Imperial mathematician scoops $3M Breakthrough Prize(imperial.ac.uk)
imperial.ac.uk
Imperial mathematician scoops $3M Breakthrough Prize
https://www.imperial.ac.uk/news/203853/imperial-mathematician-scoops-3m-breakthrough-prize/
110 comments
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.
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.
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...
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.
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.
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
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.
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.
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.
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.
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.
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.
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'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.
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> I don't know why this is.
> I say this having studied at Oxford and Cambridge
Hah! So not so smart after all then...
> 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 ;)
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
https://en.wikipedia.org/wiki/Russell_Group
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> 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?
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.
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.
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?
> He won the Fields Medal in 2014
Damn. I'm sure he appreciates the $3M (elsewhere he joked that he could finally afford to buy a house in London) but the Fields Medal is a much bigger deal in the world of mathematics.
Damn. I'm sure he appreciates the $3M (elsewhere he joked that he could finally afford to buy a house in London) but the Fields Medal is a much bigger deal in the world of mathematics.
Martin Hairer also has a software company making audio editing tools (https://hairersoft.com/) - I love this Fields medal comment in the middle of an otherwise mundane support forum thread about MacOS compatibility! https://hairersoft.com/forum/viewtopic.php?f=1&t=2574&p=8222...
Which actually made me wonder - where/how do London academics live? I find it hard to imagine them commuting for hours from the suburbs - it does not seem very consistent with an academic life - but I do not see them being able to afford to live near their universities either.
The same way that everyone else does; buying a 1.5M 2 bed flat in Zone 1 isn’t possible on UK tech salaries either, even if you reach the top tiers for UK tech pay which usually tops at around £125K base you aren’t buying central London properties either.
But then who is buying them? I see plenty of young families that seemingly live in those 1.5M zone 1-2 houses and flats, and many do not appear to be renting (although maybe they are? But not like renting is THAT much cheaper either).
FYI: How Stanford University handles that now is that they have a new subdivision on campus, and chosen professors are given title to a nice house. When they move later, they are given the assessed profit of any rise in house value over the years.
This was necessary because house prices in Palo Alto are in the $2+ million range, which is not affordable to profs, and prevents them from the normal housing ladder investment seen in the rest of the USA.
A lot of the profs use bicycles to ride the mile or so to class.
This was necessary because house prices in Palo Alto are in the $2+ million range, which is not affordable to profs, and prevents them from the normal housing ladder investment seen in the rest of the USA.
A lot of the profs use bicycles to ride the mile or so to class.
At Imperial: They mostly commute (but not for hours), because it's basically impossible to find a decent flat in South Kensington. It works, because Imperial has matching childcare. Also, many mathematicians tend to work from home frequently.
> I find it hard to imagine them commuting for hours from the suburbs...
Why? It's as easy to commute from certain places outside of London as inside. For instance, it takes longer for me to get from where I live in south London to e.g. Kings Cross than it would to get there from Cambridge. The amount of time you save by living more centrally is probably less than 20 minutes.
Why? It's as easy to commute from certain places outside of London as inside. For instance, it takes longer for me to get from where I live in south London to e.g. Kings Cross than it would to get there from Cambridge. The amount of time you save by living more centrally is probably less than 20 minutes.
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Costs you a mighty penny too, though. Commute Reading to Kings Cross should be close to 5k a year (not including tube), no?
Ha I agree with the broad point, but as someone who (used to until Covid) commute from South London to Kings Cross everyday, this doesn't seem true timewise until you live quite far South in London. And I live a 15 minute walk from a tube station.
Having said that, I agree with the sentiment!
Having said that, I agree with the sentiment!
Tooting -> Kings X is 49 minutes according to citymapper. Cambridge -> Kings X is a 48 minute train. I personally wouldn't consider Tooting to be deep south, but maybe we have different definitions. I have a friend who lives near Kingston, it's roughly an hour commute for him.
I don't know how City Mapper is getting that number to be honest. TFL gives 35 minutes, and that includes 5 minutes for walking out the tube at Kings Cross.
The trick is you have to change at Stockwell onto the Victoria Line.
Nb. I did almost this journey every day pre-lockdown and the numbers are accurate for me at least.
The trick is you have to change at Stockwell onto the Victoria Line.
Nb. I did almost this journey every day pre-lockdown and the numbers are accurate for me at least.
I imagine that a knighted professor at Imperial can comfortably access a mortgage in London, so I doubt this applied to Martin Hairer.
But, post-graduates in London (if they have no other source of support) do tend to have a difficult lifestyle. Not recommended.
But, post-graduates in London (if they have no other source of support) do tend to have a difficult lifestyle. Not recommended.
No not really. With the average price of a house in London approaching £1m https://www.home.co.uk/guides/house_prices.htm?location=lond... and an average professor at Imperial earning £80k https://www.glassdoor.co.uk/Salary/Imperial-College-London-P...
Looking more closely on glassdoor: it's unlikely to be true that Imperial professor salaries average £80k and University College London salaries average £101k, and these figures are more likely biased by small, self-selecting samples.
[Updated to note: Imperial College quotes a fixed minimum salary of £79,080 for professors in 2019 with performance-related increases - so the Glassdoor figures quoting lower than that cannot be right]
The home.co.uk site quotes the median price of property listings is £600k (is that close to £1m? ok sure). It also identifies that houses priced higher than that are listed for significantly longer, i.e. they count with more weight in this stat despite not selling. Therefore, I understand the median sale price to be lower.
[Updated to note: Imperial College quotes a fixed minimum salary of £79,080 for professors in 2019 with performance-related increases - so the Glassdoor figures quoting lower than that cannot be right]
The home.co.uk site quotes the median price of property listings is £600k (is that close to £1m? ok sure). It also identifies that houses priced higher than that are listed for significantly longer, i.e. they count with more weight in this stat despite not selling. Therefore, I understand the median sale price to be lower.
> I imagine that a knighted professor at Imperial can comfortably access a mortgage in London
You don't get paid for being knighted. And these universities have a mostly fixed pay scale it's not like Google where you can just demand whatever you want if you're good enough.
You don't get paid for being knighted. And these universities have a mostly fixed pay scale it's not like Google where you can just demand whatever you want if you're good enough.
Well, there does exist a fixed pay scale for base salaries, but for senior academic grades in many occasions this simply defines the minimum salary, and the rest is negotiable (particularly if the academic has a good record of obtaining research grants).
Then again, there exist Business Schools, where due to the different funding model (most income comes from MBAs, as opposed to research grant overheads, and undergraduate tuition fees), full professors can easily make near-£200k in base salary.
Then again, there exist Business Schools, where due to the different funding model (most income comes from MBAs, as opposed to research grant overheads, and undergraduate tuition fees), full professors can easily make near-£200k in base salary.
Even with a salary of 200k per year, it's unlikely they will be able to afford a 2 or 3 bedroom flat in South Kensington. According to Zoopla/Foxtons, the average price is around 2M.
Senior professors negotiate their pay.
I don't know what you think that looks like in practice... but it's going to be very very modest at a British public university.
>I imagine that a knighted professor at Imperial can comfortably access a mortgage in London
You have a lot to learn about the London housing market and UK salaries.
You have a lot to learn about the London housing market and UK salaries.
Imperial, on the whole, is one of the better-paying Universities in the UK, and certain Departments are able to provide considerable supplements upon base salaries.
The vast majority of academics with families live in the outer zones in London, or commute by rail from the suburbs just outside. London has a very dense and efficient public transport network, and therefore a typical commute time is around 40 minutes, and in most cases less than 1hr.
The price of accomodation remains an issue with younger academics, who arrived in London after the housing booms (1st surge around 2004, 2nd around 2010). Consultancy, enterpreneurship etc do provide good additional income streams for many, and therefore it still all makes sense.
More recently Imperial has been developing some of its own accomodation for junior staff and graduate students, which is made available at subsidised rates.
The vast majority of academics with families live in the outer zones in London, or commute by rail from the suburbs just outside. London has a very dense and efficient public transport network, and therefore a typical commute time is around 40 minutes, and in most cases less than 1hr.
The price of accomodation remains an issue with younger academics, who arrived in London after the housing booms (1st surge around 2004, 2nd around 2010). Consultancy, enterpreneurship etc do provide good additional income streams for many, and therefore it still all makes sense.
More recently Imperial has been developing some of its own accomodation for junior staff and graduate students, which is made available at subsidised rates.
It's somewhat common for London office workers to park at an overground station 30mins-1hr out of london and commute in.
Is London compatible with your idea of an academic life?
A friend rejected a job at Imperial because he didn't want to live in a metropolis. Another friend stays at UCL because she can't bear to leave London.
A friend rejected a job at Imperial because he didn't want to live in a metropolis. Another friend stays at UCL because she can't bear to leave London.
Oh, it's actually called the Breakthrough Prize.
I thought perhaps three of the Millennium problems had been solved, and the apocalypse were here.
BTW, for those interested in P=NP and not so much in the direct mathematical research, one interesting way to approach is via hash functions. If we had P=NP, then hash functions would be more easily invertible (eh, left or right invertible). I think in polynomial time. Sorry for the "I think", this isn't my field and I try to find ways to reinterpret it.
I thought perhaps three of the Millennium problems had been solved, and the apocalypse were here.
BTW, for those interested in P=NP and not so much in the direct mathematical research, one interesting way to approach is via hash functions. If we had P=NP, then hash functions would be more easily invertible (eh, left or right invertible). I think in polynomial time. Sorry for the "I think", this isn't my field and I try to find ways to reinterpret it.
P,NP, and the invertability of most hash functions are not related, as far as is known. Most one-way functions of use are not known to be NP hard or NP complete, so having P=NP or P != NP would not affect currently widely used hash functions.
https://en.wikipedia.org/wiki/One-way_function
https://www.quora.com/Is-cryptographic-hash-inversion-believ...
https://en.wikipedia.org/wiki/One-way_function
https://www.quora.com/Is-cryptographic-hash-inversion-believ...
While not NP complete, reverting a hash function is in NP(), so it is very much affected if P=NP.
() Ok obviously it can't be in NP as it's not a decision problem, but asking "is there a preimage starting with 1, with 1A, etc." _is_ in NP. From the it's trivial to generate a preimage in P.
() Ok obviously it can't be in NP as it's not a decision problem, but asking "is there a preimage starting with 1, with 1A, etc." _is_ in NP. From the it's trivial to generate a preimage in P.
Inverting hash functions isn’t in NP, except that it’s constant time, so it’s also trivially in P. Thus P=NP is irrelevant. It’s just the constant is large. Since each common hash function is fixed size, inverting them is fixed size.
For a problem to be of interest regarding the P=NP question, the problem needs to have arbitrarily large size. 3-SAT can be arbitrary sized, thus is a candidate to ask if it’s NP hard, complete, etc. If we consider 3-SAT with fixed, bounded size, then 3-SAT is constant time.
For example, inverting SHA-512 requires at most on order of 2^512 ops to invert. This is constant time, not even polynomial time.
So no, hashing is not generally affected by P=NP.
For a problem to be of interest regarding the P=NP question, the problem needs to have arbitrarily large size. 3-SAT can be arbitrary sized, thus is a candidate to ask if it’s NP hard, complete, etc. If we consider 3-SAT with fixed, bounded size, then 3-SAT is constant time.
For example, inverting SHA-512 requires at most on order of 2^512 ops to invert. This is constant time, not even polynomial time.
So no, hashing is not generally affected by P=NP.
Chris, I am a bit over my head usually with P=NP, since it's not my area and I have to warp it before it is.
One question I would have on your comment is: What kind of proof or counterexample for P ?= NP would in fact influence our study of hash functions? This is a subjective question of course, but essentially I am wondering what approach to P ?= NP might introduce new mathematics that indeed would have something to say about hash functions.
One question I would have on your comment is: What kind of proof or counterexample for P ?= NP would in fact influence our study of hash functions? This is a subjective question of course, but essentially I am wondering what approach to P ?= NP might introduce new mathematics that indeed would have something to say about hash functions.
>What kind of proof or counterexample for P ?= NP would in fact influence our study of hash functions?
None. Hash functions are almost all O(1) to invert, that is, constant time. It's just we designed that constant to be prohibitively large.
And hash functions are not generally based on NP hard problems - they're based on bit mixing, which for all common hash functions are completely orthogonal to the question of P and NP.
Quantum computing, via Grover's algorithm, did impact hash functions one and all, since it allows searching N unstructured items in O(sqrt(N)) time, while classical computers require O(N) time. But this simply turns a 512 bit hash into a 256 bit hash, still intractable.
Again, however, this has nothing to do with P?=NP.
For a problem to be changed by P?=NP, since most think P != NP, that problem must be in NP/P, and hash functions are not (almost ever, and no common ones) from that class of problems. Also the problem has to part of an infinite family of such problems with unbounded sizes. Hash functions again are not in this class.
Of course, it may be that we can build computers in the future with closed timelike loops (CTL), in which case all problems are constant time, and that may prove for that class of machines that the complexity hierarchy collapses, but that is a long time off, if ever. We may be able to build machines that exploit topological quantum field theories (TQFTs) some day, like in Friedman's work, and again, that may break things, but again that is a long time off, if ever.
I'd personally bet on P!=NP being a fundamental law of physics, built into the fabric of the universe, in the It from Bit idea from Wheeler and others. I think this is becoming more and more the mainstream science belief, as the universe is looking more and more like computation.
None. Hash functions are almost all O(1) to invert, that is, constant time. It's just we designed that constant to be prohibitively large.
And hash functions are not generally based on NP hard problems - they're based on bit mixing, which for all common hash functions are completely orthogonal to the question of P and NP.
Quantum computing, via Grover's algorithm, did impact hash functions one and all, since it allows searching N unstructured items in O(sqrt(N)) time, while classical computers require O(N) time. But this simply turns a 512 bit hash into a 256 bit hash, still intractable.
Again, however, this has nothing to do with P?=NP.
For a problem to be changed by P?=NP, since most think P != NP, that problem must be in NP/P, and hash functions are not (almost ever, and no common ones) from that class of problems. Also the problem has to part of an infinite family of such problems with unbounded sizes. Hash functions again are not in this class.
Of course, it may be that we can build computers in the future with closed timelike loops (CTL), in which case all problems are constant time, and that may prove for that class of machines that the complexity hierarchy collapses, but that is a long time off, if ever. We may be able to build machines that exploit topological quantum field theories (TQFTs) some day, like in Friedman's work, and again, that may break things, but again that is a long time off, if ever.
I'd personally bet on P!=NP being a fundamental law of physics, built into the fabric of the universe, in the It from Bit idea from Wheeler and others. I think this is becoming more and more the mainstream science belief, as the universe is looking more and more like computation.
I wonder how prize winners feel about such huge sums of money. Especially that very succesful people who win such prizes tend to win multiple prizes.
Also, what does a tenured professor of mathematics do with such a sum other than spend it on himself? It's not like he's going to build out a lab and hire a bunch of research staff.
Some don't seem to care, which makes sense to me. It's not like people go into research math for the money. Andrew Wiles gave up their prize for the Fermat's last theorem.
Interesting perspective. I guesss you can ask Roger Federer at his prime and other tennis players.
"to focus fully on the world of ideas" - very interesting choice of words.
That's not what "scoops" means!
A scoop is publishing something before a rival can. You scoop the rival, not the story/prize.
A scoop is publishing something before a rival can. You scoop the rival, not the story/prize.
> That's not what "scoops" means!
It does in British English, and this is a British university writing in their native language.
It does in British English, and this is a British university writing in their native language.
Pretty common to hear scoop be used in this context. Maybe it's a UK thing?
"If you scoop a prize or award, you win it."
https://www.collinsdictionary.com/dictionary/english/scoop
"If you scoop a prize or award, you win it."
https://www.collinsdictionary.com/dictionary/english/scoop
I've never heard of scooping a rival - otherwise this is the same usage. A publisher 'gets the scoop' (a great story, a win) or scoops the story just as a mathematician scoops a prize.
Journalists get a scoop on their rivals when they publish impactful news first.
I've never heard that usage before either. ('on their'.) Whenever I've used or heard it, the scoop is the prize-analagous story.
[deleted]
Kinda sad that emminent mathematicians can only rent...
This prize isn’t too highly regarded. The physics prize has mostly consisted of string theorists giving it to their friends in the field.
What an ignorant thing to say.
Care to expand on why and give a correction?
Examples of criticism of the physics prize:
https://physicsworld.com/a/breakthrough-prize-criticized-for...
http://www.math.columbia.edu/~woit/wordpress/?p=11138
http://backreaction.blogspot.com/2019/08/special-breakthroug...
https://physicsworld.com/a/breakthrough-prize-criticized-for...
http://www.math.columbia.edu/~woit/wordpress/?p=11138
http://backreaction.blogspot.com/2019/08/special-breakthroug...
> What an ignorant thing to say
> (...)
> http://www.math.columbia.edu/~woit/wordpress/?p=11138
> http://backreaction.blogspot.com/2019/08/special-breakthroug...
Thanks for that, because my comment applies exceedingly well to people like Peter Woit and Sabine Hossenfelder; I've never heard of Michael Banks.
> (...)
> http://www.math.columbia.edu/~woit/wordpress/?p=11138
> http://backreaction.blogspot.com/2019/08/special-breakthroug...
Thanks for that, because my comment applies exceedingly well to people like Peter Woit and Sabine Hossenfelder; I've never heard of Michael Banks.
They are all related to a single award -- 2019 (special) for supergravity.
They are just examples - and intended as counter to the "ignorant" accusation which implies there was no truth to the idea of criticism.
Fair enough.
They’ve been giving awards to failed ideas since the start.
"This prize isn’t too highly regarded."
[By whom?]
"The physics prize has mostly consisted of string theorists giving it to their friends in the field."
Firsty, the Breakthrough Prize is given in Life Sciences, Mathematics and Fundamental Physics. This post is about the Breakthrough Prize in Mathematics.
As for Fundamental Physics, apart from 2019 (special) for supergravity, it doesn't seem to go to string theorists:
2021 Special Breakthrough Prize In Fundamental Physics -- Steven Weinberg, “continuous leadership in fundamental physics, with broad impact across particle physics, gravity and cosmology, and for communicating science to a wider audience.” [0]
2021 Breakthrough Prize in Fundamental Physics -- Eric Adelberger, Jens H. Gundlach and Blayne Heckel, University of Washington. Citation: For precision fundamental measurements that test our understanding of gravity, probe the nature of dark energy, and establish limits on couplings to dark matter. [1]
2020 Breakthrough Prize in Fundamental Physics was awarded to all 347 members of the Event Horizon Telescope Collaboration representing 60 institutions in 20 countries. [2]
2019 Breakthrough Prize In Fundamental Physics -- Charles Kane and Eugene Mele – University of Pennsylvania. Citation: For new ideas about topology and symmetry in physics, leading to the prediction of a new class of materials that conduct electricity only on their surface. [3]
2019 Special Breakthrough Prize In Fundamental Physics -- Jocelyn Bell Burnell – University of Dundee and University of Oxford. Citation: For fundamental contributions to the discovery of pulsars, and a lifetime of inspiring leadership in the scientific community. [3]
2018 Breakthrough Prize In Fundamental Physics -- WMAP experimental team. Citation: for detailed maps of the early universe that greatly improved our knowledge of the evolution of the cosmos and the fluctuations that seeded the formation of galaxies. [4]
There are some string theorists further in the past, but they still don't warrant the use of the word 'mostly'. [5]
[0] https://breakthroughprize.org/News/61
[1] https://breakthroughprize.org/News/60
[2] https://breakthroughprize.org/News/54
[3] https://breakthroughprize.org/News/47
[4] https://breakthroughprize.org/News/41
[5] https://en.wikipedia.org/wiki/Breakthrough_Prize_in_Fundamen...
[By whom?]
"The physics prize has mostly consisted of string theorists giving it to their friends in the field."
Firsty, the Breakthrough Prize is given in Life Sciences, Mathematics and Fundamental Physics. This post is about the Breakthrough Prize in Mathematics.
As for Fundamental Physics, apart from 2019 (special) for supergravity, it doesn't seem to go to string theorists:
2021 Special Breakthrough Prize In Fundamental Physics -- Steven Weinberg, “continuous leadership in fundamental physics, with broad impact across particle physics, gravity and cosmology, and for communicating science to a wider audience.” [0]
2021 Breakthrough Prize in Fundamental Physics -- Eric Adelberger, Jens H. Gundlach and Blayne Heckel, University of Washington. Citation: For precision fundamental measurements that test our understanding of gravity, probe the nature of dark energy, and establish limits on couplings to dark matter. [1]
2020 Breakthrough Prize in Fundamental Physics was awarded to all 347 members of the Event Horizon Telescope Collaboration representing 60 institutions in 20 countries. [2]
2019 Breakthrough Prize In Fundamental Physics -- Charles Kane and Eugene Mele – University of Pennsylvania. Citation: For new ideas about topology and symmetry in physics, leading to the prediction of a new class of materials that conduct electricity only on their surface. [3]
2019 Special Breakthrough Prize In Fundamental Physics -- Jocelyn Bell Burnell – University of Dundee and University of Oxford. Citation: For fundamental contributions to the discovery of pulsars, and a lifetime of inspiring leadership in the scientific community. [3]
2018 Breakthrough Prize In Fundamental Physics -- WMAP experimental team. Citation: for detailed maps of the early universe that greatly improved our knowledge of the evolution of the cosmos and the fluctuations that seeded the formation of galaxies. [4]
There are some string theorists further in the past, but they still don't warrant the use of the word 'mostly'. [5]
[0] https://breakthroughprize.org/News/61
[1] https://breakthroughprize.org/News/60
[2] https://breakthroughprize.org/News/54
[3] https://breakthroughprize.org/News/47
[4] https://breakthroughprize.org/News/41
[5] https://en.wikipedia.org/wiki/Breakthrough_Prize_in_Fundamen...
Whom was me and others in the physics department I was associated with. You can find more discussions on the prize on the not even wrong blog https://www.math.columbia.edu/~woit/wordpress/?p=8958
Okey, let me quote another post by Peter Woit from 2016:
"One thing that strikes me about these things is that the situation with the physics prize has changed dramatically since the first three years, when they went mostly to string theorists. Having a heavily promoted much larger cash prize than the Nobel, given largely to theorists for ideas many of which haven’t worked out, raised obvious questions about the wisdom of the whole thing. The last two years have seen a 180 degree turn, with the prizes going to experimentalists for successful experimental results. Even better, there has been an unusual emphasis on making an award to entire experimental collaborations, not just a small number of “great men” identified as collaboration leaders or spokespersons. I don’t know of any other major prizes that do this. The lack of an experimental Nobel for the Higgs discovery is one reflection of that problem, it’s great that the Breakthrough Prize people are doing something about it."[0]
Basically, we have two criticized recent physics awards (2019 special and 2017) and several in the very beginning. That still doesn't qualify as 'mostly'.
[0] http://www.math.columbia.edu/~woit/wordpress/?p=8088
"One thing that strikes me about these things is that the situation with the physics prize has changed dramatically since the first three years, when they went mostly to string theorists. Having a heavily promoted much larger cash prize than the Nobel, given largely to theorists for ideas many of which haven’t worked out, raised obvious questions about the wisdom of the whole thing. The last two years have seen a 180 degree turn, with the prizes going to experimentalists for successful experimental results. Even better, there has been an unusual emphasis on making an award to entire experimental collaborations, not just a small number of “great men” identified as collaboration leaders or spokespersons. I don’t know of any other major prizes that do this. The lack of an experimental Nobel for the Higgs discovery is one reflection of that problem, it’s great that the Breakthrough Prize people are doing something about it."[0]
Basically, we have two criticized recent physics awards (2019 special and 2017) and several in the very beginning. That still doesn't qualify as 'mostly'.
[0] http://www.math.columbia.edu/~woit/wordpress/?p=8088
> This prize isn’t too highly regarded.
Wow this is an astronomically absurd Hacker News put-down.
Wow this is an astronomically absurd Hacker News put-down.
See other comments for context. It was harsh, and perhaps a little out of date, but there has been criticism of the physics prize in the past.
A little moderation on both sides on this point wouldn't go amiss.
A little moderation on both sides on this point wouldn't go amiss.
> This prize isn’t too highly regarded.
> there has been criticism of the physics prize in the past
Those... aren't the same thing. I'm sure you could dredge up a few criticisms of the Nobel Prize in Physics as well, but would anybody say that the prize isn't highly regarded in general?
https://en.wikipedia.org/wiki/Nobel_Prize_controversies#Phys...
> there has been criticism of the physics prize in the past
Those... aren't the same thing. I'm sure you could dredge up a few criticisms of the Nobel Prize in Physics as well, but would anybody say that the prize isn't highly regarded in general?
https://en.wikipedia.org/wiki/Nobel_Prize_controversies#Phys...
Please don't quote me selectively if it distorts the point.
It was harsh, and perhaps a little out of date
It was harsh, and perhaps a little out of date
I don't see any distortion of the point. All I'm saying is that the fact that something has been criticized in the past does not (necessarily) equate to justification for a position of "it's not highly regarded".
I mean, it's not that impressive. I have like 3 of them.
Asking out of ignorance. When the article says that
> The Breakthrough Prizes are the largest prizes in science
Do they mean the prize comes with more money?
> The Breakthrough Prizes are the largest prizes in science
Do they mean the prize comes with more money?
So it is like Nobel Prize
https://www.quantamagazine.org/hearing-music-in-noise-martin...