Quote by Knuth

[Christopher Dimech <dimech@gmx.com>]

> Sent: Sunday, July 18, 2021 at 6:43 AM
> From: "Marcin Borkowski" <mbork@mbork.pl>
> To: "Christopher Dimech" <dimech@gmx.com>
> Cc: "Emanuel Berg" <moasenwood@zoho.eu>, help-gnu-emacs@gnu.org
> Subject: Re: Quote by Knuth
>
>
> On 2021-07-15, at 08:21, Christopher Dimech <dimech@gmx.com> wrote:
>
> >> Sent: Thursday, July 15, 2021 at 6:06 PM
> >> From: "Marcin Borkowski" <mbork@mbork.pl>
> >> To: "Emanuel Berg" <moasenwood@zoho.eu>
> >> Cc: help-gnu-emacs@gnu.org
> >> Subject: Re: Quote by Knuth
> >>
> >>
> >> On 2021-07-15, at 00:53, Emanuel Berg via Users list for the GNU Emacs text editor <help-gnu-emacs@gnu.org> wrote:
> >>
> >> > But without the symbolic notation it isn't really math, is it,
> >> > because the natural language, no matter how careful one is,
> >> > can still be misinterpreted, interpreted in several ways, it
> >> > can be translated, made fun of ...
> >>
> >> Interesting, but false.  What Greeks did was most certainly mathematics
> >> even if they had little to none symbolism.
> >
> > We don't do greek mathematics anymore.  It was mainly geometric, which became
> > an ingrained technique that stall development until Liebniz introduced some useful
> > notation.  Magneto-Hydro-Dynamics needs compact notation.  Inverse Estimation
> > is another example.
>
> Well, don't we do the very same mathematics as ancient Greeks did, only
> expressing it in a different language?  (And of course, we now know
> more, since our knowledge grows.  OTOH, many things in contemporary
> mathematics are not very trustworthy due to the complexity and high
> probability of errors.)

We don't do the same mathematics as ancient Greeks did.  Greeks mathematics
can be understood by many people.  Then came Differential and Integral
Calculus (and fractional calculus, tensor calculus), mostly covered in
undergraduate mathematics, considered difficult by non-mathematicians, but
within grasp of 20 year olds.  With Special Relativity and beyond, very few
understand the mathematics of 100 years ago.  With current published mathematics,
much of it goes beyond graduate level, some so specialised that only if you work
directly in that specific field would you understand the notation.

Go to a lecture by Simon Donaldson at Imperial, and tell me how much you would
understand his particular solution to the equations of Yang-Mills Gauge Theory.
Or about how the Hermitian-Einstein Metric is well-defined in a holomorphic vector
bundle.

His most recent work centers on complex differential geometry and the existence of
Kahler metrics.