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.

Comments: 366 • Responses: 50  • Date: 

JamesGrime137 karma

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.

EmC_9863 karma

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?

JamesGrime66 karma

Oh, and I can juggle five balls badly. Obviously three clubs, rings, knives or flaming torches are no problem.

JamesGrime65 karma

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.

Diverskii55 karma

Have you ever noticed, as I have, the incredible sexual tension between Brady and yourself?

JamesGrime86 karma

I have. How do we resolve it?

susiethebanshee42 karma

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

JamesGrime61 karma

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!

erazmus42 karma

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

JamesGrime67 karma

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!

oh_horsefeathers41 karma

Asking as someone who hasn't always been the best at math, how similar is numberphile to numberwang?

JamesGrime78 karma


TheSpaceOfAdes38 karma

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

JamesGrime76 karma


CoconutM1lk36 karma

What is your favorite number(s) and why?

JamesGrime113 karma

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.

sarahbau67 karma

I will give you the real answer

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

JamesGrime121 karma

I knew I shouldn't have used that word.

adolpwned27 karma

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

JamesGrime103 karma

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.

Pugs50126 karma

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?

JamesGrime40 karma

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!

erazmus23 karma

James, what's your Erdös number?

JamesGrime43 karma

Infinity. I'm not very popular.

NillieK17 karma

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

JamesGrime41 karma

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.

macaco300115 karma

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

JamesGrime36 karma

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.

Line6spider414 karma

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

Huge pieces of paper + marker = a risky situation.

JamesGrime27 karma

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.

sml256513 karma

What's your favorite field of Mathematics and why?

JamesGrime43 karma

I'm a pure mathematician. An algebraist. It is just something that appeals to me. I think maths is like sticklebricks. Analysis is all about the details, the patterns in the pins of the bricks. Algebra takes a step back and can see the brick as a whole. You can see the edges and see it as one chunky object. I can then take this chunky object and stick it to another brick and make a new object. It's chunky maths.

shycapslock13 karma

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

  2. 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?

JamesGrime15 karma

  1. 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.

  2. 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.

green_meklar12 karma

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.

JamesGrime37 karma

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

jessebeach11 karma

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

JamesGrime19 karma

I'm still puzzled by it now!

NapoleonBonerpartee10 karma


JamesGrime14 karma

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.

Deadeadoe10 karma

What is one of the most interesting detail about Turing's life that isn't very well known by the public?

JamesGrime22 karma

Turing publically supported the asylum of Jewish refugees into Britain. He sponsored a couple of lads who were a bit sciencey, made sure they had a place in a school, took them out boating. I think that is often overlook, and shows he wasn't just involved in the war intellectually.

tom93589 karma

Can you program, and if so, which languages do you speak?

JamesGrime34 karma

That's actually a massive hole in my nerd credentials. I know that I can if I decide to learn, but I people for that sort of thing. I do prefer to solve things with pen and paper. I'm very old fashioned in that way. I've just bought a big blackboard for my house and I'm thrilled!

galaxxus9 karma

What are your thoughts on actuaries?

JamesGrime23 karma

I have nothing against them.

EmCdeltaT8 karma

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.

JamesGrime15 karma

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!

Lionhead18 karma

what do you find the most difficult field of mathematics?

JamesGrime41 karma

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

TheBottomLime6 karma

Will you watch this video I made for a project about Alan Turing and give me your thoughts? http://m.youtube.com/watch?v=MLgz_2-KJx0

JamesGrime11 karma

I'm loving it. Hang on, I'll do more of this AMA, but then I'll watch it properly. Good work.

anappropriatename6 karma

If the answer is 42, what is the question?

JamesGrime25 karma

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

reddit122215 karma


JamesGrime5 karma

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!

Ramn475 karma

How did Turing really die?

Also you are AWESOME at Numberphile and singingbanana videos.

One more: would you rather fight 100 duck-sized horses or one horse-sized duck?

JamesGrime10 karma

I expected someone to ask, so let's get it out the way... one horse sized duck. One target. Simpler.

NillieK6 karma

You would also have the square/cube law in your favour, as CGP Grey pointed out when he answered this very question.

JamesGrime7 karma

I will apply Lanchester equations of warfare and let you know.

nongrockle5 karma

Dogs, cats, fish, or monkeys?

JamesGrime15 karma

Dogs, naturally.

iDoNotDegree5 karma


JamesGrime6 karma

I'm sorry to hear you were scoffed at! An investigation into something like that might be called recreational mathematics, but can often be difficult problems to solve which is good practice for you, and who knows what you have to develop to solve it.

GrimBeast5 karma

How would one pursue a career related to Enigma?

JamesGrime8 karma

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.

marsmenfrommars5 karma

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?

JamesGrime13 karma

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.

brightonia214 karma

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?

JamesGrime25 karma

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.


Simons_Mith4 karma

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 ;-)

JamesGrime9 karma

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.

lizardrancher4 karma

Have you read Neil Stephenson ' s Cryptonomicon? If so how do you feel about Dr. Turing ' s portrayal?

JamesGrime6 karma

I haven't, but people tell me I should, like daily.

_pmcp_4 karma

I know you like your shlocky horror VHS stuff, can you recommend something we're unlikely to have seen?

JamesGrime6 karma

Biggles Adventures in Time. Or Buckaroo Banzai. They are special. Sorry, that wasn't horror, I watched Fright Night for the first time last time and loved it!

OroLight4 karma

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

JamesGrime6 karma

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!

EmilySpinach3 karma

I don't know much about Turing but I would like to hear more from you, especially as it seems you're wanting to talk about him!... So just just going off of one of your previous answers, can you tell us more about his work on mathematical biology? What part of it are you most impressed by?

JamesGrime7 karma

If you don't know this it's pretty cool. Alan wanted to answer the question, why do Zebras have stripes, leopards have spots, cows have patches. He model the development of the pigmentation with mathematical equations similar to the equations that describe waves. He called it "waves on cows and waves on leopards". This is something he did in 1952, so after the war and a couple of years before his death. It is still a fundamental paper in mathematical biology.

dariussavory3 karma

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

JamesGrime15 karma

You are so weird. Like, uncountably weird.

viccie2112 karma

The important question, are we going to see another one of your silly dances?

JamesGrime7 karma

I'll do you a fancy dance. We need video here.

Professor2262 karma

If you love numbers so much, why don't you marry them?

JamesGrime9 karma

Maybe I will.

SW98762 karma

I always view professional mathematicians as human calculators so to speak, so to what extent is this true? Would you say the reason you are a good mathematician is more because you are knowledgable or because you're brain is naturally very fast with numbers? Another way of saying this is, could someone who cannot process mental math quickly become a good mathematician?

JamesGrime4 karma

The opposite it true I think. A lot of mathematicians are terrible at arithmetic, and that's ok because that is not what we. I don't think I've had to use a number bigger than 4 since 2002. Mathematics is more about logic and solving problems. Very rarely do I need a numerical solution.

bassplayer33952 karma

Hi James, I remember you giving an amazing talk to Carisbrooke High School 4 years ago about the enigma machine only to discover you were starring in Numberphile! Do you often give talks to schools? If so how often do you do them?

JamesGrime8 karma

I do that pretty often. I think it's very important. I didn't go to a great school, and I would have loved something like that to come to my school. So that's a good reason for me to do it, for the pupils like me.

PaulOfPauland2 karma

Ive been taught by my dad that every number that its figures add up to a number that can be divided by 3, can be divided by 3 itself. Example: 135 1+3+5=9 ==> 135 can be divided by 3.

It is true however I use it, but I cant figure out why is that?

JamesGrime6 karma

If a number is divisible by 3 then it has no remainder after division by 3. If I take a number like 457 we can break this into 4x100 + 5x10 + 7.

A property of remainders is that we can find the remainder by looking at the remainders of each part of 4x100 + 5x10 + 7. 100, 10 and 1 all have remainder 1 after division by 3. So the remainder of 457 becomes 4x1 + 5x1 + 7x1 = 4+5+7 i.e. add up the digits.

In this example, 457 has remainder 16. And 16 has remainder 1 after division by 3.

However, 459 has remainder 18, which has remainder 0 after division by 3 - that means it's a multiple of 3.

(Some people won't like me using the word remainder instead of the proper modular arithmetic, but hey, it's only an introduction).

repux2 karma


I got hooked on Brady's channels some time ago and always enjoyed your video's.

You seem quite young for someone in your profession, (I might be mistaken). What did your career path look like? Did you always have a passion for math?

JamesGrime4 karma

Einstein was 28 when he came up with relativity. Turing was 28 when he broke Enigma codes. We don't all start of a crazy-hair old men. I got my PhD when I was 26, that's pretty normal. I'm 34 now.

creeps_for_you1 karma

James Grime! Love your singingbanana videos! When will the next come out? I want my mathematical puzzle fix dammit!

What is your favorite part of making online videos? What is your favorite math card trick?

JamesGrime3 karma

Yup yup yup. I've been busy, and decided to slow down a bit on the extra curricula stuff. But I will be back.

I like the writing of the videos. How to best explain and present a thing is like a puzzle to be solved.

Gilbreath Principle, or Kruskal's Count.

javiergzzl-2 karma

Hello Mr. Grimes. Being a mathematician, do you believe extraterrestrial life has visited us?

JamesGrime10 karma

Being a mathematician gives me absolutely no insight into this question whatsoever.