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• $\text{Blackboard Bold Symbols}:$

$\mathbb{N}:~\text{The set of natural numbers}$

$\mathbb{Z}:~\text{The set of integers}$

$\mathbb{Z}_n:~\text{The cyclic group modulo}~n$

$\mathbb{Q}:~\text{The set of rationals}$

$\mathbb{J}:~\text{The set of irrationals}~(\mathbb{Q}\cup\mathbb{J}=\mathbb{R})$

$\mathbb{R}:~\text{The set of real numbers}$

$\mathbb{R}^n:~\text{The}~n\text{th dimension real coordinate system}$

$\mathbb{C}:~\text{The set of complex numbers}~(\mathbb{R}\cap\mathbb{C}=\varnothing)$

$\mathbb{H}:~\text{The set of quaternions}$

$\mathbb{O}:~\text{The set of octonions}$

$\mathbb{D}_f:~\text{The domain of a function}~f$

• $\text{Toeplitz Conjecture}:$

$\text{Let}~J~\text{be the set of all Jordan curves and let}~j_k~\text{be an arbitrary element of}~J.\text{ Show that}$

$\text{there exists four points}~p_1,p_2,p_3,p_4~\text{on}~j_k~\text{such that}~p_1,p_2,p_3,p_4~\text{form the vertices of a}$

$\text{square}.$

$\text{Riemann Hypothesis}:$

$\text{Show that all non-trivial zeroes}~s~\text{of the Riemann zeta function}$

$\zeta(z)=\sum_{n=1}^{\infty}\frac{1}{n^z}$

$\text{satisfy}~\Re(s)=\frac{1}{2}$

$\text{Goldbach's Conjecture}:$

$\text{Show that, for all even natural numbers}~n~\text{there exists two primes}~p_1,p_2~\text{satisfying}$

$p_1+p_2=n$

$\text{Erdos - Strauss Conjecture}:$

$\text{Show that}~\exists{a,b,c}~\text{to the Diophantine equation}~\frac{4}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$

$\text{for all}~n\in\mathbb{N}$

• A Dream Within A Dream - Edgar Allen Poe

Take this kiss upon the brow!
And, in parting from you now,
Thus much let me avow-
You are not wrong, who deem
That my days have been a dream;
Yet if hope has flown away
In a night, or in a day,
In a vision, or in none,
Is it therefore the less gone?
All that we see or seem
Is but a dream within a dream.

I stand amid the roar
Of a surf-tormented shore,
And I hold within my hand
Grains of the golden sand-
How few! Yet how they creep
Through my fingers to the deep,
While I weep- while I weep!
O God! Can I not grasp
Them with a tighter clasp?
O God! Can I not save
One from the pitiless wave?
Is all that we see or seem
But a dream within a dream?

“A weapon based on Time . . ." mused Viktor Mulciber. "Well, why not? The one force no one knows how to defeat, resist, or reverse. It kills all forms of life sooner or later. With a Time-weapon you could become the most feared person in history."
"I'd rather be loved," said Root.
Mulciber shrugged. "You're young.”

- Thomas Pynchon, from Against the Day

“The rest of us, not chosen for enlightenment, left on the outside of Earth, at the mercy of a Gravity we have only begun to learn how to detect and measure, must go on blundering inside our front-brain faith in Kute Korrespondences, hoping that for each psi-synthetic taken from Earth's soul there is a molecule, secular, more or less ordinary and named, over here - kicking endlessly among the plastic trivia, finding in each Deeper Significance and trying to string them all together like terms of a power series hoping to zero in on the tremendous and secret Function whose name, like the permuted names of God, cannot be spoken... plastic saxophone reed sounds of unnatural timbre, shampoo bottle ego-image, Cracker Jack prize one-shot amusement, home appliance casing fairing for winds of cognition, baby bottles tranquilization, meat packages disguise of slaughter, dry-cleaning bags infant strangulation, garden hoses feeding endlessly the desert... but to bring them together, in their slick persistence and our preterition... to make sense out of, to find the meanest sharp sliver of truth in so much replication, so much waste...

- Thomas Pynchon, from Gravity's Rainbow

Heiligenstãdter Testament - Ludwig van Beethoven

O ye men who think or say that I am malevolent, stubborn or misanthropic, how greatly do ye wrong me, you do not know the secret causes of my seeming, from childhood my heart and mind were disposed to the gentle feelings of good will, I was even ever eager to accomplish great deeds, but reflect now that for six years I have been a hopeless case, aggravated by senseless physicians, cheated year after year in the hope of improvement, finally compelled to face the prospect of a lasting malady (whose cure will take years or, perhaps, be impossible), born with an ardent and lively temperament, even susceptible to the diversions of society, I was compelled early to isolate myself, to live in loneliness, when I at times tried to forget all this, O how harshly was I repulsed by the doubly sad experience of my bad hearing, and yet it was impossible for me to say to men speak louder, shout, for I am deaf. Ah how could I possibly admit such an infirmity in the one sense which should have been more perfect in me than in others, a sense which I once possessed in highest perfection, a perfection such as few surely in my profession enjoy or have enjoyed - O I cannot do it, therefore forgive me when you see me draw back when I would gladly mingle with you, my misfortune is doubly painful because it must lead to my being misunderstood, for me there can be no recreations in society of my fellows, refined intercourse, mutual exchange of thought, only just as little as the greatest needs command may I mix with society. I must live like an exile, if I approach near to people a hot terror seizes upon me, a fear that I may be subjected to the danger of letting my condition be observed - thus it has been during the past year which I spent in the country, commanded by my intelligent physician to spare my hearing as much as possible, in this almost meeting my natural disposition, although I sometimes ran counter to it yielding to my inclination for society, but what a humiliation when one stood beside me and heard a flute in the distance and I heard nothing, or someone heard the shepherd singing and again I heard nothing, such incidents brought me to the verge of despair, but little more and I would have put an end to my life - only art it was that withheld me, ah it seemed impossible to leave the world until I had produced all that I felt called upon me to produce, and so I endured this wretched existence - truly wretched, an excitable body which a sudden change can throw from the best into the worst state - Patience - it is said that I must now choose for my guide, I have done so, I hope my determination will remain firm to endure until it please the inexorable parcae to bread the thread, perhaps I shall get better, perhaps not, I am prepared. Forced already in my 28th year to become a philosopher, O it is not easy, less easy for the artist than for anyone else - Divine One thou lookest into my inmost soul, thou knowest it, thou knowest that love of man and desire to do good live therein. O men, when some day you read these words, reflect that ye did me wrong and let the unfortunate one comfort himself and find one of his kind who despite all obstacles of nature yet did all that was in his power to be accepted among worthy artists and men. You my brothers Carl and [Johann] as soon as I am dead if Dr. Schmid is still alive ask him in my name to describe my malady and attach this document to the history of my illness so that so far as possible at least the world may become reconciled with me after my death. At the same time I declare you two to be the heirs to my small fortune (if so it can be called), divide it fairly, bear with and help each other, what injury you have done me you know was long ago forgiven. to you brother Carl I give special thanks for the attachment you have displayed towards me of late. It is my wish that your lives be better and freer from care than I have had, recommend virtue to your children, it alone can give happiness, not money, I speak from experience, it was virtue that upheld me in misery, to it next to my art I owe the fact that I did not end my life with suicide. - Farewell and love each other - I thank all my friends, particularly Prince Lichnowsky and Professor Schmid - I desire that the instruments from Prince L. be preserved by one of you but let no quarrel result from this, so soon as they can serve you better purpose sell them, how glad will I be if I can still be helpful to you in my grave - with joy I hasten towards death - if it comes before I shall have had an opportunity to show all my artistic capacities it will still come too early for me despite my hard fate and I shall probably wish it had come later - but even then I am satisfied, will it not free me from my state of endless suffering? Come when thou will I shall meet thee bravely. - Farewell and do not wholly forget me when I am dead, I deserve this of you in having often in life thought of you how to make you happy, be so -

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