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Author Topic:   Is mathematics a science?
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 25 of 48 (239878)
09-02-2005 7:11 AM
Reply to: Message 20 by nwr
09-01-2005 6:04 PM


Re: Whitehead and Russell
From my perspective, the development of axiom systems such as ZF is an important part of mathematics. That is where much of the creativity and inventiveness is needed. By looking at only proofs derived from axioms, and ignoring the origin of the axiom systems, you omit some of what I consider to be the most important parts of mathematics.
But this is, in part, what considering different topoi is all about. And it's not exactly an inactive area of research...
You first have to introduce new concepts, new definitions, new axioms (such as the defining axioms of a Banach space).
What makes you think we can't build Banach spaces from ZF? Not that I've ever tried but there's nothing especially exotic about a Banach space.
Ph.D. was related to fixed point properies on topological groups.
Cool! My life seemed to revolve around topological groups for several years (though usually Lie groups in my case).

This message is a reply to:
 Message 20 by nwr, posted 09-01-2005 6:04 PM nwr has replied

Replies to this message:
 Message 26 by nwr, posted 09-02-2005 8:21 AM cavediver has replied
 Message 31 by Chiroptera, posted 09-02-2005 11:11 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 27 of 48 (239888)
09-02-2005 8:48 AM
Reply to: Message 26 by nwr
09-02-2005 8:21 AM


Re: Whitehead and Russell
With much patience and even greater resolve
How long did it take R&S to get to 1 + 1 = 2 ?
But surely this is the same as asking how long it would take to come up with micro-biology armed with just a knowledge of QCD and electroweak? It's a long job but in principle it can be done.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 32 of 48 (239923)
09-02-2005 11:32 AM
Reply to: Message 31 by Chiroptera
09-02-2005 11:11 AM


I could never understand the algebraic topologists who had no need to draw pictures. How they could calculate smash products without at least a sketch? I guess that I could never quite beat the physicist out of me
The only way that I could convince myself that we weren't all deranged in applied maths and theo physics was to walk next door into pure maths and math' statistics It almost made me feel normal. Then again, if you want REALLY weird, you want to try Oxford and Penrose's crowd. Off the planet!

This message is a reply to:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 33 of 48 (239925)
09-02-2005 11:38 AM
Reply to: Message 29 by crashfrog
09-02-2005 10:14 AM


That the axiomatic conditions that mathematical reasoning depends on are ultimately arbitrary?
Of course, and the Platonic Realm holds all of them
their position seems to be based more on a need for their work not to simply be logic puzzles and symbol games rather than an actual "math" that exists somewhere in the universe.
Odd comment. It's those of us in theo physics that tend to get converted to at very least a weak Platonism because we keep finding all of the maths supposedly reserved for "logic puzzles and symbol games" firmly embedded in the universe.
The 1st Law of String Theory: no area of mathematics is sacred

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 36 of 48 (239945)
09-02-2005 12:23 PM
Reply to: Message 35 by Chiroptera
09-02-2005 11:43 AM


Re: Hee hee hee -- I couldn't resist!
Oh yeah? Well, what about all the stuff you wouldn't have without us theo physicists? Wormholes? Warp drive? Teleport? Holodeck?
Hmmm... that's Star Trek isn't it? It's so hard drawing a distinction sometimes

This message is a reply to:
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Replies to this message:
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