The biggest hand calculation in a century! [Pi Day 2024]

in 2024 hundreds of number enthusiasts gathered in  a school hall in London to try and calculate pi to a record number of digits by hand a project which  would require untold hours of doing laborious calculations with nothing but paper and a pen this  was all the fault of ridiculous maths person Matt Parker and it was not going well it is uh where  we now 10 7 we're about to start packing up on the end of Friday day four of six and I'm still  working on a sheet here which goes up to digit the 10

0th digit so that's as far as we've got and  the record is 527 I don't think we're going to do this we're going to do this it's the first day we  have a small number of Volunteers in setting up all the sheets working out the systems getting  it up been going it's all going so well we are a few short days and several hundred volunteers  away from a record amount of pie by hand it had started well enough on day one a core group of  50 or so nerds had gathered to do the preliminary setup calculatio

ns Matt and his team explained how  the pi formula was going to work and what initial calculations needed to be done as the rest of the  week would be spent doing long divisions a lot of time tables had to be generated for the various  devisers these would be referred to extensively in all future calculations it wasn't exciting work  but everyone was in high spirits so far it's very exciting um very busy I think there's a lot of  the initial admin that needs doing that you forget about um but it

's nice to get get calculating  um and I'm now we've started I'm more hopeful than I was yesterday we haven't actually done a  calculation like this in 80 years we don't need to do this calculation it's just you know can  we still do it do we still have the ability to do these things I think that's interesting to find  out well I'm sort of I'm cautiously optimistic I'm fairly confident we'll beat the 2022 record yes  this wasn't the first time Matt and the team had tried to calculate pi by hand

he had made several  attempts by himself since 2016 but never getting more than six digits correct in 2020 he had a team  of five people for one day who managed five digits in 2020 2 20 people gathered for 2 days to achieve  11 digits this time Matt wasn't messing around up to 200 people a day would churn out calculations  for six solid days and Matt had a whole new formula there was a category of Pi equations  known as Machin-like formula and of the hundreds available we picked this one Pi / 4

equals  and then you've got the sum of seven different arctans each with a coefficient out the front this  means in theory we're doing seven different arctan calculations which can all be done independently  this is quite parallelizable so we can keep track of them we gave them all names and we went through  the rainbow of colours as well and so the final answer is pi itself we preemptively multiplied  all the coefficients by four and all we have to do now is calculate a lot of arctans the recor

d to  beat was set in the 1870 by British school teacher William Shanks over several decades Shanks had  calculated 707 digits of pi but it wasn't until the 1940s that someone found a mistake in the  528th digit making the current world record of digits of pi computed by hand 527 digits Matt had  even brought a little momento of shank's work to help keep him motivated yes I bought an original  1873 print of shank's calculation which is right there that's that's shank's pie that they thought  was

right um made a mistake little embarrassing we're hoping to fix that um but I thought it' be  nice just you know this is kind of my spiritual predecessor having it here today I can't take  it actually in where we're doing the calculation because as well as being a No Calculator Zone  which makes sense no calculation devices in there um I probably shouldn't take in 527 correct  digits a pie as well as the setup the day one crew did start doing a few of the main calculation  steps and the answers

which came back were not as correct as they had hoped yeah we're getting  a lot more mistakes than we expected um I'll be honest I was hoping most of the sheets would  match when they come back in again but the folks over here you can see the discussion on  the checking table they estimate when they get two like duplicate sheets back in again they  don't match 75% of the time which means we're getting a lot of mistakes now we' got systems in  place now we're going to over here we're going to se

nd out more copies so be three each time  which will slow us down a bit but everyone's having fun um so we'll see how that impacts us  when we have a room full of people in on day two day two and 100 new human calculators have  joined the core team bringing the room total up to 150 people Matt had asked in previous YouTube  videos for volunteers and people had shown up from around the world the only requirement was the  ability to do long division because division is all you need to compute an a

rctan how do you  actually calculate an arctan thankfully there is something called a tailor series it's an infinite  series of things you have to add and subtract together to give you the value of your arctan  you're adding and subtracting these different fractions with odd powers and odd coefficients  underneath we just need to calculate enough of these we did it in two steps because the powers  are always the next odd power power up we could first of all work out 1 /x and then we just  divide

that by x^2 and then we divide that by x^2 and each time if we divide by x^2 we will  get the next 1 /x to the power of some odd number once we have those we then separately divide  each one by its appropriate odd value to put the three the five the seven the 11 and so on back  in and by following those steps we have the chain of dividing down that main spine of values and  separately with dividing by the odds the process for each human calculator was simple they would  join the queue and wait

to be issued a calculation which needed to be done from one of the seven  handout desks one desk per arctan then they would visit the pi-brary to borrow the devisor times  tables they would need and then find a seat on the calculation floor and get cracking once their  calculation sheet was complete they would hand it back in at the check-in desk return their times  table to the pi-brary and start the process again we're doing the pi-brary section so our job is to  make sure that when people com

e down to do their divisions they need their appropriate division  table so if you're dividing by seven we got a seven table right here and if you're dividing  by Pacific Square Pacific squared which is this absurdly large number well you get that table and  they've all been checked and double checked uh for errors and mistakes so our job is to make sure  people know what to divide by I just finished dividing by do squared which is the largest  number that we have I completed it and I give it to

checkin and all I know at this point is it  was legible so it's been accepted the error rate in the first days was higher than we expected and  so we have put some stuff in place to catch more errors um we are we're handing more sheets out at  once so we're originally going to hand out three copies of a sheet and if two of them come back  correct we then check them more thoroughly um we're often getting three come back incorrect so  for the critical pass we're now doing five copies at once so r

ather than three come back then you  wait we send the another out and wait again for that to come back we're doing all of it at once  and hoping that that means we only after a single time by the double time for those computations  but for this to work the arctan calculation needed to be split into tiny chunks which could  be done individually one at a time by a swarm of different humans here's how we actually calculated  the arctan in practice we did it in chunks of 20 digits at a time so first

of all we calculate the  zeroth digit to the 20th digit then we do 20 to 40 40 to 60 and so on down the main one divided by  X whatever X is for that arctan spine we divide all of those by x² to get the equivalent set of  digits for 1X cubed 1 x 5 and so on the issue is once you've done one chunk of digits whatever the  remainder is has to feed into the next chunk of digits so each sheet of working out is waiting  for the sheet above it to be finished and the sheet before it to be finished to v

isualize the  step we can turn this wonderful 2D grid into a 3D Arrangement where now every single chunk has to be  divided by the corresponding odd number to get us our actual series for the arctan and like before  each of these requires the appropriate spine chunk to be done before it can be done dividing by the  odd number and there's a carry value which rolls from each chunk to the next chunk after it in  the series this ridiculous plan devised by Matt, Katie, Scroggs and the rest of the Pi-

by-hand  Council meant that there were thousands of pieces of paper that both depended on and fed into other  Bits of Paper in an attempt to make tracking the pages easier each sheet was colour coded pink and  green for positive and negative spine terms and yellow and blue for positive and negative odds  terms surely that would help keep mistakes at All right day three I feel like we are still  making a lot of mistakes I I think we're still over half the sheets of a mistake somewhere on  them wh

ich is fine we have systems in place but I think we've caught all the errors we it's now  definitely got a lot more complex we've had a lot of logistical challenges today where we've had  to invent new tasks recruit people to do various checks we've had to buy a lot of clipboards uh  this it turns out moving 10,000 pieces of paper around a room that all rely on one or two other  specific Bits of Paper and have to feed into one or two others is a logistical nightmares but I'm  pretty sure we' fou

nd all the ones we lost all recreated them we've audited all the gaps my  job now is just to finish this long division very carefully uh the slogan we've got now is  we want long division not wrong division so ah when a complete sheet was given to the check-in  desk they would do some initial checks to make sure it had been filled in correctly and then  pass it on to the next stage the verification station would wait for two duplicates of the same  calculation to be handed to them and see if the

y match if there was a match they would pass the  paper on if the incoming answers conflicted more copies of the same calculation will be sent out  to be done again until two results were the same next The Mod Squad would perform mod arithmetic  checks on every calculation these calculations are not able to produce the full answer but they  can verify the answer matches the inputs mod 9 10 and 11 now convinced the answer is probably  correct the team moves the pages on to processing and staging

where the sheets sit waiting for any  other outstanding calculations needed before they can progress once all the dependent calculations  are in a complete pack of previous results and new blank sheets are given to the human photocopier  who copy the required info onto the new sheets which are then given to the handout tables and  the cycle continues so behind us we have a table the verification station right they are getting  uh calculations from two independent people and if they match which w

e hope they do they come  to us and we're checking to see if they match by a fluke or if it actually correct so we're  doing a little mathematical check of casting out nines which is what we used to do years ago  and if it passes our check then we can say yes this is actually mathematically true and not just  randomly happen stance happens to be equal to each other uh unfortunately everything coming to us is  passing our checks here are casting out N9 check except for very dramatic moments yeste

rday yeah  absolutely so we had a super dramatic moment where we checked the nines cast out the nines it's all  good checked the 10 cast out 10 it's all good and then they had Els and we checked it we checked it  again and we checked it again and we realized that there was definitely an error and this was quite  early in the calculation um so what happened is two people had made exactly the same mathematical  arithmetic error um that our casting 11s checked otherwise it would have all been passe

d into  the sums and everything would have gone very good yeah everything from that point on would  have been wrong the next three and a half days and most of the stuff we're getting is passing  which is a Lely sanity check because without this we wouldn't know that things are actually  working so we are we can tell you things are actually working and and dramatically cut out a  mistake that's it it was very exciting my five all around the record I think is something that  we've all kind of got

in mind as it would be nice to be able to break that record um and  I guess comparing it to what Shanks did was literally just sit on his own and work on it and  that's fine if you've got you know 30 years um but given that we've got a week we kind of need to  compress that into a much smaller time scale which is going to mean a lot more people are involved  it's a lot more I think it sort of scales badly right so the more people you have involved the  more time you need to spend briefing them t

he more Logistics you need around all of that um so  scaling up doesn't necessarily just mean you know this much time times this many people or whatever  um but I think from what we did last time we've kind of figured out maybe how to scale it up  and we did all of the maths on like how many more sheets of paper we need how many terms are  we going to need depending on which formula we use you know how is that going to change um but  even then there's going to be things that you don't anticipate

so like delays in terms of um  you get little backlogs you get little kind of bottlenecks where one particular calculation  gets done by a few people and they come back and they don't match so you have to resend them  out or you have to do again we have to find where the error is that then slows down not just that  one but all the ones after that so that kind of thing makes it take longer than you're expecting  it to right you can sit at home and do some long division but you can't calculate pi

on your own  um and I think the fact that people will come here to to get involved is partly because they  want to you know contribute to that and also to be able to say actually that was me I was part  of that thing um and I guess wherever we get to um we've all done something we'd never otherwise  have normally done uh and it's a fun time it's a good excuse uh to come and also the these people  are great like we we've met so many new like all the volunteers new friends new um cool Max people 

that we didn't know before uh and I think that's really nice also in the room was the current world  record holder for computing Pi by any means Emma I happen to work for a cloud service provider and  I had access to you know re Computing resources I could use and my team was celebrating Pi Day every  year so when we were planning for 2019 Pi Day I realized maybe we have enough Computing resources  to break the world record I see these are these are two separate categories and humans like human

  processors and as a software engineer or someone in computer science I see this whole process as um  someone said microarchitecture but yeah it's it's a processor like par process processing system  so you have a large number of um computers and human calculators uh doing the long divisions  and then we have so in in the actual computer you have when you look at the CPU you have actual  Processing Unit in a tiny portion of the overall processor and then the rest is keep to keep these  processe

s pet so you break down the instructions reorder them and then um re retire so take so and  dispatch them out of order and then reorder them so everything is in in in package process and I  find this process really like similar and to that that analogy and I enjoy kind of watching this  kind of mechanism and system processing running smoothly day four and things are only getting  more complicated the collapsing station has now kicked into action they are taking the  final results coming in for e

ach arctan and start adding up all of the terms together  it's slow methodical work meanwhile at the far end of the room a new department has sprung  into existence the Central Intelligence archive originally envisioned as a cardboard box where  used papers could be dumped the archive now had a full staff of people maintaining a highly  organized record of the calculation thus far and running extensive double checks and audits  on the pages they have also trained up several progress Enforcement

Officers one for each arctan  who roam the hall with clipboards making sure all the pieces of paper are accounted for and are  moving through the system but despite all this admin the papers are not moving fast enough  day four and we're excited that we got to 60 digits which is I mean good 60 very far very  carefully calculated digits but it's not it's not 600 is it for the record so uh we've got  a a room full of 200 people working very hard to maybe get to 100 by the end of day four so  uh ye

ah I mean I've just got to keep dividing with ever increasing complexity and still a high error rate Matt realizes the world  record has slipped out of his grasp Matthew why aren't you doing your long division  Shanks is it you well yeah yes even though there are no confirmed pictures of me I think we can  probably agree this is bang all the money yeah no good point look I can I call you William  Will Billy Billy no Mr Shanks is fine okay Mr Shanks emphasis on the mister Mr Shanks I  cannot beli

eve having been through all this that by yourself you were able to do 700 7 digits  with a single mistake well I've had years decades toiling away on my own and I'm better at maths  than you okay valid point but but I've got you know over a 100 people most of which are better  at maths than me and we I don't know we're doing this for a week and we are going to struggle to  get to 100 in my day I had to work alone it took me years by myself and when I was finished and  dead no one even checked fo

r over 70 years but you look at your vast group you put a call  out on this YouTube and hundreds of nerds descended from around the globe and sometimes  the real irrationality is the friends you made along the way that's that's transcendental of  you is everyone having fun and a good time you know I think everyone is well then W dividing  hard enough and you get back to work yes sir that's Mr Sir Mr Shanks sir goodbye and get  back to work Matt did he divided harder and more carefully than ever

before doing his part  as a tiny cog in a massive calculation machine day five and no one seems to be giving the record  a second thought the room full of 200 number fans continued working away way as fast but as  carefully as they could everyone now fully in the swing of doing something which hasn't  been attempted for over a century everyone was curious to know just how far through  the digits of pi they would be able to reach I think a lot of us there's a lot of people  here who have done mat

hs in the past and kind of just missed doing the simple stuff say simple  long dividing by 150 billion is an exactly simple it's uh it's just a nice to reminds yourself  of uh I guess where your roots are in a way yes we've only got a couple hours left before  um we're done on kind of the last day tomorrow we have to do the final calculation and we've  realized we're not going to get past 140 and what's amazing is everyone's having a great time  and working together and and no one's sad that we'

re not I mean obviously it would be great  to have gotten more digit but everyone is so excited the prospect of 140 just just like that's  a thing we might be able to achieve is great and we're over a 100 digits we're confident about  and I mean there's 200 people 200 people who are despite everything that's happened to us  are dividing but they're not divided with one day remaining it became very clear that if the  team wanted to hit the next digit Milestone they would need to try something dif

ferent so the  core team planned out the Hail Mary protocol the new plan was simple the human machine which  had evolved over the week would continue as is for all sheets up to digit 120 anything above 140  was cancelled no so the check is still happening but the check is happening concurrently to  the next division happening so that we can hopefully go faster try and get down these last  returns we get yeah we kick off the next division before we've checked the previous one as long  as we know

we got two copies that are the same that's a kind of facing Lev check we start  the next one and then the more thorough check happens sort of in parallel with that so we end  up if there is an error we can kind of chase it back and go stop come back do that one again uh  but it means that we can just jump straight to the next one so we've been able to do uh the  remaining trunks for the whole of the next I guess set of digits in the space of 3 hours so  it's been fast it's been faster than yeste

rday but we also have made no progress for the next 20  there's no point now starting the next 20 because they are there's even more things to do on those  because it's long more yeah I think we're sort of secretly in our heads wondering if this is  actually a better method to use for next time or what the problems with it are um and we're  sort of I guess we'll we'll continue thinking about that until we try this again if we try  this again when we try this again when we try this again the fina

l steps were adjudicated by  ardent Tau fan and someone who would find it very funny if Matt's calculation had a mistake  Steve Mould if there's any uncertainty about how how legit this calculation has been we  have an independent observer who's just here to check everything as we're wrapping up from  the right place yeah and and I haven't seen any calculators come out uh it's all been above what  everything seems to have been done by hand I've checked some of the numbers as well you know I  lov

e half to day um I don't know why we do it on the half uh but that's just you've got You'  got a special word for it haven't you I follow Steve around to make sure you doesn't try and  multiply anything by two when I'm not looking the collapsing station is carefully summing  up all the final positive and negative terms into two grand totals these are dutifully copied  out onto two large pieces of paper for the final Grand subtraction digit by digit Matt subtracts  one number from the other with

hundreds of eyes watching out for even the smallest mistake number  now all that is left to do is to verify the final answer and see how many digits of pi are correct  if they get fewer than the previous attempts 11 digits this is going to be really embarrassing  you got Pi got Pi so we're going to do it like we did before I'm going to read it out Katie's  going to say yes or yep or or uh-huh and Sophie's doing the over the shoulder checking I think  I will I just point I'll just point and when

when we get to the bit that's wrong I'll  draw a sad face job done okay to be clear Sophie's also going to check that we don't walk  backwards into anything oh that's true that's a very important to us halfway we'll swap and I'll  go back and you can be you can be okay three uh yeah so it's on a different line that's a  good point that's a good point the three is like yeah yeah yeah I like no  I was expecting one no three point one yep four yep one yep five yep nine  yep two yep six yep five yep

three yep five yep eight yep nine yep I don't think  anyone is surprised so far seven yep nine yep three yep two yep three yep eight yep  four yep six yep we're ahead of last time okay how can such a chaotic flurry of calculations  give such a predictable result like maths ah two yep six yep four yep 3 yep three yep 8 yep three  yep 2 yep 7 yep 9 yep 5 yep zero yes two yep eight eight yep eight yep four yep one yep 9 yep s yep  one yep genuinely surprised okay that's that's four if you want to

swing around over there try  not to say numbers that's really confusing I just instinctively said eight yeah it's fine mix it  up "do a Scroggs" as we call I'm I'm not going to say any numbers that's not it's not happening  okay now we've just read 971 yes okay six yes nine yep three yep nine yep nine yep three yep seven  yep five yep one yep zero yes five yep 8 yep two yep yep zero yep 9 yep 7 yep four yep N9 yep four  yep four y 5 yep 9 yep 2 yep 3 yep Zer yep 7 yep 8 yep 1 yep six yep four ye

p zero yep 6 yep 2 yep  8 yep six yes two yep Zer yes8 yep n yep nine y yes okay okay okay [Music] okay I've got to stop sounding so  surprised every digits I feel like I'm going to get increasingly surprised at  some point instead of yes I'll just say some what eight yes six yep two yep 8 yep zero yep 3  yep 4 yep 8 yep 2 yep 5 yep 3 yep four yep two yep one yep one yep seven yes zero yep six yep seven  yep 9 yep 8 yep 2 yep 1 yep 4 yep eight yep Z yep 8 yep 6 yep 5 yep 1 yep 3 yep 2 yep awfull

y  drawn eight yeah it's all right on here okay just when I think my respect for Shanks couldn't  get any higher two yes three yes zero yep what yep did you say zero and I heard no I said  yes oh said yes you said zero I think I'm I think I'm just slipping into a dreamlike trance  yeah it's good that we got the three tiredest people in the room this is really good so just to  recap we just had 230 yes now we are coming up at 120 digits so we are we are safely into the  hundreds we'll see how far

we can get now so let's get to 120 we just said 23 0 it then goes  six yes six yes four yep seven y okay okay okay final I mean what's nice bit of a miracle I me what's nice is we were if there  was a mistake like we were so confident we check so much I don't know how we'd reverse  like it I was it be some systematic or you know Phantom error but we're okay now now we  hit the uncertain Zone we're semi-confident with the first 15 so let's check those  zero yes nine yep three yep 8 yep four yep

four yep 6 yep zero yep 9 yep five yep  five yep zero yep five yep eight yep two yes we can't applaud every digit so join us we need moral support yes I I will  fall over it's not a race okay I'm they can't see them I'm blocking  them okay here we go we just did 582 yeah then there's another two yes three  yes [Music] yeah one y [Applause] no [Applause] okay okay I mean uh this  is a lucky dip seven [Applause] yes six no that's it that's pretty [Music] [Applause] [Music] good I'm I'm as surprise

d as anyone that's phenomenal  that's it huge thanks to the Pi Day organizing Committee of Alex, Ayliean, Ben, Christian,  Deanna, James, Katie, Max, Nicole, Scroggs, and Sophie who've been working on this for the past 2  years and thanks to all the volunteers who stepped up and did all sorts of phenomenal work above and  beyond the call of duty that made this possible more names than I can possibly possibly think  they're all scrolling by here and if you want to be involved in something like or

maybe this in  the future there's a link in the description below you can sign up and I'll let you know when I'm  next planning something this ridiculous and this was funded by my Kickstarter funders who funded my  Humble Pi standup special filming I said I'd use the Surplus funding on something else and that's  what paid for this ridiculous Pi Day calculation if you want to help fund other videos and projects  uh of course you go to my patreon get involved the more support I get the more ridic

ulous maths  occurs in the world thank you so much everyone I'm feeling great we got so many digits I I really  can't believe that I was really fun and now I got to go back and finish my PhD I took a week off  for this I came here for for pie and all I got was sandwiches yeah it was like ComiCon just for  mathematicians pretty emotional feels like the end of a um pretty incredible couple of days um  pretty sad it's over but I think we did a pretty good job great I really enjoyed the bit with the

  mats I should probably get some sunlight and some sleep uh I'm looking forward to calculating  more things I had such a good week I was here since Wednesday and honestly everyone here  is absolutely lovely um and we we calculated a number I think the mathematical Community  will be shaken by our new discovery that pi just ends abruptly at 139 digits this has  been some of the most incredible few days of my life to be surrounded by so many people  all passionate about the same thing has been an

incredible experience say what you want  but that surprise ending came out of nowhere incredible results I can I literally cannot  believe it this was very worth the trip yeah well I mean after at all you know Matt was  going on about how once the only remainder that he has left is the good memories we'll do  it again but I can't help but think if that's the remainder where's the quotient yeah well  I mean I don't like giving things a scale from 0 to five but I give this one probably a a  3.141

5 honestly it just felt kind of nerdy