Utility of integer factorization.

jwaltos · 2015-05-13, 16:40

Other than the obvious, RSA and P:NP, how would the ability to factor integers of any magnitude affect the sciences?
A natural extension includes factors such as complex (Gaussian) primes and quotients.
Will such a tool provide deeper insight into the results of numerical calculations, fundamental physical or mathematical constants?
PSLQ has provided insight into some structures and Plouffe (unsuccessfully as far as I am aware) attempted the same for some physical constants. (Regarding constants, Steven Finch's expositions are a good complementary reference.) The work of Mandelbrot and Thom has helped to conceptualize order from apparent disorder and I was wondering if `reversing the multiplicative process (a solid notion of primality is crucial)` would have a similar effect. Mandelbrot's, "The Fractalist", is a bargain in paperback and for those with some time, any of the books in the "Library of Living Philosophers" are worth [the] while. As usual, Google and Wikipedia will point and introduce the sources but will not replace them. Rational creativity, I guess, would be a way of encapsulating the above.
Looking at "Wired's" review of Mandelbrot's memoir, this point is a carry-over from prior thread, "... Mandelbrot was a brilliant idealist who struggled with the gap between thought and language..." which may be
considered as an aspect of the S-W hypothese.

Nick · 2015-05-16, 22:18

Hendrik Lenstra jokingly encourages his students to solve such problems so that number theory will lose its value to cryptography and commercial companies and return to being an area of research where you only meet people who are passionate about the mathematics for its own sake.

LaurV · 2015-05-17, 05:17

Quote:

Originally Posted by Nick

... an area of research where you only meet people who are passionate about the mathematics for its own sake.

i.e. mersenneforum...

R.D. Silverman · 2015-05-17, 05:41

Quote:

Originally Posted by LaurV

i.e. mersenneforum...

Bull. The vast majority of people here do not care one whit about the math.

xilman · 2015-05-17, 07:13

Quote:

Originally Posted by R.D. Silverman

Bull. The vast majority of people here do not care one whit about the math.

Bob: I seriously recommend that you get your irony detector serviced as it appears to have gone very badly out of calibration.

ATH · 2015-05-17, 13:49

Quote:

Originally Posted by xilman

Bob: I seriously recommend that you get your irony detector serviced as it appears to have gone very badly out of calibration.

R.D. Silverman · 2015-05-21, 16:25

Quote:

Originally Posted by xilman

Bob: I seriously recommend that you get your irony detector serviced as it appears to have gone very badly out of calibration.

Not based upon the person who made the comment. LaurV is constantly making erroneous and ignorant
comments. He just made another one about factors of Fermat numbers.

LaurV · 2015-05-22, 02:14

Quote:

Originally Posted by R.D. Silverman

Not based upon the person who made the comment. LaurV is constantly making erroneous and ignorant
comments. He just made another one about factors of Fermat numbers.

Huh? Where?

jwaltos · 2015-05-22, 12:20

FFT improvement, quantum wave functions, commutative and non-commutative representations...etc.

2015-05-13, 16:40	#1
jwaltos Apr 2012 2³×3²×5 Posts	Utility of integer factorization. Other than the obvious, RSA and P:NP, how would the ability to factor integers of any magnitude affect the sciences? A natural extension includes factors such as complex (Gaussian) primes and quotients. Will such a tool provide deeper insight into the results of numerical calculations, fundamental physical or mathematical constants? PSLQ has provided insight into some structures and Plouffe (unsuccessfully as far as I am aware) attempted the same for some physical constants. (Regarding constants, Steven Finch's expositions are a good complementary reference.) The work of Mandelbrot and Thom has helped to conceptualize order from apparent disorder and I was wondering if `reversing the multiplicative process (a solid notion of primality is crucial)` would have a similar effect. Mandelbrot's, "The Fractalist", is a bargain in paperback and for those with some time, any of the books in the "Library of Living Philosophers" are worth [the] while. As usual, Google and Wikipedia will point and introduce the sources but will not replace them. Rational creativity, I guess, would be a way of encapsulating the above. Looking at "Wired's" review of Mandelbrot's memoir, this point is a carry-over from prior thread, "... Mandelbrot was a brilliant idealist who struggled with the gap between thought and language..." which may be considered as an aspect of the S-W hypothese. Last fiddled with by jwaltos on 2015-05-13 at 16:56 Reason: corrections

2015-05-22, 12:20	#9
jwaltos Apr 2012 101101000₂ Posts	Aspects of factorization. FFT improvement, quantum wave functions, commutative and non-commutative representations...etc. Last fiddled with by jwaltos on 2015-05-22 at 12:37

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2015-05-16, 22:18	#2
Nick Dec 2012 The Netherlands 3053₈ Posts	Hendrik Lenstra jokingly encourages his students to solve such problems so that number theory will lose its value to cryptography and commercial companies and return to being an area of research where you only meet people who are passionate about the mathematics for its own sake.