Why are numbers beautiful?

[Guest]

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]

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]

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.

[Guest]

Relevant Reference Link:

'Cellular Automaton',

https://en.wikipedia.org/wiki/Cellular_automaton.

[Guest]

'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.

[Guest]

"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.

[Guest]

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

'Mandelbrot Set',

https://en.wikipedia.org/wiki/Mandelbrot_set.

[Guest]

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

[Guest]

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

[Guest]

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]

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! ...

[Guest]

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].

[Guest]

"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.

[Guest]

"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.

[Guest]

"I DO NOT KNOW ...!"

[Guest]

"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."

[Guest]

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

https://www.thegreatcoursesdaily.com/the-origins-of-pi/.

[Guest]

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/.

[Guest]

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.

[Guest]

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!