Exploring the Evolution of Mathematics: What's Next for Understanding the World?

[sbmarantz]

Hello,

I work in architecture, and so math and physics is pretty fundamental. However, I'm not here for basic engineering. Architecture and I think math in general is going through a transition of how we understand things.

What do I mean by that?

Example:

Think of the pythagorean theorem, described and plotted as you understand it.

Now realize that co-ordinate graphs were invented by Descartes.

Recall that the muslims invented variable-based algebraic expressions.

And realize that this theorem was articulated by Euclid, who knew of neither co-ordinates, nor algebraic equations.

So that begs the question: what needs to be developed now for us to understand things better and more clearly? Math changes, the world changes, yet many of the things we investigate remain constant. That is my primary focus within this forum. Thank you all for the support and insight.

 

[Greg Bernhardt]

Welcome to PF! Please ask your questions in the other forums, thanks!

 

[Mark44]

Think of the pythagorean theorem, described and plotted as you understand it.
Now realize that co-ordinate graphs were invented by Descartes.
Recall that the muslims invented variable-based algebraic expressions.
And realize that this theorem was articulated by Euclid, who knew of neither co-ordinates, nor algebraic equations.
So that begs the question: what needs to be developed now for us to understand things better and more clearly?

I'm not sure what your point is. The geometry of Pythagoras was about 2500 years ago, and the algebra of al-Khwarizmi goes back about 1200 years.

Math changes, the world changes, yet many of the things we investigate remain constant.

What areas of mathematics have seen fundamental changes lately?

 

[rootone]

Math is a good way of describing stuff in a way that everyone can agree on, but it doesn't change what the stuff is.
Welcome to PF

 

[sbmarantz]

Hi Mark, the timeline you state is exactly my point. The fact that Pythagoras developed a theorem that did not get the "clothes" we know it by today until more than a thousand years later demonstrates that human culture's idea of what "number" itself is can radically change over time. For an in-depth elucidation of that idea take a look at the early chapters of Oswald Spengler's "Decline of the West."

And as far as evidence of our concept of math changing lately, well … examples abound. Newton was convinced of space as an absolute, Einstein amended that. I remember attending a talk given by physicist Brian Greene where he stated that all the current research being poured into the endless math on string theory is a symptom of our current shapes of math simply not being commensurate to the task of description of quantum mechanics. The last time this kind of shift happened was right before the discovery of calculus. The area of an ellipse was approximated by dividing it into n-number of triangles. The higher up n goes, the higher the precision. Calculus saved a lot of headaches, and interplanetary telemetry would simply be unworkable without that shift.

And that is not even to mention the (once heretical) non-euclidean geometry and fractional dimensions described in chaos theory.

There is a new paradigm waiting to be discovered. And it is common to not see that point before the discovery manifests itself. Yet as culture historically develops, all the work that all of us do adds to the eventual presentation of it.

I'm not sure what your point is. The geometry of Pythagoras was about 2500 years ago, and the algebra of al-Khwarizmi goes back about 1200 years.
What areas of mathematics have seen fundamental changes lately?

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

Hi @sbmarantz and Welcome to the PF.

Please start a new thread in the General Math forum if you would like to discuss these issues. That thread may end up getting moved to the General Discussion forum, depending on how technical it is. This Introduction thread here will remain closed.

Thanks!