parallels of finite-number versus infinite-number and direct vs. indirect Euclid IP #4.07 Correcting Math
in [Math]
|
Prev: can we expect logical answers from math journal editors? #4.06 Correcting Math
Next: DECLARED ASSERTION TO THE BEST MATHEMATICIAN OF CURRENT MATHEMATICS--DR EDGAR ESCULTURA PHD, U.W MADISON ,1 and 0.999 a final resolution
From: Archimedes Plutonium on 22 Jul 2010 17:45 We can use the Fall, 2009 Mathematical Intelligencer article Prime Simplicity to showcase how slow the math community operates. The reason Twin Prime Infinitude was never proven is because of a fault or error in doing the Euclid proof via Indirect. That no-one could see that P-1 and P+1 are necessarily new primes in the Indirect Method. So when no-one could do a proper Indirect Euclid IP, well, Twin Primes will remain unproven. It was pointed out to the Logic journal editor at Notre Dame University in the early 1990s that a Twin Primes proof exists the moment that the error in Indirect is corrected. The lady editor dismissed my claim and proof of the Infinitude of Twin Primes telling me that, much like Chandler Davis with Mathematical Intelligencer, telling me that Euclid's proof was a closed, ended proof. So here we have two historical math references, one of the ill-defined finite-number concept. It has been assumed as long as mathematics was around, that finite-number was understood by all and that no-one needed to formally define what finite-number meant. So that when Wiles chased after FLT in the 1990s, he just assumed like everyone else what finite-number meant and that his use of p-adics in his offerings were not finite-numbers. Peano axioms never defines finite versus infinite number. I should not say that the concept of finite-number versus infinite- number was ill-defined. For it was not even given a initial definition. There were no definitions and it was left up to every individual person to "think what is a finite number." In the case of Euclid's Infinitude of Primes proof IP, there was the problem of mixing up methods of Direct and Indirect. To the point where everyone was doing the same proof steps and calling it willy nilly either direct or indirect. The parallels of these two case studies of finite number and Euclid's IP is that conjectures remain open so long as concepts are ill defined. To define finite number versus infinite number you need to have a boundary number that says 10^500 is the boundary between finite and infinite. Then conjectures like FLT or Riemann Hypothesis have proofs, otherwise they are never proveable. In the case of Euclid's IP, if you leave the Indirect method in a mess, then you cannot prove the Twin Primes conjecture and slews of other conjectures about infinite set of primes. And here it is clear why math is the slowest moving of the sciences. Math needs judgement calls to tell if correct or wrong. Those judgement calls are often faulty and erroneous. Whereas physics, chemistry, biology never need judgement calls to arrive at truth, because it is experiment driven that decides on truth or falsity. Math is still doing Ancient Greek problems of Twin Primes, whereas physics, chemistry, biology have no ancient Greek questions open on their subject. The slowness of math is seen by the fact that I published on sci.math the Twin Primes proof by 1993-1994 and showed the correction to Euclid's IP Indirect, yet by 2009 some 15 years later in a math magazine, Mathematical Intelligencer, we still see flawed Euclid Indirect IP claims. If physics moves at the speed of a jet airplane, then math moves at the speed of a crawling snail. And the reason is that math does not have experiment as its arbiter. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |