Changes

*[[Henry Ford]]'s mass-production techniques, which turned automobiles from a curiosity into the backbone of American industry despite Ford's lack of formal education.

*[[Henry Ford]]'s mass-production techniques, which turned automobiles from a curiosity into the backbone of American industry despite Ford's lack of formal education.

*the investigation of the [[Challenger Disaster]] by maverick physicist [[Richard Feynman]]

*the investigation of the [[Challenger Disaster]] by maverick physicist [[Richard Feynman]]

*the solution to the greatest unsolved problem of our time, Poincare's conjecture (see below)

*the solution one of the greatest unsolved problem of our time, the [[Poincaré conjecture]] (see below)

*[[Evariste Galois]], an unknown teenager, developed [[group theory]] and it took the mathematical experts a century to appreciate it

*[[Evariste Galois]], an unknown teenager, developed [[group theory]] and it took the mathematical experts a century to appreciate it

*[[Bill Gates]] and [[Steve Jobs]] both chose to eschew the academic confines of college and instead implemented their own ideas in computer software and hardware, eventually creating multi-billion dollar companies.

*[[Bill Gates]] and [[Steve Jobs]] both chose to eschew the academic confines of college and instead implemented their own ideas in computer software and hardware, eventually creating multi-billion dollar companies.

A traditional, expert-dominated inquiry would dismiss the contributions of Student B, since he has not an "expert" - he has not received the official approval of the gatekeepers.  A "best of the public" approach would accept the contributions of both Student A and Student B, since they are both members of the public.  However, it would not place Student A's contributions on a pedestal and make them sacrosanct and immune to questioning.  Student B would be free to bring in HIS expertise as well; as a result, the ensuing discussion would be much less one-sided and more comprehensive, and thus far more likely to result in accurate and truthful insights.  Perhaps many ideas coming from people like Student B would be wrong, unprofitable, and therefore rightly rejected; the "best of the public" approach recognizes that not all ideas from the public are better than those of experts. However, it is very likely that some ideas from people like Student B will be true and helpful.  This is the difference between the two approaches:  such ideas will be heard under the "best of the public" method.

A traditional, expert-dominated inquiry would dismiss the contributions of Student B, since he has not an "expert" - he has not received the official approval of the gatekeepers.  A "best of the public" approach would accept the contributions of both Student A and Student B, since they are both members of the public.  However, it would not place Student A's contributions on a pedestal and make them sacrosanct and immune to questioning.  Student B would be free to bring in HIS expertise as well; as a result, the ensuing discussion would be much less one-sided and more comprehensive, and thus far more likely to result in accurate and truthful insights.  Perhaps many ideas coming from people like Student B would be wrong, unprofitable, and therefore rightly rejected; the "best of the public" approach recognizes that not all ideas from the public are better than those of experts. However, it is very likely that some ideas from people like Student B will be true and helpful.  This is the difference between the two approaches:  such ideas will be heard under the "best of the public" method.

== Solution to Poincare's Conjecture ==

== Solution of the Poincaré Conjecture ==

The solution to the [[Poincare's conjecture]], one of the greatest unsolved math problems of the 20th century, was by the little-known Grigory Perelman who worked on his own and merely posted his solution on the internet.  He had never been offered a permanent job and was critical of the lack of openness among mathematical experts as he described a rare exception:<ref>[http://www.notablebiographies.com/supp/Supplement-Mi-So/Perelman-Grigory.html Grigory Perelman Biography (emphasis added)], Encyclopedia of World Biography.</ref>   

The solution to the [[Poincaré conjecture]], one of the greatest unsolved math problems of the 20th century, was by the little-known Grigory Perelman who worked on his own and merely posted his solution on the internet.  He had never been offered a permanent job and was critical of the lack of openness among mathematical experts as he described a rare exception:<ref>[http://www.notablebiographies.com/supp/Supplement-Mi-So/Perelman-Grigory.html Grigory Perelman Biography (emphasis added)], Encyclopedia of World Biography.</ref>   

{{cquote|He actually told me a couple of things that he published a few years later. He did not hesitate to tell me. Hamilton's openness and generosity—it really attracted me. '''I can't say that most mathematicians act like that'''.}}

{{cquote|He actually told me a couple of things that he published a few years later. He did not hesitate to tell me. Hamilton's openness and generosity—it really attracted me. '''I can't say that most mathematicians act like that'''.}}

At great monetary sacrifice, Perelman refused to accept the awards conferred on him by experts after they eventually recognized the brilliance of his proof.  A leading expert was accused of improperly trying to take credit for Perelman's work.

At great monetary sacrifice, Perelman refused to accept the awards conferred on him by experts after they eventually recognized the brilliance of his proof.  A leading expert was accused of improperly trying to take credit for Perelman's work.