Monthly Archives: January 2013

It’s undecidable!!!

A conditional sentence is constructed in a statement formed like “if (hypothesis), then (conclusion)”
Nerdy Notation:
If (statement H), then (statement C)
Can also be written as: H => C
This symbol => in mathematics means implies
For example: (f(x) differentiable) => (f(x) is continuous)

“To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession.” – Blaise Pascal

“To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession.” – Blaise Pascal
In this quotation Pascal expresses his reserved love and gratitude towards mathematics. I find it interesting that Pascal compared his profession, mathematician, to a common artisan as if they are related. I have to admit that I struggled to understand the meaning beneath this quotation. I do not know if Pascal is trying to downgrade mathematics or if he trying to compares math’s beauty to art. In conclusion I would have to ponder this quotation further to gain more understanding. I will probably try to revisit this quotation towards the end of the year to see if I gained any new knowledge that will help me decipher this quotation.

“God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved.”—Hermann Klaus Hugo Weyl

“God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved.”—Hermann Klaus Hugo Weyl
In this quotation Weyl linked religion with mathematics, and by doing this he ultimately gave an improvable argument. God, seen as all mighty and good, is compared to the consistency on mathematics. This comparison expresses Weyl’s positive outlook of the consistency of math. On the other hand, the devil, seen as an evil figure, is compared to the incapability of proving math’s consistency. Although we believe math is consistent there is no way to prove its consistency, thus the conundrum at hand.

“We are servants rather than masters in mathematics.” –Charles Hermite

“We are servants rather than masters in mathematics.” –Charles Hermite

It is to my understanding that Charles Hermite expresses the idea that mathematics is not something we accomplish, but rather math leads us in different directions.  By this I mean we can understand and comprehend mathematics, but yet math still is dominant foundation.  Charles Hermite was the first to prove that e is a transcendental number, which aided the discovery π being a transcendental number as well. I think Hermite’s discovery brought him to this conclusion, “ we are servants rather than masters in mathematics,” because he learned that mathematics holds no boundaries and that we, as humans, are at the mercy of math’s indefinable limits.

“The product of mathematics is clarity and understanding. … The real satisfaction from mathematics is in learning from others and sharing with others.” – William Thurston

“The product of mathematics is clarity and understanding. … The real satisfaction from mathematics is in learning from others and sharing with others.” – William Thurston

This quotation expresses the idea that mathematics is something that should be shared and interrupted together. Also by sharing and learning with others one can gain further knowledge about the mathematics in which he or she didn’t observe individually. I think this quotation directly correlates with this class, foundation of mathematics. As a class, we are to learn from each other and to further our understanding not only as individuals, but as a unified group.  The blog, assignment, and participation that go towards our grade should be a group effort. If every individual in our class helps each other positively then ultimately we should all come out of FOM with a good grade.

The Goldbach Conjecture

The Goldbach Conjecture was first discovered in a letter written to Euler in 1742 and has not yet been able to proved. The Goldbach Conjecture states that every even integer  n  greater than two is the sum of two primes.  Also written as two primes such that (p,q)  p+q=2n if and only if n > 2.

 

 

“Mathematics is a game played according to certain simple rules with meaningless marks on paper.” ~ David Hilbert

I would have to agree with the quotation presented. I think David Hilbert’s point is that math is not discovered on paper that  hold’s limitations and mistakes, but rather through the mind.  Through my own mathematical experiences my thoughts on this quotation stand. For example,  I am one to over analyze and exaggerate a math problem, but in accordance to the quotation (which I should know  by now) a math problem can be broken down and simplified.  Math has very simple rules that have been embedded in us since elementary school and the addition of new mathematical theories are just meaning marks on paper without that foundation.

“Mathematics is a game played according to certain simple rules with meaningless marks on paper.” ~ David Hilbert