This week our roving reporters Katie and Paul have gone on a trip to Heidelberg in Germany, where the world’s foremost undergraduate, masters, PhD and postdoc students in maths and computer science are gathering for the fifth annual Heidelberg Laureate Forum.

The event has been running since 2012, and gathers students from across both subjects for talks, discussions and workshops with some of the world’s foremost laureates – top-level researchers and scientific leaders, including recipients of the Abel Prize, ACM A.M. Turing Award, ACM Prize in Computing, Fields Medal and the Nevanlinna Prize. It’s described as ‘the Oscars of maths conferences’, and we’ve already had a quite impressive bag of freebies on arrival so maybe that’s not too far wrong. Look out for an epic group selfie taken at the conference dinner.

We’ll be around for the whole week and will watch as many of the talks as possible – our mission is to produce blog posts for the HLF’s official in-house blog, and we’ll be reproducing all of our posts here at The Aperiodical as well, so you can see what the latest topics are at the top of maths and computer science research, and hear from the greatest minds in the subjects.

We’re excited to hear from (among others) Michael Atiyah, Stephen Smale, both Whitfield Diffie and Martin Hellman (hoping they’ll exchange some keys) and Manuel Blum. Sadly the list of laureates this year only contains one female speaker (Barbara Liskov), and isn’t otherwise massively diverse, but this seems to be a consequence of the lack of diversity within the awards the conference uses to select their speakers. However, our conference pack includes a booklet with a list of all the workshop leaders and delegates, who are from universities all over the world and many different backgrounds, and we’re excited to meet them all.

Watch this space for our write-ups on the latest maths proof techniques, quantum computing (if we can understand any of it), and many other topics, plus press conferences, interviews, a math-art exhibition, and poster presentations by the student delegates.

]]>Thomas Woolley has written in to tell us about the new podcast he’s launched with a couple of friends.

It’s called “Maths at: the Movies” (I suspect the colon is leaving them wiggle room to look at other media) and features co-hosts Thomas and Ben M. Parker chatting about films with “interested observer” and asymptotically anonymous woman “The Wonderful Liz”.

They’ve sent us this blurb:

Maths at: the Movies is a brand new, twice-monthly, podcast that celebrates, critiques and laughs at all the movies that have ever tried to portray the beauty of logical thought on the silver screen.

Helping to untangle the presented numerical mysteries are the scatter-

brained mathematicians, Dr Thomas E. Woolley (Cardiff University) and Dr Ben M. Parker (University of Southampton), whilst the voice of the interested observer is ably supplied by The Wonderful Liz.The general knowledge of the hosts will also be supported by special guests with specific expertise.

Through watching epic mathematical films, such as: 21, Proof and Donald Duck in Mathmagic Land your hosts attempt to answer questions like:

- How do you win in a casino?
- Did Fibonacci keep Rabbits?
- What IS mathematics?
So come and listen to our dulcet tones of as we take a lighter look at mathematical movies.

If that sounds like something you’re interested in, the first episode is online now, about 2008 card-counting drama *21*, and a second is soon to follow.

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>Here, in his own words, are a few things that happened at a conference recently attended by one of my friends.

Someone asked what area I work in. When I told them, they asked if I’d heard of the work of “X, Y and some other guy”.

I’m the other guy.

During a talk, the speaker referenced our curvature upper bound, saying they forgot the names of the authors, but it didn’t matter because they weren’t there.

I was there

*Did you say anything?*

A few other people pointed and laughed at me.

I did something similar during my talk. Someone said he was working on such and such. I said that sounded like the work Lipner does.

I was talking to Lipner.

Someone brought a colleague over to introduce me to him, because we have similar research interests.

We’d already written 3 papers together.

The discovery was made on 29th August, and was double-checked before being announced on 2nd September. PrimeGrid uses a distributed computing approach and uses spare computer time donated by volunteer computers connected to their network.

A generalised Fermat prime is a prime number of the form $a^{2^n} + 1$, with $a \gt 0$. It’s called ‘generalised’ because ‘Fermat prime’ is the name for the particular case $a=2$.

Much like Mersenne primes, there are special tests which make it much easier to check if a number of this form is prime than for a general number. For this reason, they’re a good place to look for new large primes.

Until now only 392 generalised Fermat primes had been found: this new discovery makes 393. At 6,253,210 digits long, it’s now the 12th largest of all known primes, and the second-largest known non-Mersenne prime.

PrimeGrid have put out an announcement in PDF format giving some more details about the search, and credits for the many people involved writing algorithms and providing computers to run them on.

The PrimeGrid homepage has more information about the many different prime number searches they run, and how to join in the search with your own PC.

]]>We’ve pulled out some of the mathematics-related events in the main programme – from theatre reproductions to puzzle workshops and plenty of talks and lectures, there’s something for everyone!

*Tuesday 5 September, 13.00 – 14.00*

*W100, Westlain Building, Falmer Campus, University of Brighton*

**Daniel Colquitt** (University of Liverpool) researches the mathematics of invisibility. Invisibility cloaks have been created for light, sound and water. If we can make all these invisible, what else can we design cloaks for? It was once hoped that invisibility cloaks would allow us to protect buildings from earthquakes, but it was deemed impossible. Discover how mathematics provides us with an elegant solution.

**Mathematical Sciences Section Presidential Lecture & Reception**

*Tuesday 5 September, 15.30 – 16.30 (followed by drinks reception)*

*Gardner Tower, Attenborough Centre, Brighton BN1 9RA*

The code-breaker Alan Turing kicked off the study of what problems can be solved by computers. Many of them become easier when they have symmetries: finding a route is easier in a city with a grid of streets than in one with a chaotic layout. **Colva Roney-Dougal** explores how mathematics can be used to crack symmetrical problems, and shows that sometimes symmetry itself is the issue.

The reception following the event is sponsored by the London Mathematical Society.

*Wednesday 6 September, 12.00 – 13.00*

*C218 Checkland Building, Falmer Campus, University of Brighton*

Exceptional performances tend to occur in exceptional circumstances, but people often mistake luck for skill when evaluating these outliers. This has led **Chengwei Liu** to argue that perhaps we should be rewarding second place. With evidence from the sporting world and business, Chengwei ponders that skill, in the face of luck, may not be all it’s cracked up to be.

*Thursday 7 September, 11.30 – 12.30*

*Gardner Tower, Attenborough Centre, Falmer Campus, University of Sussex*

From assembling Ikea furniture to complex computing, using intuitive shapes and diagrams can open up new opportunities for communicating and solving problems. If you enjoy puzzles come and find out from **John Howse** how diagrammatic reasoning can improve your problem solving and see if you can crack some fiendish challenges.

*Friday 8 September, 13.30 – 14.30*

*A1, Asa Briggs Arts, University of Sussex*

How do we develop drugs that prevent HIV transmission? The answers are clinical, political, personal and statistical. Yet not everyone “does statistics”, meaning their voices are lost in debates about research and treatment. **Robert Cuffe** will help you spot bluff masquerading as statistical expertise in science, with focus on HIV prevention.

*Friday 8 September, 16.00 – 17.00*

*C122 Checkland Building, Falmer Campus, University of Brighton*

The Mathematikado, produced and performed by female students in 1886, parodied Gilbert and Sullivan’s The Mikado to argue that women could master college-level maths. Find out how female students of maths and science responded to social critique of their participation in traditionally male fields of study.

*Friday 8 September, 16.30 – 17.30*

*A2, Asa Briggs Arts, University of Sussex*

Abdominal aneurysms are often symptom-less and can be life-threatening if not spotted early. **Alexander Movchan** and **Luca Argani** (University of Liverpool) describe a distinctive new model used to combat abdominal aneurysms known as ‘EVAS’. Discover the future of EVAS and how it is impacting on treatment for the disorder.

*Friday 8 September, 17.00 – 17.45*

*Horatio’s Bar, Brighton Palace Pier*

Folk mathematician and 2016 FameLab winner, **Kyle Evans** and his trusty guitar take you on a comedic musical tour through some unexpected parallels between maths and pop culture.

*Saturday 9 September, 15.00 – 16.00*

*Old Courtroom Theatre, Brighton*

**Hermes Gadelha** (University of York) applies mathematics to understanding what makes “good” sperm and envisions how this will impact, if not revolutionise, our understanding of fertility; from treatments to contraceptives, and even the development of “robo-sperm”.

The London Mathematical Society yesterday launched its Mathematical Sciences Directory (LMS MSDirectory), a directory of mathematical scientists in the UK. Entries include some personal information, academic networks and social media, current employment and information on education/qualifications. Yes, it’s yet another place to list all this information.

The LMS website suggests a set of benefits for being on the list, including networking with others in UK mathematical sciences and the opportunity to contribute data anonymously to projects such as the Mathematical Sciences People Pipeline, which are used “to make representation to national policy-makers regarding the mathematical sciences”.

Those eligible to be listed include people with a maths degree from a UK institution, those currently working in mathematical sciences in the UK with or without a maths degree, and current students. You don’t have to be an LMS member to be on the list. The FAQ suggests the list was initially populated with data from “over 5,000 mathematicians” (though some may have opted-out before launch – they first emailed me in March asking me to check my data or opt-out) and people can opt to join.

Further details and information on how to join the list from the LMS.

]]>My video features two games which *SPOILER* turn out to have maths in them. I’m also doing a bit of a giveaway on Twitter, where you can win the actual cards used in the video (I will post them out in the IRL post mail), so reply to this tweet if you want a chance to win:

Here’s my video again from the other day. If you’d like to win a set of cards, reply with your own version of ⭐& : https://t.co/rppBeftpbf

— Katie Steckles (@stecks) August 17, 2017

James has also posted his video, which is about a different game:

]]>“Proofs” one way or the other turn up on the arXiv pretty much every day, but this one might actually be correct. At least, it’s not immediately obvious it isn’t.

Here’s the abstract:

Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev’s function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. This implies $\mathrm{P} \neq \mathrm{NP}$.

John Baez has very quickly put together a post explaining the very basics of Blum’s argument. Even more briefly, Blum claims to have shown that the best-case complexity of a function solving the clique decision problem is exponential, not polynomial.

Colin Wright reckons that the proof passes all of Scott Aaronson’s immediate ‘sniff tests’ for a claimed proof of a big problem, and his supplementary list for proofs to do with P versus NP. Those help you spot charlatans and Walter Mitty types, rather than looking at the actual mathematical content.

Obviously, none of us are qualified to even offer a hot take on this, so we’ll all have to wait until more experienced sorts have had a good look.

So, watch this space.

*(Personally, my money is on this not quite working, purely based on my natural pessimism)*

Removing four lines at once with an I-piece in Tetris is the most efficient way to score, which creates a tension: on one hand, you want to build high enough to score quickly, but on the other, building too high puts you at risk of ending the game. The balance between the two is *exquisite*.

I mention that, because I was about to grumble that the corresponding balance in MEI Maths’s new game app thingummy **Factris** isn’t quite as good – of course it isn’t. Nothing ever will be.

This phenomenon is common enough to earn the name “the Tetris effect”.

Between getting hold of it for the ZX Spectrum in the 1990s and realising in 2007 that I had… let’s say a bit of a problem, Tetris was always my go-to game. At one point, I had the 17th-best score in the world on the Linux version and Tetris blocks falling in front of my eyes as I tried to get to sleep.

You can try to leave the glamorous world of world-class Tetris, but it always draws you back in for one last job.

Tetris is mentioned, briefly, in my forthcoming book *The Maths Behind…*, available from October 2017, wherever good books are sold.

The game’s name is a combination of tetromino and tennis.

Here are the seven tetrominos of Tetris.

In case you lived under a rock for the entire 1990s, here’s how Tetris works: the game assigns you a tetromino, which you rotate and drop onto the pile of blocks below. Whenever you complete a 10-piece line across the board, the line vanishes and everything drops down; you get a bonus for removing several lines at once. When your blocks pile up too high, the game is over.

Factris takes the line-removal concept and gives it an arithmetic spin: instead of throwing down tetrominos, the game gives you rectangles of a particular area – anything from 4 to 16, but also the monsters 18, 20 and 24.

Instead of rotating the blocks, you can rearrange them into any pair of factors. A 6-block, for example, can be used as a horizontal 6 × 1, a flattish 3 × 2, a stubby 2 × 3 or a vertical 1 × 6. Primes, obviously, have only two possible configurations; 24, on the other hand, has eight possible ways to drop (In principle, at least – in practice, neither 1 × 24 nor 24 × 1 is possible). However, you’re only allowed to move through the possibilities in one direction – the pieces start as flat as possible, and become gradually taller as they’re resized (“Resized” is the game’s terminology. I reckon the size is constant, and we’re reshaping. Also, I will fight you).

You are shown the next five pieces you will be given, which allows a certain amount of forward planning; you are also allowed to discard a piece every twenty moves, which is often convenient when faced with monsters. You’re shown where the piece will land when it’s dropped, a development that would have probably made me even better at Tetris.

The game board is 16 squares wide and 16 squares tall, a design choice that has several interesting implications. Firstly, some of the pieces – the monsters – don’t fit on the board in two of their possible orientations. Secondly (a minor point), as long as you have space on the board, you can drop a 16-block horizontally and have it vanish immediately. (This is a useful way to buy time, or to get rid of a block without using up a discard.) Thirdly, and probably the key thing to Factris as a strategic game, is it opens up the possibility of clearing the entire board with a single block – removing 16 lines at once, a Factris.

And a Factris – like a tetris – means big points. Removing \(n\) lines at once scores you \( 50\cdot 2^n \) points, so a Factris is worth 3,276,800 points. Removing 12 lines at once is worth just 204,800.

As far as I can make out, the idea behind Factris is to ingrain in its players the factorisations of the numbers in play. I can’t really speak to the effectiveness of that – I was pretty good with factorising small numbers even before I started – but I can easily believe that regular play would leave you with instant recall of the relevant facts.

You mean to say… that was *maths*? But I was enjoying it!

There are presumably side goals of improving speed of thought and general mathematical fluency – again, I can’t see how Factris could fail to improve those skills almost on the sly.

I have some quibbles with Factris. I dislike the one-way nature of reshaping the blocks (for me, making and correcting mistakes is part of maths), but appreciate that this was a deliberate design choice – the makers consider that this would make the game too easy.

I’m also in two minds about the scoring system. In Tetris, you have a fair amount of leeway in scoring your tetrises because the board is five times as tall as the biggest block – once you’ve set up a column an I-piece will slot into, you can build elsewhere while waiting for it to arrive. By contrast, to get a Factris, you *have* to build to the top, you *have* to have a 16-block lined up next in the next two – and if not, you *have* to destroy your work. For me, the balance between skill and luck is a bit off here; I don’t instinctively feel that a 16-row clearance is worth 16 12-row clearances.

Original Mode allows you unlimited time, while Crunch Mode has a ten-minute timer.

Despite those grumbles, it’s a *really* addictive game. The strategy is rather deeper than in Tetris, and the pace a bit slower, giving the player a bit of thinking time. (That is balanced, at least in Crunch Mode, by having a certain amount of time pressure).

The Factris team is still adding tweaks; I look forward to seeing the improvements they still have up their sleeves!

You can reach the responsive development team at @MEIMaths on Twitter (or the hashtags #Factris #LikeTetris #ButMathsier).

Factris is available for iPhone and iPad in the App Store and Android devices via Google Play.

Factris has a homepage on the MEI site.

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