Simon Plouffe

I present the Inverter 2014, a large set of mathematical tables aimed at
finding what a number is made of.  There are 3 large sets.  The first one is a
table of real numbers at 64 digits of precision and with 10.4 billion entries
all categorized into 26 types.

That large database is accompanied with a super-sized version of the OEIS
(On-Line Encyclopedia of Integer Sequences) with 105 billion entries.  The 3rd
set is the first 100 billion zeros of the Zeta function.  I will present the
standard tools such as the plouffe_inverter program which uses, GFUN (a maple
package for generating functions) and about 8000 lines of code using the
so-called PSLQ program, generalized expansions of real numbers and such.

I will also present a new tool that uses specialized filters to do some data
mining in search of coincidences among numbers.  This tool is flexible and fast
enough to measure a distance, a notion of closeness with numbers.  For example,
using the recurrence Z(n+1) -> Z(n)^2 + c, and starting with a rational complex
number will usually lead to a simple algebraic number.  The filters can detect
that kind of pattern easily.

The last tool that will be presented (if times permit) uses properties of the
human eye to see patterns.  Some examples will be presented.