Why are numbers beautiful?

Re: Why are numbers beautiful?

Postby Guest » Sat Nov 02, 2019 6:13 pm

Hmm. Some Food for Thought:

"The essence of mathematics lies in its freedom.

In mathematics, the art of proposing a question must be held of higher value than solving it.

A set is a Many that allows itself to be thought of as a One
." -- Georg Cantor.


"Chaos is the score upon which reality is written." -- Henry Miller.

"Nothing in Nature is random... A thing appears random only through the incompleteness of our knowledge." -- Spinoza.
Guest
 

Re: Why are numbers beautiful?

Postby Guest » Sat Nov 02, 2019 9:15 pm

Guest wrote:Hmm. Some Food for Thought:

"The essence of mathematics lies in its freedom.

In mathematics, the art of proposing a question must be held of higher value than solving it.

A set is a Many that allows itself to be thought of as a One
." -- Georg Cantor.


"Chaos is the score upon which reality is written." -- Henry Miller.

"Nothing in Nature is random... A thing appears random only through the incompleteness of our knowledge." -- Spinoza.


"The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living." -- Henri Poincaré.
Guest
 

Re: Why are numbers beautiful?

Postby Guest » Thu Nov 07, 2019 2:58 pm

Hmm. Here's some food for thought:

"The development of an organism may [...] be considered as the execution of a 'developmental program' present in the fertilized egg. The cellularity of higher organisms and their common DNA components force us to consider developing organisms as dynamic collections of appropriately programmed finite automata. A central task of developmental biology is to discover the underlying algorithm from the course of development." -- Profs., A. Lindenmayer and G. Rozenberg,

Relevant Reference Links:

'Automata Theory',

https://en.wikipedia.org/wiki/Automata_theory;

'Automata, Languages, Development', by Profs., A. Lindenmayer and G. Rozenberg, 1975;

'Diagram of Intelligence Agent/Network or System',

https://www.researchgate.net/publication/300125399_Diagram_of_Intelligence_Network_or_System.
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Re: Why are numbers beautiful?

Postby Guest » Thu Nov 07, 2019 3:28 pm

Relevant Reference Link:

'Cellular Automaton',

https://en.wikipedia.org/wiki/Cellular_automaton.
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Re: Why are numbers beautiful?

Postby Guest » Thu Nov 21, 2019 10:16 pm

'Math is only beautiful to the initiated, to the people who do it." -- John T. Tate.

Relevant Reference Link:

'John T. Tate, Familiar Name in the World of Numbers, Dies at 94.
Many of his explanations of fundamental ideas now bear his name, a much-honored one among mathematicians.'

https://www.nytimes.com/2019/10/28/science/john-t-tate-dead.html.
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Re: Why are numbers beautiful?

Postby Guest » Sun Nov 24, 2019 3:39 pm

"Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." -- John von Neumann.

Relevant Reference Links:

Wow! 'John von Neumann',

https://en.wikipedia.org/wiki/John_von_Neumann;

Hmm. '38 Great Quotes By John Von Neumann That Will Spark Your Interest In Mathematics',

https://quotes.thefamouspeople.com/john-von-neumann-481.php.
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Re: Why are numbers beautiful?

Postby Guest » Mon Nov 25, 2019 6:38 pm

Hmm. There are theme, variation, scale, complexity, unexpectedness, and of course, beauty in numbers...

'Mandelbrot Set',

https://en.wikipedia.org/wiki/Mandelbrot_set.
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Re: Why are numbers beautiful?

Postby Guest » Tue Dec 03, 2019 9:22 pm

"We will rather be wrong with absolute certainty than to be right with some nagging uncertainty." -- Dave.
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Re: Why are numbers beautiful?

Postby Guest » Tue Dec 03, 2019 9:52 pm

Guest wrote:"We would rather be wrong with absolute certainty than to be right with some nagging uncertainty." -- Dave.
Guest
 

Re: Why are numbers beautiful?

Postby Guest » Sat Dec 07, 2019 1:26 am

Guest wrote:Hmm. Of course, the Riemann Hypothesis (RH) is sound!... Go Blue! :)

And it is okay to agree to disagree about the soundness of RH or its purported proofs. But where is your proof or disproof?

There is a good reference link below on some proofs/disproofs of RH.

We especially enjoy reading those RH proofs involving some wonderful and powerful ideas from physics.

However, mathematicians have developed and refined sufficient and powerful mathematical methods to solve the RH problem without the need of assistance from the wonderful world of physics. Hmm. Do you agree?

Relevant Reference Link:

'proposed (dis)proofs of the Riemann Hypothesis',

http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproofs.htm.


Oops! I was wrong! And I thank very much the late great Albert Einstein for his words of wisdom on simplicity in science.

"Everything should be made as simple as possible, but not simpler." -- Albert Einstein, a great scientist.

Dave.
Guest
 

Re: Why are numbers beautiful?

Postby Guest » Sun Dec 08, 2019 4:55 pm

Guest wrote:
Guest wrote:Hmm. Of course, the Riemann Hypothesis (RH) is sound!... Go Blue! :)

And it is okay to agree to disagree about the soundness of RH or its purported proofs. But where is your proof or disproof?

There is a good reference link below on some proofs/disproofs of RH.

We especially enjoy reading those RH proofs involving some wonderful and powerful ideas from physics.

However, mathematicians have developed and refined sufficient and powerful mathematical methods to solve the RH problem without the need of assistance from the wonderful world of physics. Hmm. Do you agree?

Relevant Reference Link:

'proposed (dis)proofs of the Riemann Hypothesis',

http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/RHproofs.htm.


Oops! I was wrong! And I thank very much the late great Albert Einstein for his words of wisdom on simplicity in science.

"Everything should be made as simple as possible, but not simpler." -- Albert Einstein, a great scientist.

Dave.


RH is true because it is simply the best! ...
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Re: Why are numbers beautiful?

Postby Guest » Tue Dec 10, 2019 12:14 am

With the best choice in hand, the Riemann Hypothesis (Re(z) =1/2), there's no room for exceptions, Re(z) [tex]\ne 1/2[/tex].
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Re: Why are numbers beautiful?

Postby Guest » Sun Dec 29, 2019 10:54 pm

Guest wrote:
Guest wrote:"We would rather be wrong with absolute certainty than to be right with some nagging uncertainty." -- Dave.


"We should always strive be the first to discover our mistakes and to admit them." -- Dave.
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Re: Why are numbers beautiful?

Postby Guest » Sun Dec 29, 2019 10:58 pm

Dave wrote:"We would rather be wrong with absolute certainty than to be right with some nagging uncertainty." -- Dave.


"We should always strive to be the first to discover our mistakes and to admit them." -- Dave.
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Re: Why are numbers beautiful?

Postby Guest » Mon Dec 30, 2019 6:33 pm

"I DO NOT KNOW ...!"
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Re: Why are numbers beautiful?

Postby Guest » Tue Dec 31, 2019 12:30 am

"Math is hard work! And math is also fun! And people who do mathematics with a open mind are always hopeful of the best outcomes."
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Re: Why are numbers beautiful?

Postby Guest » Mon Jan 06, 2020 12:07 am

FYI: 'Pi: The Most Important Number in the Universe?'

https://www.thegreatcoursesdaily.com/the-origins-of-pi/.
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Re: Why are numbers beautiful?

Postby Guest » Mon Jan 06, 2020 12:28 am

FYI: 'Okay, Maybe Proofs Aren't Dying After All.
Experts argue that proofs are doing fine, contrary to a controversial 1993 prediction of their impending demise.
'

https://blogs.scientificamerican.com/cross-check/okay-maybe-proofs-arent-dying-after-all/.
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Re: Why are numbers beautiful?

Postby Guest » Mon Jan 06, 2020 2:08 pm

Guest wrote:FYI: 'Okay, Maybe Proofs Aren't Dying After All.
Experts argue that proofs are doing fine, contrary to a controversial 1993 prediction of their impending demise.
'

https://blogs.scientificamerican.com/cross-check/okay-maybe-proofs-arent-dying-after-all/.


"Another roof, another proof ..." -- Paul Erdös, a great mathematician.

FYI: 'To Prove and To Conjecture: Paul Erdös and His Mathematics',

https://www.jstor.org/stable/2589077?seq=1.
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Re: Why are numbers beautiful?

Postby Guest » Tue Jan 07, 2020 8:08 am

Hmm. 'Why Do We Prove Theorems?' by Prof. Y. Rav.,

http://sgpwe.izt.uam.mx/files/users/uami/ahg/1999_Rav.pdf.

Remarks: It is a long and quite interesting read about why mathematicians prove/disprove conjectures... Enjoy! :D
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