## I am James Grime, mathematician, Alan Turing fan, and numberphile. AMA!

Oct 28th 2014 by JamesGrime • 27 Questions • 806 Points

Due to my involvement with the Enigma project at the University of Cambridge and my love for codebreaking, cryptography and mathematics, I am looking forward to the new film “The Imitation Game”.

The film stars Benedict Cumberbatch as Alan Turing and Keira Knightley as Joan Clarke, both working to break the infamous Enigma Code which many thought to be unbreakable.

Alan Turing was a mathematician, father of computer science, and World War II code breaker. I travel the world giving talks about Turing, and even if people have heard of him they often don't know exactly what he did. So let's talk Turing. (Among other things I'm sure).

For more information on Turing and the upcoming film, visit the official subreddit at /r/TheImitationGame.

Proof: https://twitter.com/jamesgrime/status/527204677050703872

UPDATE: Looks like things are slowing down for tonight. Thank you all for your questions. I'll pop back tomorrow and maybe answer a few more. But apart from that, thanks again and see you later, calculator.

Thanks for doing this AMA, James! I'm a pretty big fan of yours :)

Keeping things loosely based on Turing, what first got you interested in cryptography (apart from the coolness of it, of course)?

I know for me personally, it was an Enigma Project workshop five or six years ago that had me fascinated with it all. ;)

Also, how many things can you juggle at once?

One of my workshops?! How fantastic!

I think we all love codes as kids. Spy, secrets, secret messages! I know I played around with it a little as a kid. But I didn't study these things properly until I was much older.

It's such a cool, interesting and exotic use of real maths. And still a touch abstract, and as a pure mathematician that makes me happy.

How did you get involved with the Numberphile videos, and do you enjoy making them as much as it appears?

I started making YouTube videos on my own channel (singingbanana) seven years ago (or something). This was just a way for me to practice speaking in public and force me to learn new things.

I interacted with Brady a of couple times as a fan, and said "if you ever do a maths channel let me know if I can help". Eventually he did.

It's been an amazing and surprising experience. We did not know how many subscribers we would get for a maths channel. But loads of people turned out!

What is your favorite number(s) and why?

I get asked this one a lot, and I will give you the real answer - I do not have a favourite number. (shock!)

To me they are tools, and I have not anthropomorphised the numbers. Mathematicians do get asked this a lot and I think it's like asking an author "what's your favourite letter".

However, if you really want to put me on the spot, I'll say.... 1? Where would we be without the 1. In a semigroup, that's where.

I will give you the real answer

So is it safe to say it's a real number?

I knew I shouldn't have used that word.

Turing studied a lot of things as a mathematician. Do you have a particular favorite from his research?

I hoped someone would ask me this. Yes, he did a lot. And I know most about his Enigma code breaking, but the thing I am most impressed with is his original paper where he defined the "computing machine". Not only is this the birth if computing but it solved one of most important problems in mathematics at the time, called the decision problem. It's very esoteric, and that's how I roll.

But I am equally impressed with all his work, stats, mathematical biology, artificial intelligence. If I get more Turing questions I'll explore a little of all of it!

In the sense of a Quantum Computer, what would be the Global impact of a such device because of all the calculations it could preform?

The canonical example is the effect on internet encryption. Algorithms that can be performed on a quantum computer (Shor's algorithm) will perform integer factorisation in short (polynomial time), destroying current internet security that rely on the fact that this is a hard thing to do. Fortunately we do have other ideas for the future of cryptography!

Why are you a mathematician? I'm always interested in how people became one or another thing in life :)

The real answer to that is because I am lazy. And maths is the perfect subject for the lazy student. If you go to lectures you can do the coursework, if you can do the coursework you can do the exam. There are no books to read and no essays to write. Perfect! And for me it was all games and puzzles, and that's not a bad life.

Of course, I continue for more noble reasons than that. At university I really started to get interested in proof. Proof is the best thing about maths. This is where creative thought comes in. To solve a problem, to prove it, you have to take things you've learnt from other places and put them together in a new way. If it's a problem that has not been solved before then you create something completely new. And you can stand back from the work you've done and admire it, like if you were admiring a painting you just finished. Great stuff.

Which video, Numberphile and otherwise, has been your favourite one to film so far?

I think the Rubik cube ones were underappreciated. I thought, yeah, this will go viral, people like rubik cubes. It didn't. Not as popular as I wanted it to be!

I was very pleased with the one I did about Sudoku. Nice maths, fun application.

On my own channel I was very pleased with the one I made recently about the "wikipedia sized proof" (Edos discrepancy problem). It was a news story, and all I saw were terrible explanations. I thought, there must be an accessible way to do this. I think that one worked brilliantly.

I also crave novelty, so anything out of the ordinary makes me happy. (Explains a lot). I did a video for the Royal Institution about Greek mathematics which was an animation, and I did the voiceover bit. That made a change. Or filming a video recently about the Lorenz cipher machine at Bletchley Park.

If the BBC/any other media approached you to be a Science broadcaster, would you accept it? I'd love to see you on the big(ger) screen, you're like the Brian Cox of Maths. Except you're better

cough

What advice would you give to a 16 year old who wishes to study mathematics in the future?

First of all, there is no need to rush. Take an interest in things outside of the school curriculum is good. Like numberphile type things. You don't have to understand it all, but to know this stuff exists is good. This is the inspirational stuff.

Apart from that, pay attention and listen in lessons. In theory, if you understand things in class you can do the homework. If you can do the homework you can do the exams. But outside of exams, jsut generally be interested in stuff.

Hi James, love the videos that you do!

What is your favourite property of your set of 5 non-transitive dice? Mine would be that when you roll all five of them the sum is always a multiple of five.

Ha! Well the dice were designed so someone could play two people at once. I didn't invent the idea of nontransitive dice, that goes back to the late 60s. But I wondered if there could be a three player version of the game. To do that I decided to exploit the reversing property I had in some versions of the dice. The reversing property is such as surprise.

When you tell people the probabilities of nontransitive dice are like an esher staircase, that's a surprise. When you show that if you double the dice the chain of victory reverse. Double whammy!

Infinity. I'm not very popular.

Some things really are quite difficult, but I still enjoy them. I get annoyed by analysis, to fiddly, too many epsilons and deltas.

Would you say that mathematics is invented, or discovered?

I've run into a couple of discussions over this point recently (one of them here ), and there seems to be a lot of disagreement. I have my own opinions on the subject, but I'm curious to hear what a career mathematician thinks.

It's a little romantic, but I like to think maths is discovered. That just makes the universe a little more beautiful if true.

Have you ever made a mistake during Numberphile and have to start all over?

Huge pieces of paper + marker = a risky situation.

Oh yeah. Not often, but in our last session I was away on some subject, and Brady pointed out some mistake (well done Brady, proves he's listening!). I tried to fix it there and then but I couldn't. I had to abandon video. (We made a couple that afternoon anyway). I was horrified and felt terrible. I will revisit that some other day. And it will look like I knew what I was doing all along.

How is it being a mathematician?What kind of person would you recommend studying mathematics?

It takes all sorts. Strangely, I've noticed certain types are attracted to certain areas of maths. Pure mathematicians, statisticians, and applied mathematicians do have different personalities. Maybe.

If Turing would've lived and put a few more decades into active research, how would you think would our world look different today?

I have always been fascinated by Turing and the pure amount of research fields he has been active in (or even been the first one to research those areas...). With all the current buzz I've read more about him and was pleasently surprised by the readability of his papers (just finished the one about the Imitation Game). Any more reading (or movie/documentaries) you can recommend?

Who knows. The man was like 70 years ahead of his time. He contributed fundamentally to so many areas. Maybe he would have started to slow down, or maybe he would have contributed more to computing or start a whole new area of research. It's fun to speculate, but we will never know.

How about his paper on computable numbers and their application to the Entscheidungsproblem. "The annotated Turing" is very readable and takes you through the paper.

Did you have any sense when you started filming episodes that Numberphile would be so popular?

I'm still puzzled by it now!

Which 'foolish' question have you come across that turned out to be the most thought-provoking? For example, many AMAs get asked daft stuff like 'Which would win in a fight, a horse-sized duck or a duck-sized horse?' There must be dozens of these. Have you come across any that turned out to have hidden depths?

Edit: Yep, just seen a couple in this thread ;-)

I feel terrible, because I get a lot of messages, via YouTube etc, and I do want to answer them all. But actually many of the questions would take me hours to answer, or even days if it involves something non-obvious to solve. But absolutely I've had people ask me questions which I've gone away and had to solve. Sometimes I just have a short correspondence with the person who asked me the question, sometimes it becomes a video.

Ooh, yeah, like when someone (Hi Tom) asked me how he could created a game of assassin, without a gamesmaster, so everyone had a target, but no one knew who was out to get them. That turned into quite a discussion.

If the answer is 42, what is the question?

I don't know, how many roads must a man walk down?

I am an aspiring mathematician in my 3rd year of a 4 year Undergrad Masters in Maths and Physics. I've really enjoyed watching you on Numberphile. I've wanted to be an academic for years and always dreamt of grappling with serious mathematical problems. (I wanted to be the first woman to win the Fields Medal but I've been beaten to that, haha :)) But now employment in a 'normal' job is looking more and more enticing than a PhD and years of research.

What would be your advice to someone unsure whether they want to become an academic mathematician?

I can't give you advice. (What if you acted on it and it was a disaster). But I would say, trust your own instincts. You know yourself best. And anyway, if you really wanted to do it you will, despite what I say!

What's your favourite Numberphile video? Both one that you did, and one by any other numberphile person?

The numberphile videos I'm not in I watch simply as a viewer, I have no idea what the other speakers have done. I love them too. I remember one not long ago about the game "brussel sprouts" it was a lovely bit of graph theory and I thought it was delightful and fully intend to steal it and use it myself. Oh but there are many great videos. I could pick many more but I have to answer more of these questions!

Hi James, I'm a huge fan of your work on numberphile, and I hope to see a lot more of you there in the future, so thanks! My question - what is your favourite mathematics related joke? Also, do you have any bits of advice for an undergraduate mathematics student just starting at University?

Mathematics isn't funny. This is very serious business.

But if you press me, did you hear about the mathematician with constipation? He worked it out with a pencil.

Classic.

What branch of mathematics, in your opinion, would best be used to calculate the magnitude of the awesomeness of Hannah Owen?

You are so weird. Like, uncountably weird.

Hi James

How do you deal with Infinity in mathematics? And do you believe that math can be used to deal with such a complex and paradoxical topic?

Infinity is an interesting topic because the difficulties individuals have with infinity reflect the difficulties the mathematical community had with it over thousands of years. The advantage of maths is, we don't have to work everything out for ourselves from first principles. We stand on the shoulders of giants. In fact, it illustrates the importance of communication in mathematics. You may have the most brilliant idea, but if you can't communicate the idea clearly - at least to other mathematicians - then it is doomed.

So, infinity is a tricky guy, but we doing ok. We have ways to deal with it, and ways to deal with some of those tricky properties. Infinity doesn't scare us so much anymore.

The maths underneath Enigma is what I do, group theory or specifically the symmetric group. This underpins a lot of maths. Essentially when there is anything you want to preserve (length, angle, shape, volume, quantity, energy, momentum etc) you use group theory. It's used in computer games, so you can kill a zombie with an axe, with the axe preserving its shape and not going wibbly-wobbly. And it turns up in physics as it underpins conservation laws.

It turns up in crypto too. And crypto is one of the largest employers of mathematicians.