Let’s admit it, most of us are intellectually lazy, and thinking is a strange and hard activity, because it requires effort. Even philosophy, the prime discipline devoted to thinking, mostly circulates the ideas of other people, and has some similarity to journalism. Real thinking is hard, and I will always respect Kant for the simple advice he gave to […]

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If you add up all the natural numbers from 1 to infinity, you should get a really large version of infinity, but this is not the case. What you get is  minus one/twelfth. Watch the following well-made video clip in order to understand how this happens. Related posts: Fundamental Theorem of Arithmetic Nature by Numbers […]

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“There are two approaches to mathematical infinity. It can be seen as defining limiting cases that can never be realized or as existing in some philosophical sense. These mathematical approaches parallel approaches to meaning and value that I call absolutist and evolutionary. The absolutist sees ultimate meaning as something that exists most commonly in the form of an all powerful infinite God. The evolutionary sees life and all of a creation as an ever expanding journey with no ultimate or final goal. There is only the journey. There is no destination. This video argues for an evolutionary view in our sense of meaning and values and in our mathematical understanding. There is a deep connection between the two with profound implications for the evolution of consciousness and human destiny.” (Paul Budnik)

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The Clay Institute offers a prize to anyone who can solve one of these Millenium problems.  Here is a description of the problems from the Institute’s website: Birch and Swinnerton-Dyer Conjecture Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like x2 + y2 = z2 Euclid […]

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This explanation is quoted from the  The Clay Mathematics Institute, Poincaré Conjecture. (solved by: Grigoriy Perelman, 2002-3) “If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the […]

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Here are some unsolved mathematical problems: Goldbach’s conjecture: Can every even integer greater than 2 be written as a sum of two primes? Twin Prime Conjecture: A twin prime is a pair of primes with difference 2, such as 11 and 13. Are there infinitely many twin primes? Does the Fibonacci sequence contain an infinite […]

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