Newton's Calculus: Numerical Methods or a New Math?

[daniel_i_l]

When Newton wanted math to express his physics he invented calculus (i'm not trying to be totally historically correct - this isn't my main point). It seems like today we're in a similar position - there're lots of things that simply can't be exactly solved. are numerical methods the next step? or is there a chance that someday we'll come up with a new kind of math that can let us solve problems that are insolvable today?

 

[Moridin]

Well, that is kind of the point of science. Remember http://www.foxnews.com/story/0,2933,209757,00.html?

 

[ranger]

Could physics be said to be the main driving force to new mathematical developments?

 

[Moridin]

Since mathematics can be said to be a tool for problem solving in physics and science in general, sure, why not.

 

[matt grime]

Because most of the last 100 years of mathematics has developed without any impetus from physics, perhaps? Indeed, some of the more fashionable areas of physics are learning from maths, and not vice versa.

 

[Crosson]

Since mathematics can be said to be a tool for problem solving in physics and science in general

I doubt you will find any mathematician who agrees with this statement!

 

[theperthvan]

Prob and stats has kinda been 'invented' (or developed a lot) over the last century and a bit.

 

[Werg22]

I don't see where math can still make significant progress... then again I would have said the same thing if I lived 300 years ago, so who knows.

 

[d_leet]

I don't see where math can still make significant progress... then again I would have said the same thing if I lived 300 years ago, so who knows.

I would think that when there are still many unsolved problems, and undoubtedly many others yet to be discovered, that there are plenty of places that allow for significant progress in mathematics.

 

[Gib Z]

Rofl this reminds me of a hilarious teacher i have, on his homework sheets he has :If gifted students are not feeling challenged enough, try proving/disproving the countability of the real numbers, or one perhaps the Riemann hypothesis" Nice

 

[Gib Z]

O yes let me just say I am not 100% sure, but the last time a physicist "invented" math for physics solely, was back in 1923 with Werner Heisenbergs Matrix mechanics. Sadly, he didnt know matrices were already invented >.< Since then, any physics calling for mathematics has been either satisfied by known methods, or merely extended in ways that a mathematician would have had no interest for anyway, and if they did they would have bothered to.

 

[Born2Perform]

maths may advance in depth rather than in extension

 

[Doodle Bob]

O yes let me just say I am not 100% sure, but the last time a physicist "invented" math for physics solely, was back in 1923 with Werner Heisenbergs Matrix mechanics. Sadly, he didnt know matrices were already invented >.< Since then, any physics calling for mathematics has been either satisfied by known methods, or merely extended in ways that a mathematician would have had no interest for anyway, and if they did they would have bothered to.

Well... there are some recent cases of physicists certainly significantly augmenting certain topics of mathematics, if not quite inventing whole new "paradigms."

I'm thinking of Penrose's twistor theory, which began in the late 60's, as an attempt to start unifying QT and GR, but was soon grabbed hold by many geometers as a way to help understand 4-dimensional manifolds.

Similarly, I believe that Witten both helped develop the Seiberg-Witten equations (another method to grapple with 4-manifolds) and accidentally reinvented K-Theory for purely physics-related reasons.

Plus, spin networks from quantum theory have helped guide the progress of some areas of discrete geometry. And string theory has certainly put certain very abstruse mathematical ideas back on the collective map.

Granted, though, most of the above work seems to originate from the mathematical physics end of things *and* none of them have as yet had the same paradigmatic impact that Newton's and Leibniz's calculi had.

 

[matt grime]

Are penrose and witten really physicists though? In the words of McKay (roughly) the distinction between applied and pure is a sham.

 

[Doodle Bob]

Are penrose and witten really physicists though? In the words of McKay (roughly) the distinction between applied and pure is a sham.

Well, that's not really my call, since I am a mathematician. If you don't want them in your camp, we'll take 'em.

 

[matt grime]

And what makes you think I'm not a mathematician (follow the link in my signature to my homepage)?

 

[Gib Z]

matt grimes a mathematician btw Doodle.

I would say the are physicists, and they say it themselves. It is because, in their view, the use their "tool" of mathematics for the sole purpose of explaining physical phenomenon. In their view, if they advance their tools they can advance their work. A pure mathematician does it purely for the beauty of the mathematics. If it has an application, good for the physicists, but the pure mathematician won't give a damn.

 

[Gib Z]

O sorry I didn't read matts last post, it was on the 2nd page >.< well yea, now you know he's a mathematician.