Did studying maths help Emma Raducanu win the US Open?

 Emma Raducanu's feat of winning the US Open as a qualifier, without dropping a set in her ten matches, was astonishing.  In feature articles this summer, during and after Wimbledon, her A-level achievements this summer, and especially her A* grade in A-level Mathematics, have been reported,  Is there a connection between her tennis accomplishments and her study of maths?

Now, mathematics implicitly arises in tennis tactics.  I've discussed toy examples in public lectures on game theory, which (it seems to me) is relevant to choices players make - whether to serve to the forehand or backhand, and where to expect for your opponent to serve, for example. I very much doubt if players ever analyse in these terms, but they are intuitively doing game theory when making their tactical decisions.

But I think in the case of Raducanu there is a more  general point.  Several times I have heard knowledgeable commentators - most recently Tim Henman immediately after Raducanu's victory over Leylah Fernandez in the US Open final last night - talk about her qualities as a problem solver.  She thinks deeply about her tactics, adapting to opponents and match situations.  Now problem-solving is a quality which is developed in studying mathematics.  (Fernandez, who showed in her victories over three top-five opponents in New York remarkable abilities to turn around matches in which she was behind, apparently enjoys solving Rubik's cube - more mathematical problem-solving!0

Obviously her study of mathematics is not why Raducanu is a great tennis player.  But it seems to me that the problem-solving skills which she displays on the tennis court are the same skills which make her good at mathematics.  

Another dubious probabilistic argument

 Here's a variation on my previous post - another piece of hand-waving probabilistic reasoning, which I think is basically correct, but I suspect many will disagree.  

A long time ago I used to do the challenging weekly cryptic crosswords in The Listener magazine.  (The Listener has been defunct for many years, though I think the crossword continues in The Times.)  The story was that if no-one solved the crossword, it was too hard, and if more than one person solved it, it was too easy.  While that was an exaggeration, it wasn't easy, and I judged it worthwhile, if I completed the puzzle, to submit my entry for the prize draw.

I had completed about fifteen puzzles in a row, and submitted my answers each time, but hadn't won the book token.  Then there was an unusual puzzle - it was mathematical rather than word-based.  Two mathematician colleagues and I worked on it - we didn't find it at all easy - and we eventually solved it. I submitted our answer, and this time, we won the book token.

So - my conclusion was that (probably) more people solved the word-based puzzles than the mathematical one, and that therefore I was more likely to win the prize for that puzzle (as I had done) than for the others.

Is this conclusion valid?

As it happens, at the end of the year statistics for all The Listener crossword entries were published, so I was able to see if this was indeed the case.  It turned out that the mathematical crossword had attracted about three times as many correct entries as any of the others.  So my conclusion was in fact false, but I still think the reasoning was sound.

Is this analysis correct?

When I was an undergraduate, I was walking through the town centre one morning when a journalist from the student newspaper asked my views on the Rag Mag that had just appeared.  When the report came out, six students' views were quoted. Three of the six happened to be from the same cohort of six maths undergraduates at my college.  My Director of Studies concluded (jokingly) that this disproportionate representation of his tutees showed that we were spending too much time out and about when we should have been studying.

Here is a similar scenario, based on a recent experience.  Suppose that I enter a lottery.  It is open to, say, 10,000 people, but I do not know how many choose to take part.  As it happens, I win the lottery.  It seems to me that I can conclude that (with a high degree of probability) only a small proportion of those who were eligible chose to enter the lottery.  If all 10,000 people entered then my chance of winning was only ,00001, whereas if 5 people entered it was 0.02.  Since I did win, my estimate of the likely number of entrants will be at the lower end.

Now, you are my friend and you are equally friendly with all 10,000 potential participants. I tell you about it,  I think you should agree that I am right in my conclusion.  But you cannot come to the same conclusion: whichever of the 10,000 people had won the lottery would have told you of their success, so you can't deduce anything from what I have said to you about the likely number of participants.

So - I have good reason to come to a conclusion (with a high degree of probability).  You agree that I am right to come to this conclusion, but also you have no reason to suppose that the conclusion is valid.  How can this be?

Apologies if I am missing something but I think this analysis is sound. Have I read about this somewhere?

However, I haven't yet managed to persuaded anyone else to agree with me (which is perhaps ironic, or perhaps I am just wrong).  Comments welcome!

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Tomorrow's Mathematicians Today

I spent last weekend at the online conference Tomorrow's Mathematicians Today, hosted by the University of Greenwich and the Institute of Mathematics and its Applications.  This is a conference for undergraduate mathematicians to present to their peers on mathematical topics that excite them - this might be their own project work, or something they have come across in the curriculum or outside it that has fascinated them.  The conference was created in 2010 by Noel-Ann Bradshaw when she taught at the University of Greenwich, and has been held in various venues since.

We hosted it physically at Greenwich in 2010, 2013, 2016 and 2019, and before Saturday I was apprehensive that the conference would not work online.  At the physical conferences what made the event so exciting was the atmosphere - friendly and supportive of the speakers, with great enthusiasm from audience and presenters.  Would this work online? 

Well, it was obviously different, but the enthusiasm was certainly present, and the online networking sessions were well attended and worked far better than I had imagined.   Here are the words the attendees chose to describe their feelings:

The quality of student presentations was outstanding: the judges of the GCHQ Prize for the Best Presentation had an extremely difficult task deciding the winner.  The winning paper by Yanqi Cheng (UCL) was remarkable not only for its content but for Yanqi's sangfroid in managing a seamless transition to live delivery when the computer playing her pre-recorded video crashed early in the presentation.  "Honourable Mentions" were awarded to Yousra Idichchou (Greenwich) and Oscar Holroyd (Warwick), and the other shortlisted papers by Finley Wilde (Bristol), Kaiynat Mirza (Keele), Muhiyud-Dean Mirza (Warwick) and Sheeru Shamsi (Keele) were all excellent, as indeed was every single student talk.

The conference also benefited from two contrasting keynotes by established mathematicians - Colva Roney-Dougal on random games with groups and Kit Yates on the mathematics of epidemics.  It was surprising to hear from Colva how the Riemann Hypothesis turns up in group theory!

Like its predecessors the conference was inspiring in showcasing the enjoyment today's students are taking from mathematics.  It totally proved the point made by IMA President Nira Chmberlain in opening the conference when he said that the presenters were not "tomorrow's mathematicians" but are already fully qualified for the title of mathematician.

I obviously hope future TMT conferences will be held physically again, but the online conference was as friendly and inspiring as we could have hoped!