On Monday, June 23, 2003 at 10:14:32 PM UTC-8, Simon Plouffe wrote:   
   > This note explains the story of the so-called Bailey-Borwein-Plouffe   
   > algorithm   
   > and formula.   
   >    
   >    
   >   The story began many years ago in 1974 when I wanted to find   
   > a formula for the n'th digit of Pi. I was studying rational and   
   > irrational   
   > numbers. With my calculator I was computing inverses of primes and   
   > could   
   > easily find a way to compute those inverses in base 10 to many digits   
   > using   
   > congruences and rapid exponentiation. Since it appeared impossible to   
   > do   
   > the same for Pi, I wanted then to find a simple formula f(n) that   
   > could compute   
   > the n'th digit of Pi. I had that idea for 20 years.   
   >    
   > Since the computation of Pi looks   
   > more complicated than the number E , i.e. exp(1), I studied a way to   
   > compute   
   > that number instead. At that time (around 1983), I had a simple Basic   
   > program   
   > that used a spigot algorithm to compute E, as expected that algorithm   
   > worked but   
   > of course but was taking an increasing amount of memory. My question   
   > was :   
   > why can't we do it for E or Pi or any irrational numbers like sqrt(2).   
   >    
   > It was during the year 1994 that I began to compute arctan series but   
   > I did not   
   > realized that this meant a lot. I was able to use an algorithm to   
   > compute arctan   
   > of 1/5 with fast exponentiation without realizing that it could   
   > compute arctan(1/5)   
   > in base 5 very fast since the rapid exponentiation was natural in that   
   > base.   
   >    
   > Later in 1995, around august 7 of that year I suddenly realized that   
   > log(2) was   
   > fast computable in base 2. Since I had a bit of experience with spigot   
   > algorithms   
   > and also my little Basic program to compute arctan, it was not   
   > difficult to adapt   
   > the algorithm to log(2).   
   > In the next few days I made my first program : A program to compute   
   > log(9/10)   
   > in base 10 using a very small amount of memory and very fast. The   
   > program had   
   > 432 characters long.   
   >    
   > That discovery was a shock to me. I realized that I had found it yes   
   > but it was not   
   > new to me since I could do arctan(1/5) easily too but it took me 2   
   > years to realize it.   
   >    
   > This is where I began to use Pari-Gp, that program could find an   
   > integer relation   
   > among real numbers (up to a certain precision), very fast.   
   >    
   > During my stay at Bordeaux University in 1992-1993 I perfected that   
   > program I had   
   > that could interface Pari-Gp and Maple. That little Unix script had an   
   > enormous   
   > advantage of flexibility because I could set up a series of real   
   > numbers to test among 1   
   > unknown. At that time I was beginning to find new results, the   
   > programs were able to   
   > find identities.   
   >    
   > That program was the one that found the formula for Pi in hexadecimal   
   > (or binary).   
   > I also used another one : PSLQ. It was a good program but a bit   
   > cumbursome to use   
   > since it is written in fortran. Nevertheless I made an interface to   
   > Maple too.   
   > Pari-Gp was by far easier to use and faster for small cases (up to 10   
   > real numbers at   
   > the time with 100 digits precision was enough for those kind of   
   > problems).   
   >    
   >    
   >    
   > This is where I made the biggest mistake in my life : To accept the   
   > collaboration   
   > of Peter Borwein and David H. Bailey as co-founders of that algorithm   
   > and formula   
   > when they have found nothing at all. David Bailey was not even close   
   > to me when   
   > I found the formula. He was added to the group 2 months after the   
   > discovery.   
   >    
   > I was naively thinking that I could negociate a job as professor at   
   > Simon Fraser   
   > University, which failed. I am very poor at negociations.   
   > I remember that day when the Globe & Mail newspaper article went out   
   > in October   
   > 1995. I was at Jon borwein's house and he had a copy of the newspaper   
   > in hand.   
   > This is where I asked him to become a professor at SFU. He simply   
   > replied right   
   > away < don't even think about it >. I thought, this is the best chance   
   > I will ever have   
   > to become a professor there, since it failed, I decided that I had to   
   > leave that place.   
   >    
   > I was very frustrated at that time, in late 1995 after the discovery.   
   > I realized that   
   > many small details where terribly wrong. They were getting a lot of   
   > credit for the   
   > discovery and I had the impression of not getting anything in return.   
   > My strategy   
   > failed. One of those details was the article of the Globe and Mail, I   
   > asked Peter Borwein   
   > : why did they putted the photo of you and your brother on the article   
   > ? Your brother   
   > has nothing to do with this!.  He simply replied that the Public   
   > Relations at the   
   > University made a mistake.   
   > Later that year, I was invited to a ceremony in Vancouver for the CUFA   
   > (faculty of   
   > the year Award).   
   > This is a prize with plaque and mention that those 2 brothers received   
   > for the   
   > discovery of the formula. They simply mentioned my name at the   
   > ceremony and   
   > I received nothing at all. They made a toast to the queen of England,   
   > I did not   
   > stand up.   
   >    
   > In late 1995, there was that Canadian Math Soc. congress in Vancouver,   
   > I was not   
   > invited to talk about the discovery. There was even a guy (Stan Wagon)   
   > that said   
   > to me, I don't know if you have anything to do with this but in all   
   > case, this is   
   > good for you isn't ?   
   >    
   > Then in 1996, I realized that if I get up at night to hate them it is   
   > a very bad sign,   
   > it means that I have to leave that place (Simon Fraser university).   
   > I was convinced I had no future at all with those 2 guys around.   
   > I was making serious plans to leave.   
   >    
   > The story of the formula (my formula), was not the only one. The same   
   > thing happened   
   > with the ISC (the Inverse Symbolic Calculator). The story is even more   
   > ridiculous.   
   > I opened the site with my constants in July 1995 and it was an   
   > immediate success.   
   > The 2 Borweins had nothing to do with that thing, I had made the   
   > tables and all   
   > of the Unix programs to run it. The precious help I had was from Adam   
   > Van Tuyl, a   
   > graduate student, he made most of the code behind the web pages, later   
   > Paul Irvine   
   > made some additional code.   
   >    
   > At that time the local administrator of the lab. tried to convince me   
   > to stay even to pay me   
   > for maintaining the ISC, I refused. I wanted to leave with what I had   
   > : my tables of   
   > real numbers and sequences I worked for years (since 1986). This is   
   > why I opened the   
   > Plouffe Inverter with my name in 1998, to keep what was mine.   
      
   [continued in next message]   
      
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