The Bailey-Borwein-Plouffe formula

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This is an excellent story about the so-called Bailey-Borwein-Plouffe algorithm and formula. The BBP formula is an expression for calculating pi discovered by Simon Plouffe in 1995:

pi formula in base 16

This is a remarkable formula because it is a digit-extraction algorithm for pi in base 16. Simon Plouffe describes his discovery of the formula
and the consequences he suffered when sharing the credit with others. Read the full story here or the highlights here (the original story is very lengthy):

“The story began many years ago in 1974 when I wanted to find a formula for
the n’th digit of Pi… since the computation of Pi looks more complicated than the number e… I studied a way to compute that number instead.

…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

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 negotiate a job as professor at Simon
Fraser University, which failed. I am very poor at negotiations. 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… 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…

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.

…About David H. Bailey. He came after the discovery of the formula and my
small basic program , I had also a Fortran version. This is where Peter
Borwein suggested to add him as a collaborator to the discovery since he
contributed to it (as he said), this is my second big mistake. Of course he
accepted to co-write the article, who wouldn’t ?! David H. Bailey (and
Ferguson) are the authors of the PSLQ program. That program is the
version of the Pari-Gp program. I used it a little it is true,
but what made the discovery was Pari-Gp and Maple interface program I had.
So actually, that person has nothing to do with the discovery of that
algorithm and very little to do with the finding of the formula. The mistake
was mine. Saying that Bailey found the formula is like saying that the
formula was found by the Maple and Basic program.

I tried very hard to correct the situation avoiding the subject of the
actual discovery of the algorithm and the formula, I made an article in 1996
for the base 10. I thought naively again that this would re-establish the
situation, it did not. I almost accepted to do a film at one point in 1999
when a certain guy from England that wanted to make a movie on Pi and the
discovery of the formula. he asked me if I would accept to talk about my
with the Borweins. I did not wanted to go in that direction, I
should had. There was that book of Jean-Paul Delahaye (le fascinant nombre
pi) that mentioned the Plouffe algorithm and formula because I told him part
of the story. In some way I was afraid of revealing that enormous story.

Why was I so naive? I had a previous collaboration with Neil Sloane and the
Encyclopedia of Integer Sequences and the web site, this was really a big
success and Neil is the person I respect the most in mathematics so this is
why I thought (wrongly ) that my collaboration with the Borweins had to go
well, a big mistake.

Why do I write this? To tell the truth and also the arrogance of those
people makes me sick.

Will I gain something from this? I don’t care, I have nothing to loose.

Simon Plouffe Montréal, le 22 juin 2003.”

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