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Richard Elwes
Works at University of Leeds
Attended University of Oxford
Lived in Leeds
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Richard Elwes

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Personal Reflections on Analysis

The introduction of ‘dictionaries’ between two or more fields can serve as a pole-star, as Sullivan observed for Kleinian Groups and rational dynamics. Don’t forget the Number Theory - Nevanlinna Theory Dictionary, pushed by Vojta. At the same time there is a danger if you allow language to take over without having your feet on the ground. The Bourbakization of mathematics in the 1940s and 1950s led to a mostly unfruitful development within analysis, and serves as an illustration of the pitfalls awaiting a blind approach.

Lennart Carleson and Peter Jones offer some personal, and occasionally provocative, reflections on Analysis in the 2002 Archives of the EMS Newsletter. Page 25 here:
http://www.ems-ph.org/journals/newsletter/pdf/2002-12-46.pdf#page=25
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Learning to Learn from Babies

Babies are fantastically fast and efficient learners. What might the rest of us learn from them? Click through for my latest blog post.
Yesterday, my twin sons turned one. I have spent an amazing number of hours over the last year watching them. I wondered if this experience might teach me something too, about how to learn. After a...
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That bad short-term memory lasts quite a while. When trying to teach my four-year-old daughter to read, I tell her things like "e  e makes ee" or what some unfamiliar combination of letters says, and she can come to the same situation four words later and it will be as though I hadn't told her the information. Though in that case it may have more to do with receptiveness to what her father is saying than with her ability to remember it: perhaps if I said, "o n e spells wun, and in a minute's time if you can tell me what it says I'll give you a piece of chocolate," her memory would improve dramatically.
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A message worth repeating: back up your stuff

My iPhone (5c) played a terrifying trick on me a couple of days ago. I was midway though putting something in my diary when the application crashed. So far, so normal. But when I reopened the calendar app, not only had the new appointment not been entered, but everything else had been deleted! Literally my entire diary had been wiped. So far as I could see, nothing else was wrong with the phone - my contacts and so on were still all there.

At that moment of doom, I realised how utterly reliant on this single app I had become - I dispensed with paper diaries years ago. My work and home life were both contained within.

I'm relieved to report that this story has a happy ending - by sheer good luck I had synced and backed up the phone to my computer a week earlier, and was able to restore the phone to that point. All that remained was to think hard about what entries I might have made within the last seven days.

I don't know how this happened - I slightly suspect [update: or not, see comments] a malfunction with the FindMyIphone App, one of whose jobs is to wipe everything if your phone is lost/stolen - but this may be unfounded. Whatever the cause, the moral is clear and worth repeating: back up your stuff regularly! I'm sure most people follow this advice for their big important documents - but don't forget your phone and whatever other small devices you have committed your life.
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It's not just the Apple calendar either. I've seen or heard of it happening with all kinds of online sync solutions including Dropbox. A colleague lost a few days of work on a presentation when a botched Dropbox sync deleted it on both devices.

Don't use a synchronized folder or other data source as your primary storage, is the lesson. Use it for syncing, but make sure your primary source can't be altered by the synchronization.
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Fermat: First and Foremost a Judge

We are rightly used to seeing Fermat as the great mathematician and humanist scholar. But according to his conception of himself, he was first and foremost a judge. At the parliament of Toulouse he had a seat for life. Even though he could live off his possessions in Beaumont-de-Lomagne, he regarded his job as conseiller au parlement de Toulouse as his proper life's work, and his career in this institution was more important to him than his reputation as a mathematician. Only when his professional activities allowed him enough leisure, such as when parliament was not in session during the numerous religious festivals, could he devote himself to his hobby of mathematics.

Klaus Barner looks back on Pierre de Fermat's life beside mathematics, from the 2001 archives of the EMS Newsletter (page 12): http://www.ems-ph.org/journals/newsletter/pdf/2001-12-42.pdf#page=12
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Plus,+John Baez, he created problems that took hundreds of years for other people to clear up. :-)
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[...] As a professor of mathematics, William “Bill” Tutte was revered for his mathematical genius and pioneering ways, attracting top-level researchers and building the reputation of the University from the ground up.

And yet for the entire length of his decorated career at Waterloo, no one — not longtime friends, colleagues or students — knew Tutte had been one of the brilliant minds of Bletchley Park, site of the now-legendary team of wartime code breakers who worked feverishly to stop Hitler’s advance. 

And while the history of Bletchley Park was dominated by Enigma and the tragic story of Alan Turing — recently immortalized in the Oscar-winning film The Imitation Game — historians and those who knew Tutte personally believe Tutte’s contributions were far greater. [...]
Winston Churchill called war-time codebreakers “the geese that laid the golden eggs but never cackled.” A revered Waterloo math professor was among them
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Apart from bureaucratic single-mindedness, why the declassification interval was as long as it was defies sense.
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Shaw Prize 2015

We offer (belated) congratulations to Gerd Faltings and Henryk Iwaniec, winners earlier this month of the The Shaw Prize in Mathematical Sciences 2015.

The prize is awarded "for their introduction and development of fundamental tools in number theory, allowing them as well as others
to resolve some longstanding classical problems".

The Shaw Prizes were founded in 2002, under the auspices of the Hong Kong businessman and philanthropist Run Run Shaw.
Announcement The Shaw Prize in Mathematical Sciences 2015 is awarded in equal shares to. Gerd Faltings and. Henryk Iwaniec for their introduction and development of fundamental tools in number theory, allowing them as well as others to resolve some longstanding classical problems.
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Read the Masters! Read Abel!

"It appears to me that if one wants to make progress in mathematics one should study the masters and not the pupils."
 - Niels Henrik Abel

"It is as good an idea to read the masters now as it was in Abel's time. The best mathematicians know this and do it all the time. Unfortunately, students of mathematics normally spend their early years ..., and make little or no reference to the primary literature of the subject. The students are left to discover on their own the wisdom of Abel's advice. In this they are being cheated [6, p.105]." - Harold M. Edwards (1981)

These are taken from Otto B. Bekken's article about Abel, in the 2002 Archives of the EMS Newsletter. Page 12 here:
http://www.ems-ph.org/journals/newsletter/pdf/2002-03-43.pdf#page=12
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Okay, but, like, how? I don't know where to find the masters. 
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"All primes are odd, and 2 is the oddest of them all." 
- JWS Cassels
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A different twist: “2 is the only even prime number. And that's odd.”
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What does a big jerk feel like?

Velocity is the rate of change of position. Acceleration is the rate of change of velocity. Jerk is the rate of change of acceleration.

A famous physical principle (Newton's second law) says that your acceleration is proportional to the force acting upon you. So, if you are subject to a constant force (e.g. freefalling under gravity, ignoring air resistance) you accelerate at a constant rate, and your jerk is 0. Jerk is what you feel when the force on you changes (e.g. when you open your parachute or hit the ground).

Even though this principle is straightforward (jerk corresponds to change in force), somehow it is still difficult to grasp, because most familiar instances (e.g. accelerating in your car) are examples of acceleration changing from zero to non-zero, making it difficult to separate the effect of the acceleration (or force) itself from that of the jerk (change in acceleration/force).

As in the freefall described above, deceleration provides easier examples. Suppose you're slowing down in your car, decelerating at a uniform rate (meaning the time it takes to reduce from 30mph to 20 mph is the same as that it takes you reduce from 20mph to 10mph, and so on). When you hit 0, you can't decelerate any more, and instead of starting to travel backwards, the car stops, with a big jerk. This unpleasant (and dangerous) sensation is not the consequence of a force, but the sudden removal of one.  (Needless to say, this is not how good drivers do things. Instead, you should gradually reduce the rate of deceleration as you slow down, and stop with only a small jerk.)

There are words for higher order quantities too: the rate of change of jerk is known as the jounce or snap. making this is 4th derivative of position. I find this quite difficult to conceptualize. Beyond these lie the facetiously named crackle and pop. The following is due to Philip Gibbs:

Momentum equals mass times velocity!
Force equals mass times acceleration!
Yank equals mass times jerk!
Tug equals mass times snap!
Snatch equals mass times crackle!
Shake equals mass times pop!!
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In answer to your opening question: we asked Iain Duncan Smith but he declined to comment
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Pickert on Hilbert

He really wasn’t much of an imposing figure, a small man I would rather say.... I remember that his assistant Arnold Schmidt, who used to sit in the front row, had to help him out from time to time. I once talked about this fact to Hellmuth Kneser, who studied in Göttingen during the 1920s. He told me: “Well, that wasn’t due to Hilbert’s age; it was the same story when he was younger.”

In this month's  EMS Newsletter (reprinted from Mitteilungen der Deutschen Mathematiker-Vereinigung), a wonderful interview with Günter Pickert from 2014, at the age of 97. Prof Dr Pickert died in February this year.

Link (Page 41): http://www.ems-ph.org/journals/newsletter/pdf/2015-06-96.pdf#page=43
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Surveying the Complex Numbers

“The Norwegian surveyor Caspar Wessel is now recognised as the first to have given a geometrical interpretation of complex numbers and their rules of composition”

An article by Brodil Branner from the 1999 Archives of the EMS Newsletter: (page 13)
http://www.ems-ph.org/journals/newsletter/pdf/1999-09-33.pdf#page=13
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Thanks +Timothy Gowers . I have corrected the original post. (I am not sure if the edit will feed through to this and other reshares - it will be mildly interesting to see.)
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Twenty problems which embody "3-1=2"

"Tanya said: “I have three more brothers than sisters”. In Tanya’s family, how many more boys are there than girls?"

That is one of twenty problems, set by Igor Arnold in 1946, all of which are solved by the same elementary arithmetical procedure: subtracting one from three. Click through for the others - some of the are surprisingly non-trivial!

I heard about this today at an interesting, and somewhat provocative, talk by +Alexandre Borovik (at the Mathematics Teachers and Advisers Conference in Leeds) about the opportunities and pitfalls of mathematical modelling and word problems. One quote from him, to give a flavour: "Mathematical modelling is more difficult than mathematics".

There were also good presentations by +Phil Ramsden and Tomas Johannson - perhaps more about them in future posts.
What follows is a translation of a fragment from Igor Arnold's (1900—1948) paper of 1946 Principles of selection and composition of arithmetic problems (Известия АПН РСФСР, 1946, вып. 6, 8-28). I believe it is relevant to the current discussions around “modelling” and “real life mathematics”.
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+Richard Elwes and are Tanya's parents a same sex couple?
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Teaches & writes about mathematics
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  • University of Leeds
    Mathematician, present
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Leeds - Oxford - London - Freiburg
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A UK based maths lecturer & writer.
Introduction
Lives in Yorkshire, writes about Maths.
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Author of Maths 1001 & How to Build a Brain (AKA Mathematics Without The Boring Bits) & some other stuff, mostly on the subject of maths
Education
  • University of Oxford
    Mathematics, 1997 - 2001
  • University of Leeds
    Mathematical logic, 2001 - 2005
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