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David Roberts
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David Roberts

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SageMath has been accepted for +Google Summer of Code 2015.

Please spread the word about this by sharing this posting with prospective students! We are looking forward to receiving your applications ;-)
SageMath is an open-source mathematical software system. It combines numerous open-source software libraries under one umbrella and contains many unique and novice algorithms built on top of those libraries. Besides a command-line and programming-library interface, its primary user interface is ...
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Mathematicians' mental theatre

This nice video with Barry Mazur

http://youtu.be/_qvp9a1x2UM

gives a little outline of the first recorded use of a pair of complex numbers, 5±sqrt(-15), and how it perturbed Cardano. Mazur says it wasn't in the 'mental theatre' of the 16th century Italian mathematicians, but something clearly needed figuring out. In the 'extras' video

http://youtu.be/i4GCd2xOCDg

he says some interesting things about how mathematicians now get something called 'elegant confusion': being on the cusp of something we don't really understand, but it has a form about it that hints that something special is going on, and which is still appreciable despite our ignorance. I immediately thought of Mochizuki's Interuniversal Teichmüller theory - we don't really understand it, and we are having more of a 16th century response ('useless' and 'subtle') rather than a 21st century response to it.
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sqrt(-15) occurs among the cyclotomic span CZ15.  That is, you can reach it from steps of unity, in angles of 12 degrees. 

Kind of obvious, when you think about it.
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I absolutely love it when the author, who is male and a high school teacher, talks about his wife, the mathematician in the family. It so turns the usual trope on its head (female=nurturing teachery type, male=serious mathematician/scientist).

And the points about pure (and applied!) mathematics are spot on too.

#womeninstem
 
Why Do We Pay Pure Mathematicians? Or, the Many Uses of Uselessness. http://mathwithbaddrawings.com/2015/02/24/why-do-we-pay-mathematicians/ "take any random paper written by an early 20th-century logician, and you could call it similarly pointless. If you eliminated that paper from the timeline, the Jenga tower of our intellectual history would remain perfectly upright. That doesn’t make those papers worthless, because research isn’t a collection of separable monologues. It’s a dialogue."
So if "applied" means "useful," doesn't it follow that "pure" must mean... "useless"?
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This part made me want to sink to my knees and cry "OH MY GOD, YES" (I may be slightly crazed from lack of sleep and the day's teaching, though)

_Every piece of research builds on what came before, and nudges its readers to imagine what might come next. Those nudges could prove hugely valuable. Or a little valuable. Or not valuable at all. It’s impossible to say in advance.
In this decades-long conversation, no particular phrase or sentence is necessarily urgent. Much will be forgotten, or drift into obscurity. And that’s all right. What’s vital is that the conversation keeps on flowing. People need to continue sharing ideas that excite them, even—or perhaps especially—if they can’t quite explain why._
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Not quite the same as finding a typo in The Art of Computer Programming, but a good cause nonetheless.
 
Barry Mazur and I can't seem to find any more typos or mistakes in our book "Prime Numbers and the Riemann Hypothesis": http://wstein.org/rh/    Can anybody good at spotting typos see anything critical that needs to be done before this goes into production at Cambridge University Press?

David Mumford has written the following very nice endorsement for the book: "This book is a soaring ride, starting from the simplest ideas and ending with one of the deepest unsolved problems of mathematics. Unlike so many popular math books puffed up with anecdotal material, the authors here treat the reader as seriously interested in prime numbers and build up the real math in four stages with compelling graphical demonstrations revealing in deeper and deeper ways the hidden music of the primes. If you have ever wondered why so many mathematicians are obsessed with primes,
here’s the real deal.”

It goes without saying, but all illustrations and calculations in the book were done using Sage. 
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Oops, I think that goes here, I'll copy paste onto the original post. Sorry.
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Content of my talk Homgeneous bundles and higher geometey at the Edouard Čech institute while visiting +Urs Schreiber​. This was intended as a gentle introduction to higher geometry motivated by simple progression of ideas from Klein geometry. I will write notes up and post them very soon. The last few boards contain a sketch of the example from my talk at Herriot-Watt university last June.

(Thanks to Urs for taking the photos during the talk.)
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+Urs Schreiber had a 25-hour stopover in Dubai, where I had v. limited internet. Glad we could catch up, I'll keep you posted on developments.
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David Roberts

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Spot on.
 
I love how in type theory the "axiom of choice" doesn't involve making any choices you haven't already made, it just sort of collates those choices into a function. It numbers the pages you've written, puts it in a nice binder with a pretty title page.
Whereas the classical, set-theoretic axiom of choice spits out a book from scratch each time (although it doesn't let you read the text).
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In case anyone is wondering what this refers to: see for instance section 3.8 here: http://ncatlab.org/nlab/show/axiom+of+choice#HoTTBook
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Another Elsevier scandal... and another discrete, inappropriate way by this publisher of handling it, denying that anything bad happened. This kind of behavior is so detrimental to both science progress and science credibility that it makes me really angry. Many thanks to @deevybee for making this information public.
Last October, I was surprised to see a tweet from @autismcrisis (Michelle Dawson) saying "Belatedly noticed: @deevybee is on the editorial board of Johnny Matson's RASD?! Well I'm speechless. Wow." Many of those reading this...
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It'll be interesting to see if this changes any people's ideas on autism.
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That's a nice analogy for how to think of flows...
 
Claimed Retracted solution to Hilbert's 16.5th problem

Update: thanks to +Christian Perfect for pointing out that a mistake has been found.

In 1900, David Hilbert gave an influential speech to the International Congress of Mathematicians, in which he outlined some mathematical challenges for the coming century. This was later solidified into the famous list of Hlibert's 23 problems. Most of the 23 were resolved, or at least saw major progress over the 20th century. Among the exceptions are his 8th problem (the Riemann Hypothesis), and his 16th, which came in two parts.

Now a solution has been claimed for the second half of the problem. (Link below.)

So what does it say? Here's a very rough idea (meteorologists look away now). Imagine a completely flat but rather windy world. Assume (even more implausibly!) that the weather doesn't change from moment to moment - so if you view the wind-currents from above, the picture looks static. But it may change from place to place. It might be blowing a north-easterly gale somewhere, and a gentle southerly breeze somewhere else. (We also assume that the wind is as flat as the world - so air goes round and round, but never up or down.)

Now, release a balloon, and watch it get blown about. After a while (maybe a long while!) you might notice that it's got stuck in a cycle: it keeps tracing out the same path over and over again. (Not as unlikely as it sounds - remember that the weather pattern is static.) Essentially, Hilbert's 16.5th problem asks, how many of these cycles are there?

Of course, there need be no limit - there could even be infinitely many cycles. But let's suppose that the rules governing how the wind varies from place to place are actually very simple. (Technically, suppose they are given by two polynomials in the Cartesian coordinates of the position). In this simpler situation, we might hope to predict how many cycles there are. What Llibre and Pedregal claim in the linked paper is that in this case, there is indeed a manageable bound. (Technically: if the degrees of the two polynomials are at most n, then the number of limit cycles is at most 0.5*(n − 1)(4n^3 − 11n^2 + 13n − 2) .)

Via Steven Strogatz on Twitter, who wisely writes "Stay tuned – wait for experts to weigh in."

Hilbert's problems: http://en.wikipedia.org/wiki/Hilbert%27s_problems

The claimed solution: http://xxx.tau.ac.il/abs/1411.6814v1

Picture credit: Chaoli Wang and the FlowVisual Team
http://www3.nd.edu/~cwang11/2dflowvis_files/LIC.jpg
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About to leave winter for summer. Farewell, Europe - it's been fun!
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Welcome home to 35C and above :-). You luckily avoided the heat wave we had earlier this week. 
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Looks good to me...
 
Do you wish you could build your own LHC, complete with detectors and magnets, out of LEGO? Help make that a reality and vote for the LEGO Ideas design submitted by Nathan Readioff. We want to be the fastest LEGO project to get to 10,000 votes, but we need your support!

https://ideas.lego.com/projects/94885

#LHC #LEGO #CERN #ATLAS #ALICE #CMS #LHCb #LEGOideas #RestartLHC

#LHCLego
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Good films about maths are rare... George Csicsery (pronounced "Chi-cherry") has produced not one, but 13 elegant films (list below) about mathematicians & mathematics.  In his own words "Working with mathematicians is a great source of pleasure. It is the only group I know, where the answer 'I don't know' is met with excitement and motivation rather than with irritation. I hope that some of this excitement and passion filters through the film to audiences." [a]
    
Below, the 13 films.  Just watching the trailers is rewarding.  If you've never met a mathematician, these should give you a personal look into the very diverse worlds of some great modern mathematicians and to see the humanity behind the thinking.  If you're a mathematician or love mathematics, these are inspiring.

    
[1]  Counting from Infinity: Yitang Zhang & the Twin Prime Conjecture (2015)
    The central challenge of the film was finding a way to depict Yitang Zhang's dedication to working in isolation. The qualities he embraces-solitude, quiet, concentration-are the opposites of those valued in the media. Fortunately, it is a conundrum Csicsery had faced before in other films about mathematicians. He had learned that contrary to the rules, it is okay to shoot long scenes of "the grass growing," or in this case, shots of "a person just sitting with pencil and paper and thinking. The longer the scene, the more you realize that you really can see someone thinking. The human face is very expressive. Give it time and it speaks volumes."  - George Csicsery
    About: http://www.zalafilms.com/films/countingabout.html
    Trailer: http://www.zalafilms.com/films/countingtrailer.html

    
[2]  Porridge Pulleys & Pi: Two Mathematical Journeys (Hendrik Lenstra, Number Theory, Elliptic Curves & Cryptography) & (Vaughan Jones: Quantum Mechanics, Knot Theory, and DNA Protein Folding) (2004)
    Trailer: http://www.imdb.com/video/wab/vi1773798425/     About: http://www.zalafilms.com/films/pppdirector.html
    "There are several stereotypes and beliefs about mathematicians that Porridge pulleys and Pi aims to dispel. First, I wanted to show that there is no single type of person who can become a mathematician. ... given the right training, any child with the aptitude can turn into a mathematician. ... Jones and Lenstra are the opposites of the eccentric nerdy type who has come to characterize the popular conception of what mathematicians are like. Another cliche I hope to debunk is that of the tortured genius. This film contains clear evidence that mathematicians derive a great deal of pleasure from their work." - George Csiscery
    http://www.zalafilms.com/films/pppdirector.html
    

[3]  Taking the Long View: The Life of Shiing-shen Chern (one of the fathers of modern differential geometry) (2011)
    View Short: http://zalafilms.com/takingthelongviewfilm/viewfilm.html
    Synopsis: http://zalafilms.com/takingthelongviewfilm/synopsis.html
    
    “There’s a quotation from Lao Tzu, an ancient Chinese philosopher, that could have been written about Chern. ‘The master does his job and then stops. He understands that the universe is forever out of control, and that trying to dominate events goes against the current of the Tao. Because he believes in himself, he doesn’t try to convince others. Because he is content with himself, he doesn’t need other’s approval. Because he accepts himself, the whole world accepts him.’” - Alan Weinstein, UC Berkeley
    
    The true importance of Shiing-shen Chern’s role in the development of mathematics ... His influence with Chinese government leaders helped bring Western mathematicians to China and send Chinese students to study abroad. Today’s leaders in Chinese mathematics were all beneficiaries of Chern’s vision. His greatest contribution to the restoration of Chinese mathematics, however, is the establishment of the Nankai Institute of Mathematics, today known as the Chern Institute of Mathematics. The Chern Institute provided a base for these international interactions which often led to collaborations, reciprocal visits, and joint papers.
    About: http://www.takingthelongviewfilm.com/


    “He said, ‘my policy to operate this institute is very simple. Three words in Chinese. First, no meetings. Second, no plan. Third, do more.’ That means, just do your research work.”
    Molin Ge, Theoretical Physicist, Chern Institute of Mathematics


[4] Invitation to Discover: An Introduction to the MSRI (Mathematical Sciences Research Institute) (2002)
    Watch: http://www.msri.org/web/msri/online-videos/special-productions-events/invitation-to-discover     
    
[5] I Want to Be a Mathematician: A Conversation with Paul Halmos (2009)
    Trailer: http://www.zalafilms.com/films/halmostrailer.mov
    About: http://www.zalafilms.com/films/halmossynopsis.html
    "When an engineer knocks at your door with a mathematical question, you should not try to get rid of him or her as quickly as possible. You are likely to make a mistake I myself made for many years: to believe that the engineer wants you to solve his or her problem. This is a kind of over simplification for which mathematicians are notorious. Believe me, the engineer does not want you to solve his or her problem. Once I did so by mistake (actually I had read the solution in the library two hours previously, quite by accident) and he got quite furious, as if I were taking away his livelihood. What an engineer wants is to be treated with respect and consideration, like the human being he is, and most of all to be listened to with rapt attention. If you do this, he will be likely to hit upon a clever idea as he explains the problem to you, and you will get some of the credit. Listening to engineers and other scientists is our duty. You may learn some interesting mathematics while doing so." - Gian-Carlo Rota, Indiscreet Thoughts 1979


[6]  Julia Robinson and Hilbert's 10th Problem (2008)
    Trailer: http://www.zalafilms.com/films/julia.html
    About: http://www.zalafilms.com/films/jrbackground.html

    
[7]  Navajo Math Circles (in production)
    "Open-ended questions are totally new to most of the kids. Usually you have to have an answer within 20 seconds, 30 seconds, that’s what math is. Math circles are the opposite. We start with some simple questions, and we ask more questions and more questions. We get some answers along the way. The answers actually don’t matter. The more and more questions… we’re opening whole research problems, and that is something totally new to the kids. And once they like it, it’s just amazing, it’s transformative." - Matthias Kawski, Arizona State University
    Trailer: http://www.zalafilms.com/navajo/trailer.html
    About: http://www.zalafilms.com/navajo/about.html

    
[8]  Hard Problems: The Road to World's Toughest Math Contest, covering the story of the 2006 US IMO team (2008)
    *Trailer: http://www.hardproblemsmovie.com/trailer.html
    About: http://www.hardproblemsmovie.com/synopsis.html


[9]  N is a Number: A Portrait of Paul Erdos (1993)
    Trailer: https://www.simonsfoundation.org/multimedia/n-is-a-number-a-portrait-of-paul-erdos/     About: http://www.zalafilms.com/films/nisfilm.html
    Full: https://www.youtube.com/watch?v=wN4yLPPvRBgs


[10]  Erdos 100 (2013)
    Trailer: http://www.zalafilms.com/films/erdostrailer.html    
    About: http://www.zalafilms.com/films/erdos.html


[11]  To Prove and Conjecture: Excerpts from Three Lectures by Paul Erdos (1993)
    About: http://www.zalafilms.com/films/prove.html

        
[12]  The Right Spin: How to fly a broken space craft (Mir), the Story of a Dramatic Rescue in Space and the Mathematics Behind It (2005)
    About: http://plus.maths.org/content/right-spin-how-fly-broken-space-craft            http://archive.msri.org/specials/rightspin     Alternate documentary: https://www.youtube.com/watch?v=tM7fTLLmgbk


[13]  On Mathematical Grounds: A Refresh of an Introduction to the Mathematical Sciences Research Institute (MSRI) (2009)
    About: http://www.zalafilms.com/films/omg.html
    YouTube: https://www.youtube.com/watch?v=MO-JRzTiSNo     
    
References:
[a] George Csicsery, Producer & Director, Zala Films, in his own words:   http://zalafilms.com/takingthelongviewfilm/directors_statement.html

[b] The Films: http://www.zalafilms.com/films/index.html

[c] The story of George Csicsery: Math Films, Yes - But So Much More:  http://cinesourcemagazine.com/index.php?/site/comments/csicsery_math_films_yes_but_so_much_more/

[d] Science Lives, Simon Foundation & Zala Films, videos of interviews with living mathematicians  https://www.simonsfoundation.org/category/multimedia/science-lives/alphabetical-listing/
About the Film. In April 2013, a lecturer at the University of New Hampshire submitted a paper to the Annals of Mathematics. Within weeks word spread: a little-known mathematician, with no permanent job and working in complete isolation, had made an important breakthrough towards solving the ...
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Fantastic. Thank you!
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Some good discussion on women mathematicians. The image below is by Florence Nightingale, from her work in statistics.

#womeninstem  

https://3010tangents.wordpress.com/category/women-in-math/
Posts about Women in math written by redpandaoverlord, u0614258, indianacroft, marycneville, clarkclan2014, auriejo7, and chrisinsl
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I live in Adelaide, Australia.

I am a pure mathematician who works on category theory and a smattering of related fields such foundations and higher geometry.

I work as a post-doc at the University of Adelaide in the School of Mathematical Sciences.

My nLab page: http://ncatlab.org/nlab/show/David+Roberts
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