by most of the locals and unheard of to most people internationally.

'...unheard of to most people internationally.'

Taking this point further, I note there's a huge Anglo-Saxon bias in the prestige of Universities.

I don't know why this is.

I say this having studied at Oxford and Cambridge and noticed how 'unfair' it was that many French and German universities had undergraduate bodies with even higher selection standards, yet few people internationally would have heard of them.

It seems odd to me that Harvard and Oxbridge are well known, but an elite German university like TUM is not.

While I feel prestige is a nebulous thing (it partly owes to marketing, optimizing for rankings etc), it is something that has real world implications in terms of an institution being attractive to talent etc. and talent, like interest, compounds.

With respect to Anglo-Saxon institutions, I don't think all of it just mere bias.

The talent pool issue is not a negligible one. English-speaking universities simply have a larger pool to draw from, and the best American universities in particular have the advantage of being able to not only draw talent from the largest English-speaking country in the world (itself, though arguably India too if we count L2 speakers), but also tons of aspiring students around the world who also speak English (especially from large countries like China and of course India) who become alumni, achieve success elsewhere and go on to boost their alma mater in their spheres of influence. Also the spreaders of international influence (the media) tend to be predominantly English-speaking, so Anglophone universities are naturally boosted over others.

Most non-English speaking elite universities are limited in that way -- Ecole Polytechnique for instance is very famous (and very elite) in France but has trouble drawing talent from the rest of the world. Not as many people are interested in learning French vs English...

The other is "forward momentum" I think, which has to do with research $ for producing work that matters. US schools have real money to hire and do "stuff that matters", at a scale that would be inconceivable at universities in smaller countries. It's also easier to assemble the right team with when you have a big pool of people to draw from both domestically and internationally, and to provide a strong academic community for folks to thrive in.

Also universities that optimize for selective admissions at the undergraduate level tend to have different goals (say, grooming an elite class for the country's public, private sector, etc.) from research universities, whose goals are to generate discoveries (the latter tends to be considered, for better or worse, more prestigious). As such, you may not be surprised to learn, most elite universities (at the undergrad level) don't have strong research programs.

There's a metagame here, and our instinct is to think that education rigor is necessary and sufficient to produce prestigious universities, but I think in the modern world, other factors dominate.

Harvard and Oxbridge are world-class research universities, not just good undergraduate universities.

For selective undergraduate universities, there’s a whole bunch of “elite” universities in Asia — eg the IITs in India, or Tsinghua & Peking in China, or NUS in Singapore.

If someone asked me about Germany, Heidelberg probably comes to mind.

Does Heidelberg have the same cachet as Oxbridge in the UK

Like it or not English is the global lingua franca. The top global talent is unlikely interested in being educated or researching in other languages.

And national university in my opinion should educate in their nation's language(s). Even if it means losing the very crème de la crème of global talent.

If the EU could get its shit together they might some day dump more money in universities than even America does. And create some giant English based universities located on the coast of a sea, somewhere where the EU has the best climate. All just to compete with the global top universities.

I think this is at least in part due to QS ratings.

The first EU university enters in the 40s or 50s of the list and Australian universities seem perhaps overrepresented.

Closer to the ground, or, let's say, being more grounded in mundaneness, I think it's also because a lot of excellent papers are never translated to English. Asia "gets" this and pushes their English papers.

FWIW, Galois's memoirs have still not been translated, as far as I know.

Oh yes, and ETH Zurich is at least in the top 10 of the QS list.

> many French and German universities had undergraduate bodies with even higher selection standards

I've heard that this is because the French and Germans often split institutions into teaching and research, so their teaching institutions look crap to outsiders because they're not doing any research.

> I don't know why this is.

> I say this having studied at Oxford and Cambridge

Hah! So not so smart after all then...

As I said, Anglo-Saxon University prestige is overrated.

Maybe someone from a Grandes Ecoles would know ;)

I guess I would say certain non-Anglo-Saxon elite institutions are underrated, but I wouldn't say Anglo-Saxon university prestige is overrated. They are, in some sense, correctly rated.

Which ones would you recommend?

The Russell Group is probably a good place to start.

https://en.wikipedia.org/wiki/Russell_Group

Warwick is particularly well regarded for its mathematics department.

I thought it was well known it was ahead of Oxford for Maths, second only to Cambridge and Imperial

It's my impression that rankings for mathematics generally put Oxford ahead of both Imperial and Warwick and sometimes even ahead of Cambridge.

https://www.topuniversities.com/university-rankings/universi... https://www.timeshighereducation.com/world-university-rankin... https://www.thecompleteuniversityguide.co.uk/league-tables/r...

It's well known to be ahead of Oxford and Imperial for Maths, second only to Cambridge.

I don't quite follow what you mean by "Brideshead Revisited hangover" - from Wikipedia, it seems like it roughly means "nostalgia for the age of English aristocracy"?

That's about right. Think candlelit dinners with lots of claret, terribly clever undergraduates writing terribly clever 1500-word essays on their PPE course, the gentleman amateur.... Things that were great in the 19th century and have now become parodies of themselves.

I think that's an accurate portrayal of the "ivy league" type unis in the UK. They may not be what they once were, but they have a particular romanticism about them that people aspire to attend them.

Can confirm the stats department at Warwick is good & pretty active.

> doesn't have the Brideshead Revisited hangover of Oxbridge

I've watched and read Bridehead Revisited. Just curious what aspect of it you mean here: the aristocracy?

here’s his paper that won him the prize. It’s long at 180 pages.

https://arxiv.org/abs/1303.5113

Wish there was something between a Quanta article and the paper that described his thinking.

A quick search shows this:

https://arxiv.org/abs/1401.3014

which still requires a substantial mathematical background, but seems rather less technical (I've not read it). There's also a textbook on rough paths by Friz and Hairer with an introduction to regularity structures; if you're at an academic institution with access to SpringerLink, you may be able to get it easily.

Finally, Martin gives lots of talks, and he's an exceptionally clear speaker. I wouldn't be surprised if there's something on YouTube that's reasonably accessible to someone with a solid math / physics background.

Wait, does he drink Rooibos at 2:32?