[SystemSafety] Logical difficulties in mathematics

[Olwen Morgan]

All,

With the advent of March, my customary hibernation (aka Winter Blues) is 
drawing to a close ... so HELLO AGAIN, EVERYBODY :-))

One of the problems in modern mathematics is the undue quest for 
abstraction for abstraction's sake. To see what a really good 
mathematician (the late and *very sadly missed* Vladimir Igorevich 
Arnold - of KAM Theory) has said about this, go to:


https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html


Arnold got this right years ago. Most people who disagree with his 
position aren't actually good enough mathematicians to have an opinion 
worth listening to. (I'm certainly not good enough to agree with him, 
even though I do.)


Kind regards to all,

Olwen



On 24/02/2019 06:42, Peter Bernard Ladkin wrote:
> On 2019-02-15 21:09 , David MENTRÉ wrote:
>> For more "classical" use of formal methods in Mathematics, you can look
>> at Gonthier et al. proof of 4 colours theorem ... or .....
>> proof of Feit-Thompson Odd Order Theorem ... Beyond the
>> demonstration of those theorems, those works built a huge work of
>> formalized Mathematics in a mechanized way using Coq proof assistant
>> (https://github.com/math-comp/math-comp).
> There is also the substantial work on formal proofs in mathematics using the Cambridge-München
> Isabelle prover. There is an archive of formal proofs at https://www.isa-afp.org and the Isabelle
> home page is at https://isabelle.in.tum.de/index.html (one of four mirrored sites).
>
> I don't know much about Homotopy Type Theory, but Georges Gonthier was also involved in that, along
> with other luminaries such as the logicians Peter Aczel, Per Martin-Löf and Dana Scott
> https://hal.inria.fr/hal-00935057
>
> PBL
>
> Prof. Peter Bernard Ladkin, Bielefeld, Germany
> MoreInCommon
> Je suis Charlie
> Tel+msg +49 (0)521 880 7319  www.rvs-bi.de
>
>
>
>
>
>
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