Profile

Cover photo
Timothy Gowers
Worked at University of Cambridge
19,394 followers|1,939,225 views
AboutPostsPhotosVideos

Stream

Timothy Gowers

Shared publicly  - 
 
There are two categories of people: those who feel rather smug after trying out this site, and those who end up extremely sceptical about whatever algorithm is being used to guess ages from faces. I'm in the former category, since it guessed from a recent photo that I was 44.
#HowOldRobot. b_searchboxSubmit. Use This Photo. Use your own photo. Max Photo Size 3MB. Sorry if we didn't quite get the age and gender right – we are still improving this feature. Try Another Photo! Read the story behind this demo · Tweet · Privacy & Cookies | Terms of Use | View Source.
18
4
Sarai Pahla (AokageHime)'s profile photoZdenek Navratil's profile photoGuido Krause (DwayneHicks)'s profile photoMartin Bichler's profile photo
13 comments
 
So it is. That's rather disappointing.
Add a comment...

Timothy Gowers

Shared publicly  - 
 
The paper linked to below is chosen fairly arbitrarily from Neural Information Processing Systems, an open access journal with open peer review. The advantages of open peer review are clear: the reader gets useful extra information about a paper by reading what expert reviewers think about it. What about the disadvantages? I have heard it suggested that authors may be humiliated in public, or that reviewers will not be willing to share their thoughts publicly. But the few examples I've seen of open peer review show no evidence of this kind of problem. For example, if you click on "Reviews" in the page below, you are taken to a page where there are three anonymous reviews and responses by the authors. What stands out for me is just how polite and constructive the discussion is. It makes it clear that open review certainly can work very well. Maybe it sometimes leads to problems, but I've never seen any, so I think those risks are greatly outweighed by the advantages.
Eletronic Proceedings of Neural Information Processing Systems
47
14
Jan Jensen's profile photoCarol Hutchins's profile photoYohannes D. Asega's profile photoPratik Chaudhari's profile photo
16 comments
 
NIPS is a conference rather than a journal (not that it matters much for the question of review)
Add a comment...

Timothy Gowers

Shared publicly  - 
 
If you Google Pietro Boselli you find him described as the hottest mathematician in the world, a title he qualifies for by being a fashion model and a lecturer at UCL at the same time. However, it turns out that he is not quite a mathematician in the sense I would understand it: his PhD is in engineering and his maths lectures are not, I think, to mathematics students. So has anyone ever been both a fashion model (I would allow former fashion model here) and the author of a paper published in a reputable mathematical journal? I couldn't find anything by Boselli on arXiv.
Twenty-six-year-old maths lecturer and PhD student Pietro Boselli describes himself as 'nerdy', but the internet would beg to differ.
26
2
Mihir Hasabnis's profile photoanurag bishnoi's profile photoVaidotas Zemlys's profile photoJoerg Fliege's profile photo
31 comments
 
Does Ed Frenkel qualify? He acted in Rites of Love and Math. 

http://en.wikipedia.org/wiki/Edward_Frenkelhttp://www.imdb.com/name/nm3649875/
Add a comment...

Timothy Gowers

Shared publicly  - 
 
An attempt to devise a transfinite version of the Cheryl birthday puzzle.

I won't describe the original puzzle here -- just Google it if, by some miracle, you haven't seen it already. Let us define a logic puzzle of this sort to be of level N if it requires you to consider a chain of length N of the type "I know that you know that I know that you know ... etc." Then a level-omega puzzle would be one that requires you to consider chains of length N for arbitrarily large N. That's what I've tried to devise below. I do not guarantee that I have succeeded -- I may have made a silly mistake.

Cheryl presents Albert and Bernard with the following set of pairs of positive integers. For even n, let r=n^2, s=(n+1)^2 and let A(n) be the set that consists of the pairs (1,r), (r,r), (r,r+1), (r+1,r+1), (r+1,r+2), and so on up a staircase until you reach the point (s-1,s-1). For odd n, take instead the pairs (r,1), (r,r), (r+1,r), (r+1,r+1), (r+2,r+1), ... , (s-1,s-1). So, for example, A(1) consists of the points (1,1), (2,1), (2,2), (3,2), (3,3), while A(2) consists of the points (1,4), (4,4), (4,5), (5,5), ... , (8,8).

Cheryl then tells Albert the x-coordinate of a special point and tells Bernard the y-coordinate. Albert and Bernard then have the following conversation.

Albert: I don't know which point Cheryl has chosen.

Bernard: Even now you've told me that, I don't know which point she has chosen.

Albert: Even now you've told me that, I don't know which point she has chosen.

Bernard: Even now you've told me that, I don't know which point she has chosen.

and so on and so on. Eventually Cheryl gets bored and says, "Hey, can we talk about something else now? You're never going to work out the answer."

At that point Albert and Bernard both say, "Ah, now I know which point you've chosen." What was the point?
74
27
Tatchai Titichetrakun's profile photoPo Lam Yung's profile photoChor Kiang Tan's profile photoOmid Hatami's profile photo
8 comments
 
"At that point Albert and Bernard both say, "Ah, now I know which point you've chosen." What was the point?"

The point was to show how deviously complicated a puzzle can be posed by a girl who does not care about the mental sanity of her two friends ;-)
Add a comment...

Timothy Gowers

Shared publicly  - 
 
The world's oldest person has just died. This provoked me to think of a simple but I think quite interesting puzzle:  roughly how often would one expect this to happen? 

I've just done a back-of-envelope calculation and come up with an answer of about once a year. I'm not very confident that I haven't done something stupid somewhere along the line though. So as not to spoil the puzzle for anyone who might find it interesting, I won't give my reasoning for the moment, but I'll be interested to know whether others come up with similar estimates.
The world's oldest person, Japan's Misao Okawa, dies from heart failure at the age of 117.
23
3
Christian Stump's profile photoKevin Chilton's profile photoKevin Penrose's profile photoSampada Kolhatkar's profile photo
25 comments
 
This time, it was only 5 days: http://en.wikipedia.org/wiki/Gertrude_Weaver
Add a comment...

Timothy Gowers

Shared publicly  - 
 
I stood in Great Court, Trinity College this morning from about 9am till 11am, hoping to view the eclipse of the sun, which was partial when viewed from Cambridge but reached 85% at about 9:30. We noticed it get somewhat murky and a bit colder at around that time, but there was a thick layer of cloud (which looked thicker than it was because of the lessened sunlight) so we didn't see the sun at that point. There was quite a large crowd, but when the day started to get lighter again most of them dispersed. But a few diehards, of whom I was one, couldn't bear to leave when there was a chance that the clouds would get thin enough for us to see something, and we were eventually rewarded at about 10:10, and several times after that. For viewing a partial eclipse, thin cloud is pretty ideal, because you can look at the sun with the naked eye (though even then it isn't sensible to look for too long) just as you sometimes can when there isn't an eclipse at all. Here's one of several photos I took on my phone. One of my colleagues had set up some eclipse viewing equipment, and just before it ended the skies cleared to the point where it was no longer possible to look directly at the sun but one could view a very good image of it projected on to a piece of white card.

Amusing observation: of the people who stuck around for the full two hours, a large proportion were mathematicians. I was sorry to lose the work time, and sorry not to see the sun more covered, but despite that it was definitely worth it.
43
2
Deon Garrett's profile photoToby Bartels's profile photoDavid Nash's profile photosimone campbell's profile photo
5 comments
 
I live in the path of totality for the 2017 eclipse, so I'm looking forward to that.  I may take my class out to watch.
Add a comment...
Have him in circles
19,394 people
Bali Cycling Tour's profile photo
Patrick Wagman's profile photo
Adrian Firmansyah's profile photo
Dan Jackson's profile photo
Bob Boris's profile photo
Alan Bond's profile photo
Tmoocwill Editor's profile photo
Nuocca Kei's profile photo
Garrick Rettele's profile photo

Timothy Gowers

Shared publicly  - 
 
In the blog post linked to below, I argue that Nick Clegg's views about how to form agreements with other parties if no party has an absolute majority are in fundamental conflict with the values his party is supposed to represent (which I support). 
7
1
Tim Wesson's profile photoDavid Nash's profile photo
 
With Cambridge a Labour/Lib-Dem marginal, I'll be casting a Green vote. I was a leaflet-pusher for the LibDems myself, years ago, although I regret voting for party (LibDem) over the excellent constituency MP, Anne Campbell, who herself showed independence from the party line.

Julian Huppert is worth supporting over the Labour hack standing against him. I have simply decided for myself that strengthening the Green vote is a higher priority than electing the better centre-left candidate.
Add a comment...

Timothy Gowers

Shared publicly  - 
 
I'm on the editorial board of Combinatorica. Whether I should be is another matter, since it is a journal owned by Springer, one of the big commercial publishers. But I am, and as a result I have a free subscription to the journal. Today I found the latest issue in my pigeonhole, and the last paper in the issue was a paper by Csaba Tóth, entitled, "The Szemerédi-Trotter theorem in the complex plane." 

This paper is remarkable for two reasons. One, which provokes this post, is that at the beginning of the paper it says, "Received December 1999, Revised May 16 2014." So the paper is coming out over 15 years after it was submitted. Doubtless this isn't a record, but it's still a pretty big gap. I noticed it because my first reaction on seeing the title was, "But I thought this had been done a long time ago."

The other reason is the result itself. The Szemerédi-Trotter theorem states that if you have n points and m lines in the plane, then the number of incidences (that is, pairs (P,L) where P is a point in your collection, L is a line in your collection, and P is a point in L) is at most C(n + m + n^{2/3}m^{2/3}). This slightly curious looking bound is best possible up to the constant C and is more natural than it looks.

The known proofs of the theorem relied heavily on the topological properties of the plane, which meant that it was far from straightforward to generalize the result to lines and points in the complex plane (by which I mean C^2 and not C). Indeed, it was an open problem to do so, and that was what Tóth solved.

If you're feeling ambitious, there is also a lovely conjecture in the paper. Define a d-flat in R^{2d} to be an affine subspace of dimension d. Suppose now that you have n points and m d-flats with the property that no two of the d-flats intersect in more than a point. Is it the case that the number of incidences is at most C(n + m + n^{2/3}m^{2/3})? The constant C is allowed to depend on the dimension d but not on anything else. Note that even for d=2 this would be a new result, since Tóth's theorem is the special case where the d-flats are complex lines.

I should say that I haven't checked whether there has been any progress on this conjecture, so I don't guarantee that it is open. If anyone knows about its status, it would be great if you could comment below.

#spnetwork  DOI: 10.1007/s00493-014-2686-2
39
5
Julien Narboux's profile photoHelger Lipmaa's profile photoDave Gordon's profile photoCetin Kaya Koc's profile photo
10 comments
 
+David Wood thanks to the lowest bidder for the contract to outsource Springer's actual editing/publishing process, I'm sure.
Add a comment...

Timothy Gowers

Shared publicly  - 
 
A couple of years ago, someone collected a very nice set of data by testing pupils at Caddington Village School in Bedford on their multiplication tables and recording the percentages of correct answers. The data have been made into a colour chart that allows you to look at which products people find hardest to evaluate. One interesting feature (though I don't know how much it is just random noise) is that the chart is not symmetric about the diagonal. For example, 8x7 and 7x8 do not appear to be of equal difficulty. The numbers on the right are, I think, the percentages of wrong answers, so the higher the number the harder the question. Another interesting thing is that 2x1 seems to be got wrong occasionally (but not 1x2). My guess would be that from time to time people answer 3. 

One reason this interests me is that I have often seen people lazily saying that to learn your tables you have to learn 144 arbitrary facts. This is of course completely false. To begin with, as this diagram illustrates, many of those facts are not at all arbitrary: for instance, you don't "memorize" your 1 and 10 times tables. Secondly, the facts are not isolated: if you know what 7x7 is, for example (which many people don't, to judge from the chart) then you can use it to work out 8x7. Of course, you eventually want to be able to say what 8x7 is without thinking, but I see it as like driving a car: initially you should think carefully about what you are doing and after a while it should become automatic. For this reason, I would describe myself as a semi-traditionalist when it comes to tables. I think they should be taught, but I don't think they should be taught in the kind of pure rote way that many people object to.
50
9
philippe roux's profile photoTed Driver's profile photoAleatha Parker-Wood's profile photoTau-Mu Yi's profile photo
25 comments
 
I agree with the value of multiplication tables, as described in this thread.

But, as a general matter, I think that insights and knowledge that are specific to base-10 are overrated.  Sure, they're related to more general base-agnostic insights, but it's clear that that's not what we're usually emphasizing.

It seems to me that no one is interested in the question of whether students are able to do long division in base 2, which implies that they don't care one bit whether the more general inferences have been made.  They just want people to be able to do calculations without a calculator, for approximately no reason other than tradition.
Add a comment...

Timothy Gowers

Shared publicly  - 
 
My nephew +Raymond Douglas (aged 14) got me to play a very cool game of his invention today. My opponent was my 7-year-old son. We had to sit back to back. Also, he spent a bit of time explaining to each of us what to do, and it was important that we should not hear what he said to the other person.

Here were my instructions. I had a list of letters associated with the numbers 1 to 9. I can't remember exactly what they were, but it doesn't matter, as it just had to be some kind of encoding. So I had some kind of chart such as 1W, 2T, 3N, 4J, 5P, 6H, 7L, 8S, 9K. 

We then took turns calling out letters. My rules were that I was not allowed to choose a letter that my son had already called out, and my aim was to end up having chosen three letters (amongst the possibly more than three that I ended up choosing) such that the corresponding numbers added up to 15. 

The question is, what was my son doing all the while? It's fun to think about this, so here's the customary spoiler alert plus some space.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
The answer is that my son was playing noughts and crosses, and for him the letters stood for squares in a 3-by-3 grid. In other words, the add-up-to-15 game and noughts and crosses are isomorphic. What I find beautiful about this fact is that the add-up-to-15 game is very simple and yet the isomorphism is not entirely trivial. Here is how it works. You fill up a 3-by-3 grid with numbers as follows.

6  1  8
7  5  3
2  9  4

There are two properties that this grid of numbers must satisfy. First, it must be a Latin square -- that is, all rows, columns and diagonals must add up to 15. Secondly, there should be no triple adding up to 15 that is not a row, column, or diagonal. Actually, the second follows from the first, because it so happens that the number of triples of numbers between 1 and 9 that add up to 15 is precisely 8, the number of rows+columns+diagonals.

An interesting aspect of the experience for me was that I instinctively used a certain amount of standard noughts-and-crosses strategy. For instance, I thought it would be good to choose the number 5 if possible, because it would be in the most triples. Also, at one point I got into a winning position by noticing that I could choose a number that would give me two routes to a triple, with my son not able to stop both of them. He had played badly that round. However, while I know how not to lose at noughts and crosses, I didn't manage to stop my son winning the next round, so the isomorphism had been enough to blind me to quite a lot of the structure of the usual game.
67
13
Theron Hitchman's profile photoTau-Mu Yi's profile photoOmid Hatami's profile photoHaider Khan's profile photo
12 comments
 
+Robin Houston - I might have known that once, but if so I'd forgotten it.  I was wondering about it as I wrote my comment, but too busy to check it out.

I've never gotten very deep into magic squares.  Here's a paper that uses algebraic geometry to count 4x4 magic squares with a given 'magic sum':

http://arxiv.org/abs/math/0201108
Add a comment...

Timothy Gowers

Shared publicly  - 
 
We are often told that the journal system must be protected at all costs because of the value added to our papers by the rigorous system of peer review. I question that statement, but it is a respectable position to take and there are plenty of people I respect who take it.

But sometimes people start to wonder whether supposedly respectable journals are doing their job properly. One such person is Dorothy Bishop, a psychologist at Oxford, who got suspicious about two Elsevier (who else?) journals, Research in Autism Spectrum Disorders, and Research in Developmental Disabilities. In particular, she thought that editors were getting their own papers published in these journals too easily.

But how does one prove an assertion like that when the refereeing process is not public? She had the following great idea. In her words,

Evidence on this point is indirect, because the published journals do not document the peer review process itself. However, it is possible to look at the lag from receipt of the paper to acceptance, which can be extracted separately for each individual paper. I have looked at this further using merged data on publication lag with information available from Web of Science to create a dataset that contains all papers published in RIDD between 2004 and 2014, accompanied by the dates for receipt and acceptance of papers.

For her fascinating findings, have a look at the blog post I'm linking to. They don't look good ...
Elsevier, the publisher of Research in Autism Spectrum Disorders (RASD) and Research in Developmental Disabilities (RIDD) is no stranger to controversy. It became the focus of a campaign in 2012 because of its pricing strateg...
80
17
Björn Brembs's profile photoCharles Stewart's profile photoOmid Hatami's profile photoVít Tuček's profile photo
8 comments
 
This is even worse than pay-to-play journals. Sigh.
Add a comment...

Timothy Gowers

Shared publicly  - 
 
A review of X+Y by a Trinity undergraduate and recent IMO contestant. The review confirms the impression I got from the trailer. It is also notable for being unafraid to mention actual mathematics in a mainstream newspaper. 
 
There's a mathsy film out on Friday, X+Y, about a young autistic prodigy competing at the International Maths Olympiad. It's got big British stars, and is being hyped quite a bit...So, I asked a former British maths olympian to review X+Y for my Guardian blog and explain whether the movie gets it right.
The high pressure world of international maths tournaments is brought to life in the much-anticipated British movie X+Y. Here a former contestant reveals the maths, the alcohol and the sexual intrigue of these events and tells us whether the film gets it right
8 comments on original post
39
8
Omid Hatami's profile photoNinnat Dangniam's profile photoIGNACIO H. OTERO's profile photoRadu Grigore's profile photo
17 comments
 
The review says that the cards problem is "entirely trivial", so its use in preparation for IMO is "highly unrealistic". I'm not sure I buy that. A few months ago I was helping a relative to learn math. He wanted something a bit more challenging than he was doing in school. Every once in a while I was looking at IMO problems to see if I find something suitable to discuss. And here's what I once used: http://research.microsoft.com/en-us/um/people/leino/puzzles.html#A%20game%20of%202014%20cards

This was, I think, from IMO2009 (shortlisted?long-listed? used? I'm not even sure what these terms mean...) Anyway, perhaps this IMO problem is easier than your average IMO problem, and also a little more difficult than the "entirely trivial" one from the movie. Still, I wouldn't criticize that part of the movie as "highly unrealistic".
Add a comment...
People
Have him in circles
19,394 people
Bali Cycling Tour's profile photo
Patrick Wagman's profile photo
Adrian Firmansyah's profile photo
Dan Jackson's profile photo
Bob Boris's profile photo
Alan Bond's profile photo
Tmoocwill Editor's profile photo
Nuocca Kei's profile photo
Garrick Rettele's profile photo
Work
Employment
  • University of Cambridge
    Royal Society Research Professor
Links
Story
Tagline
Mathematician
Basic Information
Gender
Male