Answer each question with a minimum of 70 words per question: In mathematics, there are situations...

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Answer each question with a minimum of 70 words per question:

In mathematics, there are situations where a statement has not yet been proven or disproven. These statements are called conjectures. A famous example is Goldbach’s conjecture which states that every even integer greater then 2 can be written as the sum of two primes. Research and report on why the proof or disproof of Goldbach’s conjecture is so elusive. Give another example of a conjecture (different from the ones given by your peers in this class) whose proof or disproof has yet to be found.

Research and comment on George’s Polya’s “No Horse of a Different Color”. What is his “proof”? How was this idea considered in its day? Why is his analysis incorrect?

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Answer each question with a minimum of 70 words per question: In mathematics, there are situations where a statement has not yet been proven or disproven. These statements are called conjectures. A famous example is Goldbach’s conjecture which states that every even integer greater then 2 can be written as the sum of two primes. Research and report on why the proof or disproof of Goldbach’s conjecture is so elusive. Give another example of a conjecture (different from the ones given by your peers in this class) whose proof or disproof has yet to be found. Research and comment on George’s Polya’s “No Horse of a Different Color”. What is his “proof”? How was this idea considered in its day? Why is his analysis incorrect?

Answer each question with a minimum of 70 words per question: 1) In mathematics, there are situations where a statement has not yet been proven or disproven. These statements are called conjectures. A famous example is Goldbach’s conjecture which states that every even integer greater then 2 can be written as the sum of two primes. Research and report on why the proof or disproof of Goldbach’s conjecture is so elusive. Give another example of a conjecture (different from the ones given by your peers in this class) whose proof or disproof has yet to be found. 2) Research and comment on George’s Polya’s “No Horse of a Different Color”. What is his “proof”? How was this idea considered in its day? Why is his analysis incorrect?

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David · Accepted Answer

Goldbach’s conjecture :  Every even integer greater then 2 can be written as 
a sum of two prime numbers .   
                         N = p1 + p2           ;     N = even integer greater 
then 2  ,   p1,p2  are prime numbers  
One simple way to disprove this theorem is to produce a counter example . but 
the proof or the proper method to disprove is quite tough . 
The no. of solution for different ways in which we can write N as a sum of 
two prime numbers grows with N in a very irregular manner . 
For ex  :    if n = 180 , there are 28 different ways of writing 180 as a sum 
of two prime numbers .while if n = 182 , there are only 12 ways of writing n 
as a sum of two prime numbers . 
Since n increases , no of primes smaller to n increases which in turn 
increases no of different ways in which n can be written as a sum of two 
different primes . but we can not put an absolute limit on largest prime 
number .

Answer each question with a minimum of 70 words per question: In mathematics, there are situations where a statement has not yet been proven or disproven. These statements are called conjectures. A...

Answer To: Answer each question with a minimum of 70 words per question: In mathematics, there are situations...

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