The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Inactive » Historia-Matematica

Topic: [HM] Mathematics and Time
Replies: 18   Last Post: Apr 10, 2000 3:21 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Clark Kimberling

Posts: 20
Registered: 12/3/04
[HM] Mathematics and Time
Posted: Mar 8, 2000 9:40 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


One difference between mathematics and other sciences is the dependence of
the latter on time. Every object of the physical and natural sciences
changes with time, as each object consists of atomic constituents whose
locations and interrelationships vary with time.

Mathematics, however, inasmuch as it consists of basic assumptions,
definitions, and implications, rests on time-independent pillars, such as
Peano's Axioms, one of which is, essentially, the Principle of
Mathematical Induction. This particular pillar is curiously like time,
especially when it takes the form of an inductive definition. Consider,
for example, the sequence a(1), a(2), a(3), ... defined as follows:

Beginning with k = 1, let p(k) be the least natural number not already an
a(i), let q(k) = p(k) + k, a(p(k)) = q(k), and a(q(k)) = p(k).

The point of this example is illustrated by the use of the words
"beginning" and "already". The act of writing out terms

2, 1, 5, 7, 3, 10, 4, ...

depends on "beginning at some point in time" and "already done in time".
Nevertheless, the definition itself (which could be recast more wordily so
as to avoid "beginning" and "already") is invitingly free of time and
completely determines the object defined. For contrast, trying defining,
with comparable time-independence and completeness, a quark, atom, star,
virus, or DNA. (Here, one could become distracted with questions about
"reality" and "truth", but these are notions which, for many people, are
time-dependent and/or matter-and-energy-dependent, whereas our focus for
the moment is on definitions and implications based only on irreducibly
basic assumptions.)

These musings lead to a historical question: how far back in time can we
date recorded recognitions of the time-independence of mathematics? Or,
more largely: in what early writings is it argued that mathematics is a
separate discipline, strikingly unlike its various realms of application,
especially in its independence of time?


Clark Kimberling





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.