> > Warren D Smith:

> > I also attempted to use PSLQ to figure out whether Zeta(3)/Pi^3

> > was a low-degree low-height algebraic number.

> DJ Broadhurst:

> Had such an attempt succeeded, there would be several deeply

> unhappy Fields Medalists, who believe (as I do) in the

> Drinfeld-Deligne conjecture that the Grottendieck-Teichmueller

> algebra has precisely one generator in each odd degree.

>

> Yet that is, emphatically, not a reason for avoiding serious

> experiments to investigate a contrary hypothesis. To the best of

> my recollection, the possibility that zeta(3)/Pi^3 might be an

> algebraic number has been investigated to many tens of thousands

> of decimal digits of numerical precision. However, I am unable

> to provide a reference.

--well, you (DJB) probably have better PSLQ and better hardware

than I do (I bet) and could do so yourself...

I see Broadhurst wrote a quantum field theory paper "where do the tedious products of zetas come from?" (actual title!) which mentions the "Drinfeld Deligne conjecture"

and "GrothendieckTeichm:uller algebra" (whatever they are) as well as using PSLQ.

Unfortunately non-experts (i.e. me) will have a difficult time understanding this paper.

Even after (trying to) read it, I still have almost no clue what DDC and GTA are,

and it gives zero cites to D,D,G and T's work.

Anyhow I agree Zeta(3)/Pi^3 being an "unusual number" was a pretty low-chance proposition, but SM Ruiz's post stimulated me to look, and sure enough, negative result.

About the idea that you can produce miracles on demand if you have enough fitting freedom... well, yes, but the approach I used attempts to quantify the miraculousness,

and the TRUE miracles yield far better approximations than the amount of fitting freedom would suggest. Don't accept lame miracles, demand real miracles.