Daniel Shiu on The Mathematical Legacy of Bletchley Park

Gabrielle Birchak/ May 19, 2025/ Modern History/ 0 comments

MATH SCIENCE HISTORY TRANSCRIPTS

GABRIELLE:
Wel­come to Math! Sci­ence! His­to­ry! I have a spe­cial episode today that includes an inter­view with Daniel Shiu, where we dis­cuss his lat­est arti­cle, The Influ­ence of Bletch­ley Park on UK Math­e­mat­ics, which was pub­lished in the Tay­lor and Fran­cis jour­nal, Cryp­tolo­gia. It is such a won­der­ful arti­cle about Bletch­ley Park and the eclec­tic indi­vid­u­als that were involved in the ground­break­ing crypt­analy­sis and cryp­tol­ogy. pho­tog­ra­phy appli­ca­tions that helped end World War II. As Daniel writes in his abstract, his paper con­sid­ers how the expe­ri­ence of these and oth­er math­e­mati­cians at Bletch­ley Park informed and influ­enced the math­e­mat­ics pro­duced in their post-war careers.

It is a fan­tas­tic arti­cle that shows how much of an impact the bril­liance that came out of Bletch­ley Park had on the Unit­ed King­dom’s aca­d­e­mics. And if you are inter­est­ed in read­ing the arti­cle, I will put the link in my show notes.

So before we begin the inter­view, I’m going to tell you a lit­tle bit about Bletch­ley Park and then Daniel. Bletch­ley Park was a top secret British code break­ing cen­ter dur­ing World War II, where math­e­mati­cians, lin­guists, and engi­neers worked to decrypt ene­my com­mu­ni­ca­tions. Most famous­ly, the Ger­man Enig­ma and Lorenz ciphers. It became a hub of inno­v­a­tive prob­lem solv­ing, bring­ing togeth­er some of the great­est minds of the era, includ­ing Alan Tur­ing. Their suc­cess not only helped short­en the war but also laid the ground­work for mod­ern com­put­ing through the devel­op­ment of ear­ly pro­gram­ma­ble machines like the Bombe and Colos­sus. The tech­niques pio­neered there—such as sta­tis­ti­cal analy­sis, pat­tern recog­ni­tion, and automation—shaped the evo­lu­tion of cryp­tog­ra­phy and infor­ma­tion the­o­ry. Bletch­ley Park’s lega­cy lives on in the fields of cyber­se­cu­ri­ty, arti­fi­cial intel­li­gence, and data science.

Daniel Shiu, my guest today, began his career as an aca­d­e­m­ic math­e­mati­cian before join­ing the Unit­ed King­dom’s gov­ern­ment com­mu­ni­ca­tions head­quar­ters in Sep­tem­ber 2001. He spent twen­ty years there in a vari­ety of roles. He was the UK’s head of math­e­mat­ics research for cryp­to­graph­ic research and quan­tum infor­ma­tion pro­cess­ing. He was part of the ini­tial Nation­al Tech­ni­cal Author­i­ty func­tion assumed by the new Nation­al Cyber­se­cu­ri­ty Cen­ter, as well as the head of the Heil­bronn Insti­tute for Math­e­mat­ics Research.

Daniel is the recip­i­ent of many cryp­to­graph­ic awards. Addi­tion­al­ly, he con­tributed his­tor­i­cal arti­cles to the GCHQ web­site and For the past four years, Daniel has been work­ing in indus­try, help­ing to rethink twen­ty-first cen­tu­ry inter­net encryp­tion. And so with­out fur­ther ado, let’s have a con­ver­sa­tion with Daniel Shiu.

GABRIELLE:  Thank you so much for being part of Math Sci­ence His­to­ry.

DANIEL: Thank you. It’s a plea­sure to be here. I’m look­ing for­ward to it a great deal.

GABRIELLE:  I absolute­ly loved your arti­cle on the influ­ence of Bletch­ley Park on UK math­e­mat­ics pub­lished in Cryp­tolo­gia with Tay­lor and Fran­cis and I have so many ques­tions. It’s one of my favorite sub­jects, but I was enthralled with the peo­ple that you address, includ­ing the ones that most of us know about, Alan Tur­ing, Bill Toot, Gor­don Welch­man, and Jack Good. Tell me more about the indi­vid­u­als and their con­nec­tions through Bletch­ley Park.

DANIEL: So I think indi­vid­u­als is a great term to use. So Bletch­ley Park was full of very unique, audi­ble char­ac­ters. And this is part­ly because at the begin­ning of the war, was envi­sioned as quite a small effort and nobody was quite sure what the sort of next set of skills nec­es­sary to do crypt­analy­sis might be. So Alas­tair Den­ni­son had quite a sort of broad remit and ini­tial­ly was going around recruit­ing a very diverse bunch of peo­ple. So as well as sort of math­e­mati­cians, he was grab­bing chess play­ers, puz­zle set­ters, and magi­cians even. But amongst those were very promis­ing young ear­ly career math­e­mati­cians such as Alan Tur­ing, Gor­don Walshman.

But that was ini­tial­ly just part of a rough­ly 150 per­son set up at the begin­ning of the war. And as the sort of math­e­mat­ics real­ly began to prove itself, they real­ly began to expand and see­ing that, oh, yes, they could real­ly turn this into an indus­tri­al scale intel­li­gence oper­a­tion. So they start­ed recruit­ing more and more math­e­mati­cians until by the end of the war, they’re prob­a­bly about 10,000 peo­ple work­ing at Bletch­ley Park in total. And the net­work grew quite organ­i­cal­ly. So it start­ed off just as friends large­ly of Tur­ing and Wal­sh­man. Wal­sh­man was very unashamed about recruit­ing every­body from his col­lege, every­body he taught, even for­mer school friends. Tur­ing called on peo­ple he’d for­mer­ly worked with, such as Sean Wiley and Max New­man. But these friends had friends of friends or oth­er peo­ple they thought might be suit­ed to work. And it grew into quite a large selec­tion of peo­ple. But it was­n’t just the math­e­mati­cians as well. It’s those 10,000 people.

They also includ­ed lin­guists, engi­neers build­ing some of the machines he used there. A very, very large sort of group of peo­ple which we sort of con­sid­er per­haps an IT depart­ment these days, and those were large­ly drawn from the REN ser­vice, the wom­en’s naval aux­il­iary. Sev­en­ty-six per­cent of the peo­ple at Bletch­ley Park were women and ana­lysts on top of this. It’s the math­e­mati­cians who very much fas­ci­nate me though. I was inter­est­ed that look­ing at the names of peo­ple who worked at Bletch­ley Park, you got some peo­ple who weren’t famous per­haps for their crypt­an­a­lyt­ic con­tri­bu­tions became very, very famous as math­e­mati­cians win­ning some of the top UK awards. So these would be peo­ple like Max New­man, Hen­ry White­head, Ian Cas­tles, Sandy Green. And it was fas­ci­nat­ing to me exact­ly whether there was a con­nec­tion between the fact that they had an awful lot of their math­e­mat­ics in com­mon, as well as this Bletch­ley Park experience.

GABRIELLE:  I’m curi­ous to know, did they ini­tial­ly, the 150, did they all work togeth­er or were they sep­a­rat­ed into dif­fer­ent areas?

DANIEL: They were sep­a­rat­ed into dif­fer­ent areas even at that stage because it was a very, very large prob­lem set. Most famous­ly, Bletch­ley Park was deal­ing with an awful lot of Enig­ma sys­tems. There was a lot more cryp­tog­ra­phy fly­ing around the world at that point. Even the Enig­ma machine came in lots of dif­fer­ent vari­a­tion sizes and you had dif­fer­ent teams work­ing on dif­fer­ent types of Enig­ma machine and deal­ing with the vol­umes there as well. Old forms of cryp­tog­ra­phy such as code books are still very much in use. So there were also peo­ple, for exam­ple, work­ing on try­ing to crack the Japan­ese sys­tems, which were still very much based on hand­ing out these very, very large books full of code words, which were then super encrypt­ed and then see­ing what could be done to sort of recov­er some of those.

GABRIELLE: In your paper, you talk a great deal about Jack Good and his influ­ence there. At what point in the begin­ning did he enter into Bletch­ley Park and begin his influence?

DANIEL: So I think he was one of the ear­ly peo­ple gath­ered in by Tur­ing and Welch­man in the sort of ear­ly 40s. He was just recent­ly grad­u­at­ed from Cam­bridge. He’d come in as a sort of very pure math­e­mati­cian. He was a stu­dent of G.H. Hardy. He was very much inter­est­ed in that sort of pure math­e­mat­i­cal side of things. But was while he was work­ing at Bletch­ley Park and work­ing along­side Tur­ing that he sud­den­ly sort of had this epiphany, this sort of road to Dam­as­cus moment where he sud­den­ly real­ized, my good­ness, I can think about sta­tis­tics in a dif­fer­ent way than I have been doing and sud­den­ly do some­thing which is very, very use­ful to this crypt­an­a­lyt­ic effort. He worked very, very close­ly with Tur­ing, but his ini­tial impres­sion that he made with Tur­ing was­n’t a very good one. So the first time Tur­ing encoun­tered Jack Good, he was actu­al­ly tak­ing a nap dur­ing night shift because he real­ized that he need­ed to be sharp and focused when some­thing impor­tant hap­pened. Tur­ing was­n’t at all impressed by this, but lat­er on, as Good made some very, very good math­e­mat­i­cal con­tri­bu­tions, Tur­ing got over that and they formed a very, very good work­ing partnership.

GABRIELLE: After read­ing your arti­cle, I real­ized that I thought it was fas­ci­nat­ing. He said he had his epipha­nies through his naps, and that’s why, you know, he would often take those naps.

DANIEL: Yes. I’ve said that you’ve got a lot of eccen­tric nod balls work­ing at Bletch­ley Park, I think Jack Good real­ly leaned into that. was some­body who just got inter­est­ed in so many dif­fer­ent things and you sort of read about his life and sort of how deeply he got into chess, how he sort of act­ed and advised it to Stan­ley Kubrick work­ing on the film 2001. I got inter­est­ed in com­put­er art or the all sorts of use of com­put­ers and arti­fi­cial intel­li­gence and things like this. He got so inter­est­ed in so many things and I think leaned a lit­tle bit into his eccen­tric­i­ties on occa­sion. he, his influ­ence then leaned into Bayesian sta­tis­tics and Bayesian thinking.

GABRIELLE: How did his influ­ence change the work­flow at Bletch­ley Park and then influ­ence the math­e­mat­ics over­all in UK academics?

DANIEL: At the time lead­ing up to the Sec­ond World War, UK math­e­mat­ics was very much of the belief that sta­tis­tics should be approached from what we now call a fre­quen­tist or clas­si­cal point of view. And Jack Good was­n’t sort of hav­ing much sort of progress think­ing in that sort of way. It’s a bit of a tricky dis­tinc­tion to explain. I have a friend Mal­colm who sort of fre­quen­tists and Bayesians both do the same cal­cu­la­tions, but they think dif­fer­ent thoughts while doing them. But sort of point of Bayesian sta­tis­tics ver­sus clas­si­cal sta­tis­tics in the clas­si­cal sense, you sort of have this thought in your head, there’s this actu­al under­ly­ing truth, and all of your obser­va­tions are just sort of help­ing you get clos­er to that under­ly­ing ide­al. Where­as Jack Good now found him­self sort of think­ing in sort of Bayesian way, where instead you sort of say, no, I’m mak­ing obser­va­tions and they’re chang­ing my belief about the state of the uni­verse. And I’m using them as weight­ed evi­dence to sort of see what I should change my beliefs to. So per­haps your audi­ence will be famil­iar with some­thing like the Mon­ty Hall prob­lem, which again, it’s an exam­ple of how think­ing about sta­tis­tics in dif­fer­ent ways can become very, very con­fus­ing. Peo­ple think­ing about the same prob­lem can come to quite dif­fer­ent con­clu­sions. And to the fre­quen­tist, the idea that sort of open­ing a door and sort of say­ing there’s noth­ing inter­est­ing behind this some­how is telling you some­thing about what’s going on behind the oth­er doors is some­thing that does­n’t sit nat­u­ral­ly with fre­quen­tist. Bayesian would sort of say, oh yes, that’s telling me some­thing. And now it’s giv­en me evi­dence about my ini­tial choice of which door I use and how I should reeval­u­ate the chances of me being right because of that and what the actu­al sort of state of affairs is. And what that meant was this was a view­point which was very, very pow­er­ful peo­ple doing crypt­analy­sis. So when you’re doing crypt­analy­sis, you’re try­ing to uncov­er some sort of secret set­up, some sort of secret key, some sort of para­me­ter that the enci­pher­er has cho­sen. And begin with, you start from a posi­tion where you should be believ­ing pret­ty much any­thing is pos­si­ble. I have no rea­son to believe one thing or anoth­er. But as you study more and more of the mes­sage, cal­cu­late more and more sta­tis­tics of that, you should start chang­ing that belief, start­ing to say some of these pos­si­bil­i­ties are not going to be true, and some of them are per­haps more like­ly because of what are being seen. And Bayesian sta­tis­tics gave good ensur­ing sort of pos­si­bil­i­ty to be math­e­mat­i­cal­ly pre­cise about how those beliefs should be chang­ing. And in par­tic­u­lar, they real­ized that these cal­cu­la­tions that you can do were very, suit­able for doing auto­mat­i­cal­ly on some of the devices that were being devel­oped at the same time. So you have this won­der­ful com­ing togeth­er of being able to met­ri­cate your beliefs at the same time as being able to cal­cu­late those beliefs more effec­tive­ly because the com­put­ers that are com­ing online. And that turned into some­thing very, very pow­er­ful crypt­analy­sis that still informs an awful lot of what we do today. But at the same time, good real­ize that the ben­e­fits of this view­point weren’t going to be lim­it­ed just to crypt­analy­sis. And there whole dif­fer­ent ways in which peo­ple should be adapt­ing their beliefs based on data based on sta­tis­ti­cal evi­dence and tried there­fore to pop­u­lar­ize this Bayesian approach, writ­ing a book on the weight­ing of evi­dence prob­a­bil­i­ty and the weight­ing of evi­dence, try­ing to bring peo­ple around to this view­point. The sort of clas­si­cal fre­quen­tist body with­in sta­tis­tics was­n’t always very wel­come of that thought and the book was­n’t always very well received when it was first pub­lished. But now as more and more peo­ple came on board with the idea, it’s now sort of viewed very much as a clas­sic as he sort of then spent a career jump­ing between gov­ern­ment, acad­e­mia and oth­er places, just try­ing to con­vince peo­ple that yes, some­times the Bayesian way of think­ing about things was just going to stop you being con­fused and lead you to the right answer and be very, very effec­tive about doing it.

GABRIELLE: You bring that up and then you also bring up how it affect­ed UK math­e­mat­ics. Pri­or to Good’s book, what was the aca­d­e­m­ic envi­ron­ment like with regards to either using Bayesian sta­tis­tics or being more of a frequentist?

DANIEL: So I’d say that the most famous math­e­mati­cians in Britain at the time, like Fish­er and Jef­fries, were large­ly com­ing from the Adven­tist camp. And Jack Good, through­out his career, think, found him­self con­stant­ly hav­ing these debates with peo­ple like Fish­er who did some absolute­ly bril­liant sta­tis­tics, but did think about sta­tis­tics in a very dif­fer­ent way to Jack. Jef­freys per­haps was a bit more will­ing to sort of try and take dif­fer­ent per­spec­tives on the same things. And there was a con­fer­ence sort of say­ing that, Jef­freys him­self did some­times use the Bayesian view­point. And Jack was always sort of look­ing to sort of have oth­er evi­dence he could use to sort of say, no, some­times it’s the right thing to do. And oth­er sta­tis­ti­cians are doing this thing. The sort of major fig­ures Fish­er and Jef­fries, I’d say at the time, weren’t as wel­com­ing of a Bayesian and were more in the fre­quen­tist camp, but weren’t at all involved in any of the effort at Bletch­ley Park. And I think that gave Tur­ing and Good the sort of oppor­tu­ni­ty to sort of rein­vent sta­tis­tics from them­selves. A lot of the sort of meth­ods that Tur­ing was writ­ing down, he did­n’t real­ize that he was rein­vent­ing sta­tis­ti­cal the­o­ry that was already known. Tur­ing was typ­i­cal of doing this. did this with a num­ber of var­i­ous dif­fer­ent meth­ods. It was Jack Good who sort of turned around to him and said, “Yeah, I think I agree with that. I think it works.” “But isn’t this just Bayes’ the­o­rem?” “And Tur­ing said, oh, is it?” And was very much sur­prised him that he was recov­er­ing things that per­haps already known.

GABRIELLE: We’ll be right back after a quick word from my advertisers.

GABRIELLE: The cama­raderie that they had and the con­nec­tions that they had end­ed up chang­ing the cours­es of some of the indi­vid­u­als. And how often, I’m sure your research in this was exten­sive­ly deep, how many of those cas­es hap­pen where peo­ple became friends and all of a sud­den their career just took a total­ly dif­fer­ent trajectory?

DANIEL: So I don’t think I cap­tured every­thing, but it was very much a recur­ring pat­tern that you see. The very nature of the work, the fact that it’s the clas­si­fied com­mu­ni­ty, it inevitably makes things a lit­tle bit insu­lar. You can’t talk to any­body who’s not involved with work about the work, and you’re always a lit­tle bit on edge about giv­ing some­thing away acci­den­tal­ly. So in addi­tion to work­ing along­side these peo­ple, you tend to social­ize with them a lot more. So there’s lots of accounts of the fact that, yes, in addi­tion to work­ing togeth­er, they’d also social­ize togeth­er. They’d go to the pub togeth­er, play games of chess, set each oth­er puz­zles, do dra­mat­ic acts togeth­er. And they very much grew friend­ships as much as they grew work­ing rela­tion­ships at the same time.

And one of the real­ly nice things about Bletch­ley Park, I think, was the fact that the tech­ni­cal work was approached in a very, very non-hier­ar­chi­cal man­ner. So there you had the ear­ly career math­e­mati­cians along­side the great fig­ures of UK math­e­mat­ics, these peo­ple who’d already estab­lished their careers and pro­fes­sors, along­side peo­ple who are real­ly only just com­plet­ing their under­grad­u­ate degrees. When they got togeth­er and start­ed talk­ing about the tech­ni­cal side of things, none of that sort of out­side pres­tige mat­tered. What mat­tered was the qual­i­ty of the ideas. And you’d read about the sort of tea par­ties they’d hold and the fact that they just throw ques­tions open to every­body and It did­n’t mat­ter whether you’d been the sort of pro­fes­sor at Cam­bridge for five, ten years, or whether you’d only just real­ly start­ed learn­ing about the prob­lem from work­ing on the sys­tem as part of the rent orga­ni­za­tion. Your idea would be lis­tened to on its mer­its. I think that also kept things very infor­mal. And the sort of first name basis meant that you had these pro­fes­sors talk­ing to these under­grad­u­ates as friends. And at the end of the war, then it’s no sur­prise that peo­ple want­ed to keep these con­nec­tions going.

The pro­fes­sors who sort of take to shine some peo­ple with moves and say­ing, come along, do a PhD with me or var­i­ous the stu­dents who’d sort of enjoyed work­ing with these peo­ple sort of said, “I don’t know what your math­e­mat­ics is, but I’d love to work fur­ther with you.” So Bill Tutte, for exam­ple, when he would look for a super­vi­sor, his first thought was to look for peo­ple who’ve worked at Bletch­ley along­side him. And not just with­in the edu­ca­tion­al realm, when they got into their research careers, because they knew each oth­er, they kept track of each oth­er’s research. And so a lot of peo­ple who’d worked with David Rees, got very inter­est­ed in a very big paper he’d writ­ten about semi-groups, which was not too wide­ly cod­ed in math­e­mat­ics. They got inter­est­ed in some of the ques­tions that arose from that, and all of sud­den you have this pock­et of UK exper­tise in semi-groups that were all friends of David Rees in some ways, but only real­ly got inter­est­ed in the work because they’d known David from Bletch­ley Park. So you got this strange sec­ond order effect that because they got along so well social­ly, their math­e­mat­ics con­tin­ued to over­lap through­out their careers.

GABRIELLE: What cryp­to­graph­ic tools and appli­ca­tions were cre­at­ed from Bletch­ley Park and how did Bayesian sta­tis­tics helped to devel­op them? I know you men­tioned this in your arti­cle and I know the answer, but I would love for you to share that with my listeners.

DANIEL: So as I said, there were a lot of activ­i­ties going on at Bletch­ley Park. Every­body’s most famil­iar with the Enig­ma machines and the bomb devices that were built to attack those. Those are very impor­tant, per­haps used. Bayesian tech­niques less than the oth­er ones. I think the area where Bayesian sta­tis­tics proved itself were part­ly amongst some of that code­book work that I talked about. So some of the math­e­mati­cians such as Ian Cas­tles and Edward Simp­son found use for Bayesian sta­tis­tics attack­ing those code­books and Edward Simp­son wrote a bit about his war work doing those. But the sort of big prov­ing ground I think was in the attack on the Tun­ny sys­tem, which was used by the Ger­man High Com­mand. It was a teleprint­er cipher where the traf­fic vol­ume was­n’t as great as it was for Enig­ma. But the intel­li­gence val­ue of know­ing what the High Com­mand was think­ing was absolute­ly crit­i­cal. And there they found that, the Tun­ny device real­ly did have this very sta­tis­ti­cal attack that could be used. And they start­ed build­ing these very, very sophis­ti­cat­ed devices for the time, the Heath Robin­son machine and the Colos­sus com­put­er rit­u­al your lis­ten­ers may have heard of. Again, to do these cal­cu­la­tions of sta­tis­tics that could lead you to change what the beliefs about the set­tings of the machine were until you’re absolute­ly cer­tain that you’ve recov­ered the actu­al set­tings of the device. it was the devices such as Heath Robin­son and Colos­sus, think, which were the real­ly, real­ly big killer appli­ca­tions of Bayesian sta­tis­tics of Bletchley.

GABRIELLE: When we start­ed talk­ing, you had talked about the, quote, mythol­o­gy of Bletch­ley Park. It’s an inter­est­ing term. I’m curi­ous to know what are the mytholo­gies of Bletch­ley Park?

DANIEL: So again, it’s some­thing we’ve only sort of come to real­ize in the late half of the twen­ti­eth cen­tu­ry and the ear­ly part of the twen­ty-first. Some of the what feel like almost impos­si­ble feats of crypt­analy­sis, they were sort of tak­ing this machine, new age of cryp­tog­ra­phy that was sup­posed to be hav­ing more com­bi­na­tions than the num­ber of atoms in the uni­verse. Every­body was sort of had this very, very strong belief ought to be unbreak­able. But then they were sort of turn­ing this into an indus­try where they could break it at scale. the sort of num­ber of dif­fer­ent break­throughs that would con­tin­u­al­ly occur and often just as you need­ed the most were absolute­ly incred­i­ble. So Tur­ing was able to build on the work of Pol­ish cryp­tol­o­gists like Rejew­s­ki, Zygal­s­ki and Róży­c­ki. And when the sort of baton had been passed by the Poles, their meth­ods worked for the first part of the war, but behav­ior was chang­ing, new mod­els of enig­ma were com­ing out.

And there were huge months when sud­den­ly there’d be black­outs of traf­fic and peo­ple were just des­per­ate for the next break­through. And then some­body would just at exact­ly the right time seem to have exact­ly the right idea. The sto­ry of the Tun­ny sys­tem that I also men­tioned, sort of break­ing out by hand of an ini­tial oper­a­tor error by Brigadier Tilt­man, one of the great sort of pen­cil and paper cryp­tog­ra­phers of his­to­ry, which was then passed on to Bill Tutte to do this diag­no­sis of machine that nobody had ever seen. But he was able to deduce the entire work­ings of the device just by hav­ing this one set of out­put from it and being able to real­ize there are math­e­mat­i­cal pat­terns in that. And then being able not just to turn that into an under­stand­ing of how the machine worked, but how it could be attacked.

But the neces­si­ty of sort of the scalar com­pu­ta­tion of that, that then would be required, did­n’t seem to be too scal­able until peo­ple sort of said, oh no, we can start build­ing these incred­i­ble devices and this huge break­through after break­through after break­through, moment of genius after moment of genius, after moment of genius. To me, it is like some­thing out of myth. It is some­thing that’s leg­endary in the sort of things that they were able to achieve there. And it’s some­thing that I get very, very pas­sion­ate about, as you’ve prob­a­bly found out dur­ing the interview.

GABRIELLE: Yes, well, who would­n’t? What came out of Bletch­ley Park was mon­u­men­tal, no doubt. As Bletch­ley Park start­ed and then as it con­tin­ued to evolve into a large group of indi­vid­u­als. What was the dis­per­sion into acad­e­mia like? How did this affect acad­e­mia? And at any point with­in this, was there this con­nec­tion where acad­e­mia was work­ing almost in par­al­lel, or I should say almost in sync with Bletch­ley Park as far as math­e­mat­ics go, as far as the appli­ca­tions of sta­tis­tics and com­pu­ta­tion­al analysis.

DANIEL: Yes, I think it was a sort of very sig­nif­i­cant amount of man­pow­er that was being pulled out of acad­e­mia to work on these things. And you saw increas­ing­ly as the war went on, some of sort of teach­ing was being sus­pend­ed and the under­grad­u­ates who were part way through the degrees were actu­al­ly being pulled into the war work at Bletch­ley Park. So some peo­ple like Peter Hil­fen, for exam­ple, had done two years as an under­grad­u­ate degree before being pulled into Bletch­ley Park. As a result of his work there, they decid­ed to award him a full degree. Oth­er peo­ple had only done one year or so and so had to go back to their stud­ies after that.

Oth­er peo­ple like Bill Tutte nev­er actu­al­ly for­mal­ly tak­en a math­e­mat­ics course or been enrolled as a math­e­mat­ics stu­dent at Cam­bridge. But when he emerged at the sort of end of the Sec­ond World War, hav­ing done this mar­velous work at Bletch­ley Park, they decid­ed straight away to make him a full fel­low of Trin­i­ty Col­lege, Cam­bridge, which he was always wor­ried was a bit of a give­away that he’d done some­thing very, very impor­tant math­e­mat­i­cal­ly while at Bletch­ley Park. But yes, it’s the draw­ing of effort sort of meant that acad­e­mia was seen as the pri­ma­ry recruit­ing ground for this huge indus­tri­al sized effort.

And as a sense, there was a sort of a bit of a hic­cup in the sort of devel­op­ment pipeline of math­e­mati­cians because of that. After war, then yes, these, as I say, these asso­ci­a­tions con­tin­ued. But then you had the groups that had been formed con­tin­ue to work togeth­er and then brings an awful lot of what they’d learned into acad­e­mia. So when Max New­man went to the Uni­ver­si­ty of Man­ches­ter, he sort of said, “I want to start build­ing some of these devices that I know work and I know despite their flak­i­ness, they can make real world con­tri­bu­tions to sort of sci­ence to math­e­mat­ics. And I know the peo­ple that I want to help me with this. I want Jack Good, want Ronald Mick­ey, I want Alan Tur­ing, because they know along­side me exact­ly how to coax the best out of these very, very ear­ly exam­ples of what I think is going to be a very, very impor­tant technology.”

GABRIELLE: What I love about Bletch­ley Park is its influ­ence in so many dif­fer­ent areas. And you had not­ed in your phe­nom­e­nal paper that influ­enced aca­d­e­mics. How did it also change the appli­ca­tion of com­put­ers? I’m assum­ing Bletch­ley Park was on the front line of this.

DANIEL: So yes, the devel­op­ment of devices of the Heath Robin­son device, the Colos­sus device, these were break­ing new ground in tech­nol­o­gy as peo­ple start­ed build­ing com­put­ing devices out of valves rather than the of elec­tro mechan­i­cal adders and so forth that we’d for­mer­ly had. And peo­ple like Doc Kean and Tom­my Flow­ers were real­ly push­ing for­ward some of the tech­nol­o­gy there. And that meant that, after the war, we had this huge body of exper­tise in sort of com­pu­ta­tion­al elec­tron­ics went on to inform every­thing that was going on at Man­ches­ter build­ing the Man­ches­ter baby com­put­er at Cam­bridge at the A‑slabs try­ing to build that first gen­er­a­tion device there. And even peo­ple like Tom­my Flow­ers went on to build a very famous device called Ernie, which was used as a ran­dom num­ber gen­er­a­tor to select some of our pre­mi­um bonds draws for the UK gov­ern­ment tax sys­tem. So again, you have this fan­tas­tic body of exper­tise that was used to work­ing with these some­what flaky ear­ly devices, but had the sort of con­fi­dence to know that they worked. And I think that helped push for­ward and bring about the sort of uses of those devices with­in sci­ence to ear­li­er than it would have been otherwise.

So when you had these ear­ly devices, a lot of peo­ple said, sounds inter­est­ing, but they take an awful lot of coax­ing. Some­times they fall over. Some­times they get the answer wrong. You’ve got to be very pre­cise about the instruc­tions. But the Bletch­ley Park crowd had a lot more patience with them. So Tur­ing was using them to start doing com­pu­ta­tions. The Rie­mann zeta func­tion, one of the most sophis­ti­cat­ed uses of com­put­er tech­nol­o­gy that you’ll see, while oth­er peo­ple are still busy using them to com­pute Fibonac­ci num­bers or prime num­bers and so forth, very, very basic high school math­e­mat­ics. At the same time, you had peo­ple just won­der­ing what the extent of what you could do with these machines could be. Could you teach them how to play chess and the spec­u­la­tion about whether these real­ly could lead to a sort of arti­fi­cial intelligence?

So peo­ple like Don­ald Mick­ey, who start­ed his life as a clas­sic stu­dent and then at Bletch­ley Park became very, very inter­est­ed in all of the tech­ni­cal side of things, and fin­ished his career is a very, very sig­nif­i­cant name with­in com­put­er sci­ence and arti­fi­cial intel­li­gence became obsessed with these sorts of ques­tions as well as Jack Good and Alan Tur­ing and Max New­man. Again, I think that helped dri­ve a con­ver­sa­tion that’s still going on, per­haps is get­ting even more momen­tum these days as we move into what peo­ple are call­ing the AI era.

GABRIELLE: That being said, the AI era. How much, if you don’t mind, back­track just a bit back to Bayesian sta­tis­tics and then the appli­ca­tions at Bletch­ley Park, how much has that con­tributed, and I’m sure it’s enor­mous, how much of that do you see direct con­nec­tions with our cur­rent appli­ca­tions of arti­fi­cial intel­li­gence and machine learning?

DANIEL: So again, yes, the ideas behind large lan­guage mod­els draw an awful lot from Bayesian sta­tis­tics. You sort of gath­er a large amount of data about peo­ple’s uses of lan­guage and sort of say, okay, I’ve seen this much of a sen­tence so far, what’s the most like­ly next word? How would I base my evi­dence? I draw con­clu­sions from what I’ve seen from all the rest of this cor­pus. And I’m again using these Bayesian meth­ods to do that sort of pre­dic­tion or back­wards pre­dic­tion in some cas­es as well. I think it was a very nat­ur­al choice in the UK to name our big data sci­ence effort, the Alan Tur­ing Insti­tute. And I think that rec­og­nizes some of the real­ly keen insights he was hav­ing about the fact that Bayesian sta­tis­tics was not just a good set of thoughts to be think­ing when try­ing to sort of under­stand what’s going on with these con­nec­tions and how we should change our beliefs based on what we’re see­ing, but also that it’s very, very tied up with what you can do very, very effi­cient­ly with the com­put­er. And that’s the sort of rev­o­lu­tion that we’re con­tin­u­ing to see today. So I think the Alan Tur­ing name is not coin­ci­den­tal and very, appro­pri­ate indeed.

GABRIELLE: Most cer­tain­ly. Nam­ing it the Alan Tur­ing Insti­tute, no doubt, is more than appro­pri­ate. He tru­ly was a genius in his own right. And his con­tri­bu­tions to Bletch­ley Park, as well as the secu­ri­ty of the Unit­ed King­dom, was excep­tion­al. His con­tri­bu­tions to Bletch­ley Park, as well as to the secu­ri­ty of the Unit­ed King­dom, was excep­tion­al. So how did the work, the the­o­ries and appli­ca­tions of Tur­ing, Welch­man, Good, and the many oth­er bril­liant indi­vid­u­als at Bletch­ley Park com­plete­ly changed the appli­ca­tion of com­put­ers. Would you say it was lin­ear or exponential?

DANIEL: It’s hard to say because there was­n’t real­ly such a thing as a com­put­er before Bletch­ley Park. it was a lot of the tech­nol­o­gy devel­op­ment there that allowed them to build some of those ear­ly devices. yeah, I think the per­son­al­i­ties of Bletch­ley Park and the ear­ly days, cer­tain­ly of the UK com­put­er activ­i­ty, very invis­i­ble. Any sort of ear­ly effort you saw with­in com­put­ing, soon­er or lat­er you’d come across a name there who’d been work­ing at Bletch­ley Park and knew that these things would work. So I think it def­i­nite­ly helped accel­er­ate that and that sort of belief that these, and knowl­edge that these machines real­ly could work and be incred­i­bly effec­tive. I don’t think you could sort of real­ly sep­a­rate out what it would have been like with­out the Bletch­ley Park crew.

GABRIELLE: We’ll be right back after a quick word from my advertisers.

GABRIELLE: So as we begin to move into an era of quan­tum com­put­ing, how can the dupli­ca­tion of Bletch­ley Park prac­tices serve as a blue­print for the appli­ca­tions in clas­si­fied work?

DANIEL: Right. So my advice to the clas­si­fied com­mu­ni­ty, to the GCHQs, the NSAs of this world is the first les­son to learn is keep acad­e­mia close. These aca­d­e­mics can have won­der­ful new insights and they’re real­ly, real­ly bril­liant peo­ple. And I used to be the head of an insti­tute in this coun­try called the Har­bron Insti­tute, which is where GCHQ makes best use of the UK’s aca­d­e­m­ic math­e­mat­ics tal­ent. I think that’s a crit­i­cal resource to the sort of clas­si­fied com­mu­ni­ty to sort of keep that link strong. The oth­er les­son I’d sort of say in the sort of ear­ly days of quan­tum com­put­ers is make sure you’ve got peo­ple who know how to sort of cope with what can be some­what flaky ear­ly gen­er­a­tion devices into doing some­thing use­ful. So I’ve said that yes, a lot of the ear­ly gen­er­a­tion com­put­ers were very unre­li­able in lot of ways and they took a lot of patience and a lot of belief to work with. We’re see­ing sim­i­lar things as we real­ize that yes, get­ting these quan­tum com­put­ers to behave can be a very, very tricky thing and errors are going to creep in from the out­side world and a lot of the sort of chal­lenge of quan­tum com­put­ing is deal­ing with some of the flak­i­ness and some of that prone­ness to errors. And hav­ing that sort of core belief that things are going to work out is the oth­er thing to do. So learn how to cope with that sort of flak­i­ness, I think is the oth­er les­son for quan­tum computing.

GABRIELLE: How would that look like hav­ing the patience of work­ing with these old­er gen­er­a­tion devices look as far as apply­ing it to what we’re doing today?

DANIEL: So I think there’s a very impor­tant area of study here for what’s called quan­tum error cor­rec­tion. That’s the abil­i­ty to sort of keep your quan­tum com­put­er run­ning while it’s get­ting these gar­bles and errors intro­duced, but rep­re­sent­ing the infor­ma­tion in a redun­dant way so that all of those errors still don’t stop you from reach­ing the final answer in there. I’ve got some friends at a quan­tum com­put­ing com­pa­ny called River­lane who are very, very excit­ed about these sorts of chal­lenges and sort of say, yes, there’s an awful lot that can go wrong with these sort of ear­ly gen­er­a­tion quan­tum com­put­ers, but there’s also a very, very good chance we can work around that by doing some very, very inter­est­ing math­e­mat­ics. So, that sort of quan­tum error cor­rect­ing codes is the sort of key tech­nol­o­gy that I’d be track­ing there.

GABRIELLE: So there is hope for lega­cy appli­ca­tions in quan­tum computing?

DANIEL: There is hope that, yes, we can start get­ting ben­e­fit out of these things quick­ly. It’s a very, dif­fer­ent way of doing com­pu­ta­tions than clas­si­cal com­put­ers. I don’t think we ful­ly under­stand the space that we can explore, per­haps, yet. But just as these sort of ear­ly gen­er­a­tion com­put­ers turned out to be the killer devices that you need to sort of get this huge ben­e­fit from Bayesian sta­tis­tics, I think there are cer­tain prob­lems that quan­tum com­put­ers are going to be unique­ly suit­ed to, par­tic­u­lar­ly in mate­ri­als design and sci­ence sim­u­la­tion. I think those are going to be able to take us into places that our cur­rent clas­si­cal com­put­ers are nev­er going to be able to touch.

GABRIELLE: Yes, that’s going to be quite a move­ment. I’m look­ing for­ward to see­ing how mate­r­i­al sci­ence actu­al­ly begins to evolve out of this. then how do you think as far as the lessons in the his­to­ry that Bletch­ley Park brought us, how do you think this is going to influ­ence the future of cryp­tog­ra­phy and cyber­se­cu­ri­ty and as well as I should bring up there are oth­er insti­tu­tions like Bletch­ley Park that since closed its doors, but how do you think they can con­tribute or will influ­ence the future as we head into a whole new world?

DANIEL: Right. So I think as an exam­ple of real tech­no­log­i­cal accel­er­a­tion and unthink­able sort of speeds of break­throughs on what we con­sid­er to be intractable prob­lems, I think there’s a very, very good mod­el to be had there. And I think there might per­haps be sim­i­lar lessons to be learned by a good exam­i­na­tion of things like the Man­hat­tan Project or the Apol­lo pro­gram at the times when we have seen very, very rapid tech­ni­cal advance. But look­ing specif­i­cal­ly at Bletch­ley Park and also per­haps its US part­ners at Arling­ton Hall or var­i­ous oth­er things like that, math­e­mat­i­cal break­through, that col­lab­o­ra­tive accel­er­a­tion, I think they’re very, impor­tant to be lessons to be learned there.

So yes, the first les­son of Bletch­ley Park, I think, is to be very, very accept­ing of eccentrics and odd­balls and dif­fer­ent view­points. The diver­gent think­ing that dif­fer­ent view­points on the prob­lems can bring to you, this sort of change from sort of tak­ing the accept­ed fre­quen­tists view­point and using Bayesian sta­tis­tics instead, or look­ing to have com­pu­ta­tions done at great speed using dif­fer­ent tech­nolo­gies than they’re cur­rent­ly being tried. That’s very, very impor­tant, pro­vid­ed huge div­i­dends for every­thing they were doing at Bletch­ley Park. And I think the intel­li­gence com­mu­ni­ty needs to be con­tin­u­ing to accept these new and dif­fer­ent thinkers to have these spec­tac­u­lar break­throughs that it con­tin­ues to need.

I think the sec­ond les­son would be to return to what I said ear­li­er about the work­ing pat­terns at Bletch­ley Park being very flat and non-hier­ar­chi­cal. So the fact that you had pro­fes­sors talk­ing to under­grad­u­ates as equals on first names terms, where all that mat­tered was the qual­i­ty of the thought that was being brought to the con­ver­sa­tion. And that’s incred­i­bly impor­tant as well, that nobody feels that they can’t bring some­thing up and that it’s going to be judged on the mer­its of the idea rather than any per­ceived sta­tus that the of speak­er has. And being able to col­lect a much wider net of ideas real­ly increas­es the num­ber of good ideas you can have on that.

The third thing that I would real­ly rec­om­mend is the, again, the Bletch­ley Park les­son of being friends with the peo­ple that you work with. And the fact that they were mak­ing a social net­work at the same time that they were mak­ing an aca­d­e­m­ic col­lab­o­ra­tive net­work, I think made that net­work all the stronger and con­tin­ued it all the longer because these were peo­ple who liked work­ing togeth­er, whether it was on extreme­ly impor­tant clas­si­fied work, or a chess open­ing or try­ing to puz­zle out the lat­est word palin­drome that one of them had come up with. They just real­ly, real­ly enjoyed shar­ing ideas on all sorts of dif­fer­ent ways. And I think that’s an incred­i­bly good way to run a tech­ni­cal team to this day, to sort of work along­side peo­ple who are friends because of their com­mon inter­ests, because of their abil­i­ty to just exchange ideas on all fronts.

GABRIELLE: I think we need more of that in the work­place every­where. That is phe­nom­e­nal. Thank you for stat­ing that. Speak­ing of work­ing togeth­er and get­ting togeth­er social­ly and just the con­cept of puz­zles, because I know you’ve writ­ten some puz­zle books. I would love to hear more about that because in my fam­i­ly, we’re big on puz­zles. We love games and I love gath­er­ing with friends and that’s our social con­nec­tion. Tell me about your puz­zle books.

DANIEL: It’s going to come as no sur­prise that GCHQ is very, very fond of puz­zles and has an immense puz­zling com­mu­ni­ty. You can’t sort go into GCHQ with­out, soon­er or lat­er, some­body pre­sent­ing you with some lit­tle brain teas­er. And that’s espe­cial­ly true in the sort of cryp­to-math­e­mat­ic com­mu­ni­ty there. So it’s some­thing I quite read­i­ly fell into when I was work­ing there, and to the stage where I sort of fell into set­ting some of the puz­zles myself. And I can say that while I was there, I was asked to help with one of the very ear­ly GCHQ Christ­mas cards that we’ve now got. They’ve now got very famous for pro­duc­ing on an annu­al basis, where in addi­tion to sort of send­ing out a lit­tle card to every­body who works with GCHQ, sort of say­ing, have a great Christ­mas, they say, here’s a lit­tle puz­zle to go along­side it.

And that ini­tial one that was put out sud­den­ly caught the imag­i­na­tion of the entire inter­net by the sort of design of it. It had this mul­ti­ple set of stages that led you to ever more com­plex and tricky puz­zles. To the extent that we acci­den­tal­ly crashed the GCHQ web­site, it was becom­ing so pop­u­lar. Peo­ple got very, very excit­ed about that. And after we did that, GCHQ was approached by pub­lish­ers say­ing, peo­ple loved the Christ­mas card. Do you have more of these puz­zles sorts of things? Would you like to do a puz­zle book? And I was part of a small group that con­tributed a small num­ber of puz­zles to the GCHQ puz­zle book, which again, had a lev­el of suc­cess that nobody was quite expect­ing and was sud­den­ly charg­ing up the best­seller list. I think a threat­en­ing sup­ply of cer­tain print mate­ri­als at var­i­ous points. That was anoth­er incred­i­ble success.

I think I con­tributed maybe only about four or five puz­zles to that one. But it did lead us again to the sec­ond GCHQ puz­zle book, which we had a bit more time to think about, and I think per­haps shows a bit more of that devel­op­ment. There I was able to con­tribute a few more puz­zles as well as a few his­tor­i­cal obser­va­tions to the GCHQ puz­zle book too. And again, you can find my name in the back of that as a puz­zle set­ter, his­to­ri­an and edi­tor. Since leav­ing GCHQ, I’ve con­tin­ued to sort of com­pose puz­zles. I’ve got a week­ly col­umn in the Times of Lon­don news­pa­per called Mind­set, where each week we set three dif­fer­ent puz­zles there. And a col­lec­tion of those puz­zles, again, can be found from the Times Pub­lish­ing arm, and you can get them from most good online book­sellers, I believe.

GABRIELLE: So just to clar­i­fy, it’s through Times Publishing?

DANIEL: It’s done under the Times of Lon­don brand. I think the pub­lish­er is Harp­er Collins. But it’s Time’s Mind­set puz­zles and there’s just one vol­ume at the moment.

GABRIELLE: Fan­tas­tic. I’m wait­ing for two of them. One is the Time’s Mind­set and there is anoth­er one that I ordered as well.

DANIEL: I do hope you enjoy them. We had a lot of fun putting them togeth­er. Some of them can be very, very twist­ed in the way that per­haps only a cryp­tog­ra­ph­er could come up with that. I hope they’re all enjoyable.

GABRIELLE: Noth­ing more enjoy­able than a mind ben­der. I want to ask you what your final thoughts are because your arti­cle is so thor­ough and it goes through so much, the human con­nec­tion, the devel­op­ments, the math­e­mat­ics, its influ­ence on UK math­e­mat­ics. Do you have any final thoughts that you want to add to your paper that you could­n’t actu­al­ly put in that you would just love to say to my audience?

DANIEL: I would say that it came about because I was used to very much hear­ing the sto­ry of the dif­fer­ence math­e­mat­ics made to cryp­tog­ra­phy. I want­ed to sort of trace the reverse jour­ney of the effects that cryp­tog­ra­phy and crypt­analy­sis had on math­e­mat­ics in the after­math of Bletch­ley Park. I think it’s some­thing that I’ve viewed as incred­i­bly impor­tant to the health of both com­mu­ni­ties, both the intel­li­gence com­mu­ni­ty and the aca­d­e­m­ic com­mu­ni­ty. These con­nec­tions took place.

And my own expe­ri­ences is hav­ing worked on the con­nec­tions between the intel­li­gence com­mu­ni­ty and acad­e­mia, I think that con­tin­ues to be true. I think we con­tin­ue to see ben­e­fits on both sides. So hav­ing worked with the Heil­bron Insti­tute an awful lot where, again, we were try­ing to con­nect GCHQ with aca­d­e­m­ic math­e­mat­ics, the sort of over­all ben­e­fits not just with­in the intel­li­gence com­mu­ni­ty, but the UK as a whole, and par­tic­u­lar­ly the UK aca­d­e­m­ic com­mu­ni­ty, should­n’t be under­es­ti­mat­ed. When the UK wrote the Black­ett Report into quan­tum tech­nolo­gies, it sort of said, we think that, there’s going to be an incred­i­ble change that’s going to come about because of these new quan­tum tech­nolo­gies. And we look to orga­ni­za­tions such as the Heil­bron Insti­tute to pro­vide some of the skills nec­es­sary to exploit these. And sim­i­lar­ly, the Alan Tur­ing Insti­tute, we’re busy see­ing how data sci­ence and arti­fi­cial intel­li­gence might be anoth­er sort of plan­e­tary chang­ing oppor­tu­ni­ty technology-wise.

And again, the ideas have already been played around with sig­nif­i­cant­ly by acad­e­mia and the internist com­mu­ni­ty, bring­ing these groups togeth­er, mak­ing sure they work togeth­er, mak­ing sure the net­work works as wide­ly as pos­si­ble and that as many view­points are tak­en up as pos­si­ble, I think is absolute­ly vital for the future exploita­tion of tech­nol­o­gy that I hope we’re about to see from these areas as well.

GABRIELLE: I agree. I do too. I’m very excit­ed to see where we move for­ward. Before we go, I did want to ask, and I know we brought it up ini­tial­ly, about your MC Esch­er Lego cre­ations. I think some of my audi­ence mem­bers would be real­ly fas­ci­nat­ed to hear about that. if you would­n’t, if you’d be open to it, shar­ing some pho­tos with me via email that I could post on my website.

DANIEL: So yes, this is anoth­er dif­fer­ent hob­by. And again, I men­tioned that Jack Good was a hero of my becom­ing inter­est­ed in so many dif­fer­ent things, includ­ing math­e­mat­i­cal art and com­put­er art. I’d always been a fan of MC Esch­er. and I’d attend­ed a talk by a very good math­e­mati­cian called Lenstra who’d been uncov­er­ing some of the math­e­mat­ics behind one of Escher’s pic­tures. I was men­tion­ing this to a friend of mine who I’d been sort of say­ing, oh, you can do these mar­velous draw­ings which are based on non-Euclid­ean geom­e­try and Rie­mann­ian sur­faces. And he said, ah, doing that with draw­ings is bor­ing. We should use some com­pu­ta­tion­al pow­er. You could do this with photographs.

And we start­ed out then recre­at­ing some very, very inter­est­ing pho­tographs of our­selves, which were recur­sive and sort of turned into these, what they’re now called spi­ralis or dros­ta pic­tures. But it also sort of brought us togeth­er to sort of chat more about oth­er Esch­er pic­tures that we both liked. And he was also a huge fan of mak­ing Lego art. So he’d done var­i­ous topo­log­i­cal sculp­tures made out of Lego of min­i­mal sur­faces and oth­er math­e­mat­i­cal objects. And sort of said, “could we per­haps try to recre­ate the Esch­er print gallery pic­ture you’ve been talk­ing about out of Lego?” That project turned out to be more com­pli­cat­ed than we thought, but we did have oth­er ideas for ones that we want­ed to do. So we found our­selves quick­ly find­ing that, you could use some of these nice ways of manip­u­lat­ing dig­i­tal images to per­haps cre­ate some of these impos­si­ble effects. And some­times they did­n’t need to be that sophis­ti­cat­ed. So you may be famil­iar with the Esch­er pic­ture ascend­ing and descend­ing of the infi­nite stair­case that always appears to be going upwards and upwards and upwards or down­wards and down­wards and down­wards if you go back the oth­er way. We man­aged to make a mod­el out of that from Lego, which peo­ple found absolute­ly fas­ci­nat­ing and I love look­ing at. Sim­i­lar­ly, his pic­ture rel­a­tiv­i­ty, which has all the var­i­ous dif­fer­ent angles of grav­i­ty, was fun to do in Lego where you had studs now appear­ing on all dif­fer­ent sur­faces as well. Hap­py for you to sort of show some of those pic­tures on to your audi­ence because I think they would be fascinated.

GABRIELLE: That would be won­der­ful. Thank you. I appre­ci­ate that. Well, thank you so much for your time and for shar­ing this arti­cle. I think I’ve read it five times now. It’s absolute­ly fas­ci­nat­ing. Thank you very much for being on Math Sci­ence His­to­ry and thank you very much for your time.

DANIEL: Thank you. It’s been a pleasure.

GABRIELLE: So to con­clude, this con­ver­sa­tion has offered a remark­able win­dow into the endur­ing impact of Bletch­ley Park, not only as a piv­otal site in the his­to­ry of code break­ing, but as a pro­found influ­ence on the devel­op­ment of math­e­mat­i­cal schol­ar­ship in the Unit­ed King­dom. The spir­it of cama­raderie among its indi­vid­u­als fos­tered an envi­ron­ment of col­lab­o­ra­tion and intel­lec­tu­al growth that extend­ed far beyond the war years, shap­ing the land­scape of British math­e­mat­i­cal research for gen­er­a­tions. For those inter­est­ed in explor­ing this sub­ject fur­ther, I high­ly encour­age you to read Daniel Shue’s arti­cle, The Influ­ence of Bletch­ley Park on UK Math­e­mat­ics, in Tay­lor and Fran­cis’ jour­nal, Cryp­tolo­gia, which I have linked in the show notes. There is so much won­der­ful and reveal­ing infor­ma­tion to unpack. The cama­raderie, the con­nec­tions, the math­e­mat­ics, and as Daniel so elo­quent­ly titled the arti­cle, the influ­ence of Bletch­ley Park.

Thank you so much for tun­ing in and until next time, Carpe Diem.