Neither am I.
> Some of his ideas
> continued and considerably further developed ancient geometry.
We still call the non-polar co-ordinate system "Cartesian Co-ordinates".
But for me, his greatest achievement (one of the greatest achievemnents
of all time) is "Cogito, ergo sum".
> I see him also in the context of others, in particular Wallis who
> introduced the symbol of infinity.
Didn't know that.
> While Descartes intended avoiding arbitrariness, the application of
> his co-ordinates on the traditional notion of time implied the need
> to arbitrarily choose a point zero of reference.
I don't know how to read that. I do not accept the notion of time
as a phenomenon (let alone as a dimension of some continuum);
like number, it is a noumenon, a thing that exists only in the mind
of man. Indeed, the time line is just the number line with some minor
label changes.
> He was not at all careless
I was being ironic.
> but put into the religious belief in an alpha (creation of
> the world) and an omega (doomsday).
Hmm. Didn't know that either. Can't say I see any positive value in it.