FOM: Re: Questions for Hersh

Karlis Podnieks podnieks at
Wed Jan 21 01:55:57 EST 1998

-----Original Message-----
To: fom at <fom at>
Date: otrdiena, 1998. gada 20. janvāris 20:54
Subject: FOM: Questions for Hersh

Are the following statements "mathematics" by your definition?
Why or why not?

KP> In my Jan. 5 posting I proposed to distinguish between the
concept of "mathematical theory" (which can be defined
precisely) and the purely organizational term "mathematics"
(which is hard to define precisely). I think that a fixed (i.e.
self-contained) system of basic principles is the distinguishing
property of mathematical theories, i.e. only this property
allows us to separate the "mathematical" from other arts of
human thinking.

If so, the question "What is mathematics? " can be answered
simply by listing some of the mathematical theories as the
"first class mathematics", some other - as "second class",
other - as applied mathematics etc.

>From this point of view:

(1) is mathematical, but not first class mathematics (one can
easily formulate chess rules as a self-contained "theory"),
(2, 3, 4) are not mathematical (no self-contained theory
presented up to now),
(5, 6, 7, 8) are first class mathematics - if we define clearly,
which theory will be used to discuss each of the problems. If
not - (5, 6, 7, 8) are problems of f.o.m.

Best wishes,
podnieks at
University of Latvia
Institute of Mathematics and Computer Science
Rainis boulevard 29, Riga, LV-1459, Latvia

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