[js1138]

"If experimental discoveries indeed flood in faster than they can be proved, could that change the very nature of mathematics? In their book Mathematics by Experiment (2003, A K Peters), Bailey and Jonathan Borwein advance the controversial thesis that mathematics should move toward a more empirical approach. In it, formal proof would not be the only acceptable way to establish mathematical knowledge."

[js1138]

ping

[js1138]

ping

[js1138]

ping

[Southack]

Wait until they figure out how such results have been and are being applied to simplifying the breaking of encryption algorythms!

[Dr. Faust]

I recall my excitement when I first applied Lotus 123 to the solution of some problems in chemical kinetics using linear differential equations.

It was only later that I discovered physicists had been doing the same thing from the time the program was developed!

Oh brave new world---

[krb]

Over the centuries, mathematicians have found many amazingly simple ways to express pi as an infinite sum, for instance, 1 – 1/3 + 1/5 – 1/7 + 1/9 . . . .

I don't see how that's a formula for pi.

[longshadow]

In it, formal proof would not be the only acceptable way to establish mathematical knowledge."

Slippery slope (no pun intended), IMHO.

[RightWingAtheist]

I wrote a review for the movie Colossus: The Forbin Project, in which I tut-tutted the film makers for assuming that a computer could formulate a new theory of gravity all by itself. Looks like I'll have to revise it again.

[Rocky]

The answer is 42. Now, what's the question?

[Constantine XIII]

bump!

[Boot Hill]

Author Erica Klarreich,

•"Over the centuries, mathematicians have found many amazingly simple ways to express pi as an infinite sum, for instance, 1 – 1/3 + 1/5 – 1/7 + 1/9 ..."

That series will give you pi?   (cough)...Ummm, I think you'd better go give that whiz-bang computer of yours a good solid kick in the processor.

That series produces one-quarter pi, and worse, even after running the series out to 1,000 terms (whew!), you'll only know pi to within 300 ppm. That's a heck of a lot of work for very little result.

There is a much cleaner series to use calculate pi...

pi = 2x – x³/3! + x⁵/5! – x⁷/7! + . . .

Where "x" is a seed value. Try starting with 3. To get very high precision, run the series through once and use the resulting value of pi as the seed value ("x") for a second run through the same series. The series only needs to be run out to 10 terms (x²¹/21!) to achieve an accuracy in excess of 1 part per trillion.

Those that can still recall their trigonometric series will recognize the above algorithm (except for the 2 in the first term) as the series used to calculate sin x (where x is in radians).

--Boot Hill

[guitfiddlist]

"Ladies!...Gentlemen!....PI IS EXACTLY THREE!!....I'm sorry it came to that...but I had to get your attention."

[Shryke]

Fascinating article, but....

Computer power, Borwein says, is enabling mathematicians to make a quantum leap

The journalist needs to be taken outside and forced to say "irregardless","libary", and "supposably" until he passes out. On a lighter note, I can now tell everyone to keep their IT requests to themselves, as my brain is full.

[monkey]

Thanks for this interesting post.

[aruanan]

"There's no way we would have been led to these results without the computer," Adams says. SnapPea has become an indispensable tool for studying shapes with hyperbolic geometry, he adds.

Knotty but nice.

[<1/1,000,000th%]

Computer power, Borwein says, is enabling mathematicians to make a quantum leap akin to the one that took place when Leonardo of Pisa introduced Arabic numerals—1, 2, 3, . . .—to European mathematicians in the 12th century.

There are no Arabic numerals.

One of the important sources of information which we have about Indian numerals comes from al-Biruni. During the 1020s al-Biruni made several visits to India. Before he went there al-Biruni already knew of Indian astronomy and mathematics from Arabic translations of some Sanskrit texts.

[Condorman]

"These patterns just pop out at you that you have no explanation for, and then slowly you explain what you see."

Of what does this remind you? Anyone? Anyone?