Interesting article in August 2011 Scientific American

[Don Shepherd]

It's called "Why Math Works" and it asks the question "Is math invented or discovered." The author is an astrophysicist and the discussion is a bit deep, but it is an interesting read for the layman, including those of us who push buttons on HP calculators.

[dbatiz]

I’m sure there are more profound thinkers out there that will take issue with my opinion. However in the spirit of discussion I offer the following: When either using linear regression to approximate values between data points, or using calculus to predict planetary movements; math seems to be validated by how well it can represent and predict situations in the real world. As such, all the interactions, cause/effect, variables and relationships already exist and are waiting patiently to be discovered by intellects capable of seeing beyond obvious, quantifying the subtle, and finding the connection between the apparently un-related.

Again, only my opinion, each discovery sheds light on the fantastic complexity, elegance and care of our creation.

Very respectfully,

David

[Thomas Radtke]

My view on this topic:

As math originated from natural philosophy, its foundation reflects our perception of the world. If a farmer owning n cows buys another cow and subsequently counts the herd, he will likely reckon n+1 cows.

Thousands of years later, observations in our nature still guiding the way math is being developed, e.g. Newtons calculus. Few hundered years ealier, Cavalieri failed to invent it. There had to be a question in physics to do it right ;-).

[Mark Hardman]

Quote:

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Thousands of years later, observations in our nature still guiding the way math is being developed, e.g. Newtons calculus. Few hundered years ealier, Cavalieri failed to invent it. There had to be a question in physics to do it right

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Careful there Thomas. Walter will be all over you that it was indeed Leibniz that invented the calculus first and not Newton. For once I'd actually agree with him ;-) Furthermore, Leibniz's invention of the calculus stemmed from his pure mathematical studies into the "tangent problem."

[Thomas Radtke]

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Careful there Thomas. Walter will be all over you that it was indeed Leibniz that invented the calculus first and not Newton. For once I'd actually agree with him ;-) Furthermore, Leibniz's invention of the calculus stemmed from his pure mathematical studies into the "tangent problem."

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I don't want to discuss that in depth, especially not with Walter ;-). To me, Newtons way to solve the problem is much more obvious. It just looks like Leibniz had taken the idea from Newton to make a theory, where other mathmaticians had to fail.

[John B. Smitherman]

Not to throw fuel on the fire... here's an interesting article on the Newton vs Leibniz debate:

Link

Regards,

John

[Thomas Radtke]

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Not to throw fuel on the fire...

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All the fuel has been burned long ago. No new insights here.

[John B. Smitherman]

Don, deep stuff and very interesting.

Here's a link to a book by the same author of the SA article - Mario Livio, "Is God a Mathematician"

Link

and another book by George Lakoff and Raphael Nunez, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being"

Link

Both are interesting reading.

Regards,

John

[David Hayden]

Math is a model of the physical world. The properties of the physical world are definitely discovered, not invented.

The model (math) is both invented and discovered. We invent pieces of it and then discover the various properties that follow from the pieces to keep it consistent. The value "i" is a perfect example. We invented i=SQRT(-1) and huge amount of math followed from this.

[Tommy]

I agree. An other beautiful example is the invention of zero as a placeholder. I think the Olmec people was first, but India often gets credit for this achievement.

[Mark Hardman]

And yet, if we were a species of infinitesimally small beings and lived in a quantum space where the laws of physics that govern the trajectories of cannonballs and planetary orbits no longer applied, I wonder what sort of mathematical framework we would have invented. It certainly would not have been the calculus of Newton and Leibniz.