The results of the 2008 Discovery Grants competition are now available: GSC 336, GSC 337. This is clearly an improvement over last year’s situation, when the budget for the mathematics GSCs was cut quite severely. I don’t have the time to do detailed statistics as I did in an earlier post on the subject, but for a quick comparison, let’s look at the top tier of GSC 336 grants. In 2007, the three highest awarded amounts were 57K, 39K and 35K; all other grants were valued at 32K or less. In 2008, the top three grants are 52K, 48K, 44K, and five more are valued at 42K each. No, it does not mean that all the best researchers applied this year. It means that last year there was much less money available, as I’m hearing from sources close to the bean counter.

I would hope that the 2007 GSC budget was a one-time screw-up and that the GSC budget will stay around the 2008 level in the future. There are, however, a couple of additional considerations that unfortunately have to be brought up.

… it’s time for some summer music.

This band is called Nouvelle Vague. What they do is cover versions of 1980s new wave songs, bossanova-style. The first time I heard them was on a trip to Europe two years ago. I arrived at my destination late in the afternoon, cranky and tired, after 3 plane flights and over 20 hours of travel. The time difference between there and Vancouver was 9 hours. I hardly got any sleep that night and was wide awake again by 6:30 am. That’s when I heard this song on the radio. Quite unbelievably, it put me in a good mood for the rest of the day.

It’s my favourite Nouvelle Vague song, by far. The lead singer here is Gerald Toto, who also records solo and with various other groups. For an encore, here’s Gerald Toto again, this time in French:

Let be a set of real numbers. We will write and . What can we say about the minimum size of or ?

It’s easy to prove that , and the equality holds if and only if is an arithmetic progression. Similarly, , and the equality holds if and only if is a geometric progression. On the one hand, both of the lower bounds above are sharp; but on the other hand, the sets minimizing and look quite different. In fact, if is an arithmetic progression, then the product set is rather large, with . Conversely, if is a geometric progression, then must be large.

Erdös and Szemerédi conjectured that at least one of and must always be large. Specifically, it is expected that for any we must have

The reason for this post is that, just very recently, Jozsef Solymosi proved the estimate

improving the previously known bounds, the most recent of which was also due to himself. (Earlier results were due to Erdös, Szemerédi, Nathanson, Ford, and Elekes.)

Or, if you’re Dennis Lehane, you might call it “the hamster wheel.”

In an age when reading for pleasure is declining, book publishers increasingly are counting on their biggest moneymaking writers to crank out books at a rate of at least one a year, right on schedule, and sometimes faster than that.

Many top-selling writers, such as John Grisham and Mary Higgins Clark, have turned out at least one book annually for years. Now some writers are beginning to grumble about the pressure, and some are refusing to comply.

Me, I’ve given up on several authors because their work felt, well, forced. Patricia Cornwell’s Scarpetta series, mentioned in the article, started out with several tight and highly enjoyable forensic thrillers, but then evolved into a combination of soap opera and introspection. Introspection, in this context, means using about 100 pages to say the equivalent of “it’s scary when a serial killer is after you.” But in the end it was the soap opera part - a familiar character confesses that she’s actually a millionaire, another character gets resurrected all of a sudden - that turned me off. Now, Cornwell is certainly not the worst of the gang. I’ve singled her out because she used to be one of my favourite writers, and perhaps she would still be if she had taken the time to get off the hamster wheel and think about what she really wanted to write.

A writer can “keep her face out there” by writing a book every year, or she can do it by writing books that the readers won’t forget. If she can do both, that’s great, but if not, I’m more likely to buy her books if she does the latter.

This post is for Hillary Clinton.

Now even in the matter of homesteads women are not allowed free land unless they are widows with the care of minor children [...] The alleged reason for this discrimination is that women cannot perform the required duties and so, to save them from the temptation of trying, the government in its fatherly wisdom denies them the chance.

But women are doing homestead duties whenever homestead duties are being done. Women suffer the hardships - cold, hunger, loneliness - against which there is no law; and, when the homestead is “proved,” all the scrub cleared, and the land broken, the husband may sell the whole thing without his wife’s knowledge, and he can take the money and depart, without a word. Against this there is no law wither!

No person objects to the homesteader’s wife having to get out wood, or break up scrub land, so long as she is not doing these things for herself and has no legal claim on the result of her labour.

- Nellie McClung, May 1916

The laws have changed over the last 90 years, but that business with claiming the fruits of our labour for ourselves is still unfinished. We may be legally entitled to equal pay, but just recently the U.S. senate blocked a bill that would have actually allowed women to enforce it. Hillary Clinton and Barack Obama both voted for the bill. John McCain did not vote, but was happy about the outcome.

Even when the results of our labour are legally ours, it’s just, well, impolite of us to insist on claiming them. Hillary has experienced it. I have experienced it. Many of us have.

I’ve never believed that women should support Hillary because of their experience of discrimination or backlash. There are better reasons to vote for a candidate, Senator Clinton or otherwise. What are her policies? How exactly is she going to help us? But it is because of that experience that we understand a little bit better what she is doing and why, regardless of whether we agree with her or not.

She didn’t quit when she was told she should? If you had given up a fight for the sake of collegiality, only to have it rubbed in your face, if you had been asked to concede time and again for no apparent reason except that it would be nice of you to do so, and if you didn’t see any of that happening to your male colleagues, you too would develop a gag reflex when it comes to voluntary concessions. You might, in fact, aim to go too far in the other direction, because that’s what you do first if you want to find a good balance.

She was negative and divisive in her campaign? Yes, she was, and that has cost her. She has tested everyone’s patience, mine included, with the Bosnian sniper fire stories and the endless speculations on how she would be winning if the rules were different. The rules are what they are, and she, of all people, should know that well enough. She’s spent too many years learning and following the rules.

But back to being divisive? Just recently, I came upon a study that claims that women don’t get elected to public offices because they’re not really interested. There will be a separate post about this, because I’m a little bit familiar with the “ambition gap,” but for now I’ll just say that this perception is a real problem for us. If Hillary had been less negative, the default assumption would have been that she didn’t really want the job all that much. She did want it, and she was negative, and that got her in another kind of trouble.

Barack Obama had a whole different set of default assumptions to fight. He handled it better, and he won. I hope that he wins in November. But this post is about Hillary.

Next time that a woman runs for the U.S. presidency, I hope that she will run a better organized campaign and that she will not have a history of politically expedient, but ultimately misguided, votes. But also, that she will not have to spend much time establishing that, yes, a woman might actually run more than a token campaign. That she will be judged on her policies, not her clothing. Perhaps she will even get to the point of being able to run without first having to make all those compromises that become a liability later on. Then she might be able to win.

And that just might be possible because of Hillary’s campaign. In the end, she did change the rules. A female candidate is no longer just a token candidate, it’s someone who might actually get the nomination. It’s someone who might have a very close fight with one of the best politicians, of either gender, that we’ve seen in a long time. Someone who does want the job and will likely be good at it if elected.

The glass ceiling is made of presumptions and beliefs. Hillary did break that.

Here’s how Nellie McClung ends her essay:

Women will make mistakes, of course, and pay for them. That will be nothing new - they have always paid for men’s mistakes. It will be a change to pay for their own; and in paying for them they will learn wisdom.

Last Spring, the NSERC Discovery Grants applicants received the following letter from NSERC (I quote from mine):

The 2007-08 Discovery Grants program budget was under great pressure despite the injection of close to 6 million of new funds. This situation was due to the substantial increase in the number of applications which could not be matched by a corresponding growth in the program’s budget. Therefore, the budget was insufficient to meet the needs of the large number of new and returning applicants. For the Pure and Applied Mathematics “A” Grant Selection Committee 336, this resulted in the budget awarded to renewal applicants being approximately 16% lower than the amount previously held by that group of researchers. This made the competition more difficult than in previous years and the resulting recommendations are reflective of this extra pressure.

You can’t just have two posts about research grants back to back. So, here’s a little bit of storytelling songwriting at its best, from 25 years ago.

As some of the readers here may know, the NSERC Discovery Grants program is under review.  An international committee was struck last year to evaluate the effectiveness of the program.  The report of that committee has now been posted on the NSERC web site.

In a nutshell, the committee says: the program works just fine. There is room for a little bit of improvement (and the report makes specific suggestions in that regard), but no major overhaul is either needed or recommended. Also, the program could use more money.

The main issue specifically addressed in the report is the following. The “success rate” in the Discovery Grants competition is roughly 70% (i.e., in any given year, 70% of applicants are funded). This is much higher than, for example, the 30% success rate in the NSF individual research grant competition. Does it mean that NSERC is not applying high enough standards? Should the Discovery Grants program support instead a smaller group of the top-ranked applicants, funding them at a higher level, and cut off the “long tail”?

Here’s what it looks like from a mathematician’s perspective.

It’s spring at last, even in Toronto…

… Yorkville is not too crowded on a weekday afternoon, but weekends are a different story…

… and if you’re at the right place on Bloor Street at the right time, you might see Aimee Mann playing a live show for free.

It’s been a good semester. I have enjoyed the conferences and other organized activities (that’s where you learn things and get ideas), but also the quiet periods in between (that’s when you actually get the work done). It’s pretty quiet right now, and I have nothing else left to organize, so that I can actually focus on research.

There will likely be a separate post on thematic programs and on the joys of organizing one. Right now I’ll just say that this has been great for my own research program. When you’re isolated - as I was for several years - it’s hard to keep up with what everyone else is doing, and perhaps even harder to stay motivated. Now I’m enjoying mathematics more than I have in years.

A few more Toronto photos under the cut.

Academic politics in England circa 1908, according to F.M. Cornford:

You think (do you not?) that you have only to state a reasonable case, and people must listen to reason and act upon at once. It is just this conviction that makes you so unpleasant. There is little hope of dissuading you; but has it occurred to you that nothing is ever done until every one is convinced that it ought to be done, and has been convinced for so long that it is now time to do something else? And are you not aware that conviction has never yet been produced by an appeal to reason, which only makes people uncomfortable? If you want to move them, you must address your arguments to prejudice and the political motive, which I will presently describe.

And what might these be? Let’s examine a few important political principles:

The Principle of the Wedge is that you should not act justly now for fear of raising expectations that you may act still more justly in the future — expectations which you are afraid you will not have the courage to satisfy. A little reflection will make it evident that the Wedge argument implies the admission that the persons who use it cannot prove that the action is not just. If they could, that would be the sole and sufficient reason for not doing it, and this argument would be superfluous.

The Principle of the Dangerous Precedent is that you should not now do an admittedly right action for fear you, or your equally timid successors, should not have the courage to do right in some future case, which, ex hypothesi, is essentially different, but superficially resembles the present one. Every public action which is not customary, either is wrong, or, if it is right, is a dangerous precedent. It follows that nothing should ever be done for the first time. [...] a Fair Trial ought only to be given to systems which already exist, not to proposed alternatives.

Another argument is that ‘the Time is not Ripe’. The Principle of Unripe Time is that people should not do at the present moment what they think right at that moment, because the moment at which they think it right has not yet arrived. [...] Time, by the way, is like the medlar; it has a trick of going rotten before it is ripe.

But surely, there must be a way to get something done?

This most important branch of political activity is, of course, closely connected with Jobs. These fall into two classes, My Jobs and Your Jobs. My Jobs are public-spirited proposals, which happen (much to my regret) to involve the advancement of a personal friend, or (still more to my regret) of myself. Your Jobs are insidious intrigues for the advancement of yourself and your friends, speciously disguised as public-spirited proposals. The term Job is more commonly applied to the second class. When you and I have, each of us, a job on hand, we shall proceed to go on the Square.

Squaring can be carried on at lunch; but it is better that we should meet casually. The proper course to pursue is to walk, between 2 and 4 p.m., up and down the King’s Parade, and more particularly that part of it which lies between the Colleges of Pembroke and Caius. When we have succeeded in meeting accidentally, it is etiquette to talk about indifferent matters for ten minutes and then part. After walking five paces in the opposite direction you should call me back, and begin with the words, ‘Oh, by the way, if you should happen …’ The nature of Your Job must then be vaguely indicated, without mentioning names; and it should be treated by both parties as a matter of very small importance. You should hint that I am a very influential person, and that the whole thing is a secret between us. Then we shall part as before, and I shall call you back and introduce the subject of My Job, in the same formula. By observing this procedure we shall emphasise the fact that there is no connection whatever between my supporting your Job and your supporting mine. This absence of connection is the essential feature of Squaring.

Remember this: the men who get things done are the men who walk up and down King’s Parade, from two to four, every day of their lives. You can either join them, and become a powerful person; or you can join the great throng of those who spend all their time in preventing them from getting things done, and in the larger task of preventing one another from doing anything whatever. This is the Choice of Hercules, when Hercules takes to politics.

Link found in the comments on Crooked Timber.