Faust in his Study (Georg Friedrich Kersting, 1829)
A depiction of Faust in his study, by Georg Kersting (1829), a depiction of the so-called Faustian mind, an unsated desire to find truth. (Ѻ)
In terminology, Faustian refers to legends surrounding the unsated "mind" archetype of Johann Faust (c.1485-1541), the story of someone—extremely tired and bored with mundane worldly existence, unsatisfied with its explanations—who sold their soul to the devil in return for knowledge, the secrets of nature, power, according to some accounts, and a truthful explanation of the meaning of it all; the gist of which seems to be captured well by the following: [1]

“I, too, have long investigated, have gone through all arts and sciences. I became a theologian, consulted authorities, weighed all, tested all,—polemics, exegesis, dogmatism. All was babble: nothing breathed of divinity! I became a jurist, endeavored to become acquainted with justice, and learned how to distort justice. I found an idol, shaped by the hands of self-interest and self-conceit, a bastard of justice, not herself. I became a physician, intending to learn the human structure, and the methods of supporting it when it gives way; but I found not what I sought, — I only found the art of methodically murdering men. I became a philosopher, desiring to know the soul of man, to catch truth by the wings and wisdom by the forelock; and I found shadows, vapors, follies, bound into a system!”
Faust (c.1770), Augsburg puppet-play version [2]

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Machiavellian encyclopedia
Faustian, according to some accounts, refers to someone who is Machiavellian (see: Niccolo Machiavelli) in his or her quest to understand the true nature of the meaning of the Prometheus myth in the context of the big riddle of the universe; a Machiavellian mind + Galilean mind in one person, so to say. Someone who is Faustian, in this context, is a “scholar of encyclopedia ambitions and Machiavellian dispositions”, as American sociologist Steve Fuller (2000) described Vilfredo Pareto, in the context of the Harvard Pareto circle, who, by no coincidence, is the third ranked social Newton behind Goethe (#1), who is aptly described by Jaroslav Pelikan (1997) as: “Doctor Faust the polymath is — as was Goethe the polymath — a man of "a hundred scholarly disciplines" [and] also a natural scientist.” [5]

Opening soliloquy
The main subject of the play, according to James Froude (1848), is the opening soliloquy, which varies per interpretation, but generally yielding to the same general theme; the following being the typical form:

At last so far in learning I have gone,
That I’m the laughing-stock of ev’ry one;
All books, from first to last, I have turn’d over,
The stone of wisdom I cannot discover.

Med’cine and jurisprudence come to nought,
In magic some assistance must be sought;
My studies in theology were vain,
My sleepless nights yet unrepaid remain.

Not one whole garment have I left to wear,
My load of debts is more than I can bear’
To pow’rs infernal I myself will bind,
That nature’s deepest secrets I may find.
— Faust (1846), "Opening soliloquy", Simrock’s version [9]

Typically, the play opens to a scene of Faust seated at a table overturning the leaves of a book:

“With all my learning, I, Johannes Faust, have accomplished just so much, that I must blush with self-shame. I am ridiculed everywhere, no one reads my books, all despise me. How fain am I to become more perfect! Therefore I am rigidly resolved to instruct myself in necromancy.”
— Faust (c.1805), performance by Schutz [2]

“I seek for learning in this book and cannot find it. Though I study all books from end to end, I cannot discover the touchstone of wisdom. O, how unfortunate art thou, Faust! The sleepless nights I have spent in fathoming the mysteries of theology! But, no! By heaven, I will no longer delay, I will take upon myself all labor, so that I may penetrate into that which is concealed, and fathom the mysteries of nature!”
— Faust (date), Geisselbrecht’s puppet-play [2]

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Puppet theatre (Goethe)
Goethe learned the story of Faust through the puppet theater; by 6½ was arranging and conducting plays on the miniature stage.
Goethean Faust
In 1753-55, German thinker Johann Goethe, aged 4½-6½, and his sister are given, by their grandmother, a puppet theater for Christmas (see: Goethe timeline). Goethe learns the story of Faust through the puppet theater; by he 6½ was arranging and conducting plays on the miniature stage. [6] By age 21, Goethe had seen the so-called “Strasburg puppet-play version” of Faust, which, supposedly, opened to a brief prologue in hell, in which Pluto order the temptation of Faust. Goethe, in his autobiography Poetry and Truth, reflected on his intercourse with German philosopher Johann Herder, in Strasburg, as follows: [7]

“The puppet-play echoed and vibrated in many tones through my mind. I, also, had gone from one branch of knowledge to another, and was early enough convinced of the vanity of all. I had tried life in many forms, and the experience had left me only the more unsatisfied and worried. I now carried these thoughts about with me, and indulged myself in them, in lonely hours, but without committing anything to writing. Most of all, I concealed from Herder my mystic-cabalistic chemistry, and everything connected with it.”
Johann Goethe (1770), reflection on intercourse with Johann Herder, in Strasburg [7]

Here, in this conviction of the "vanity of it all", we are reminded of the so-called drive-thru paradox, as depicted in the 1997 film Good Will Hunting, a semi-fictionalized elaboration on the life and times of William Sidis, about the paradoxical relation between the seeming purity of love and the apparent vanity inherent in the occupational ladder, as Faust says "how fain am I to become more perfect!", or as captured in the so-called alley equation, and the David Buss sexual receptiveness studies.

Faustian quest
The phrase “Faustian quest” tends to refer to a quest for knowledge, of truth of the universal genius variety. (Ѻ)

Faustian insight
The following quote, from Goethe’s 1832 Faust, seems to capture the notion of Faustian insight:

“To grant me a vision of nature's forces that bind the world, all its seeds and sources and innermost life ... all this I shall see... and stop peddling in words that mean nothing to me.”

In 2013, to cite usage, in the context of economic thermodynamics, during the JDNM review, Stephen Ternyik stated the following:

“The Pareto-optimum closed the scientific gap to marginal benefit (= statistical social science / 2 research articles send to you via e-mail); while working on the political economics of American Independence, I could apply his theory of elite circulation = history as cemetery of elites. Also of methodical interest is his dynamic view of speculation/speculators as drivers of socio-economic change, i.e. of 'Faustian' insight into our current monetary transition period.”

Faustian bargain
The phrase “Faustian bargain” tends to refer to refer to something made or done for present gain without regard for future cost or consequences. [3]

Faustian moment
The phrase “Faustian moment” seems to refer to a particular turning point or time at which one either has a moment of Faustian insight and or becomes Faustian. In 2005, American chemical engineer and ecologist Robert Ulanowicz, e.g., recalled when, several decades back, he had a “Faustian moment” in which he made a pact with the devil, so-to-speak, i.e. he gave up his worldly pursuits as formal chemical engineer, and switched careers to understand how the energy and matter interactions of the total set of organisms in Chesapeake Bay function. [4]

Faust-like | Modern Fausts
Roger Bacon has been categorized as “Faust-like” in legend. [10] Fritz Haber has been called a “modern Faust”, in regards to his willingness to serve any master who could further his passion for knowledge and progress. [11]

References
1. Faustian – Online Etymology Dictionary.
2. Goethe, Johann. (1832). Faust (translator: Bayard Taylor) (pgs. 230-31). Houghton, Mifflin & Co., 1883.
3. (a) Faustian – Merriam-Webster.com.
(b) Faustian bargain – Wiktionary.
4. Goldman, Erica. (2005). “Profile a Scientist for All Seasons”, Chesapeake Quarterly, Vol. 4, No. 3.
5. (a) Pelikan, Jaroslav J. (1997). Faust the Theologian (pg. 37). Yale University Press.
(b) Fuller, Steve. (2000). Thomas Kuhn: a Philosophical History of Our Times (Pareto, 13+ pgs; §3.5: The Harvard Strategy for Resisting a New Deal for Science, 162-69; Harvard’s Pareto Circle, pgs. 163-69). University of Chicago Press.
6. (a) Cox, Catharine, M. (1926). Early Mental Traits of Three Hundred Geniuses (Genetic Studies of Genius Series) (pg. 694). Stanford University Press.
(b) Friedenthal, Richard, Riedenthal-Haas, Marth. (2010). Goethe: His Life & Times (pg. 280). Transaction Publishers.
7. (a) Goethe, Johann. (1811-1833). From My Life: Poetry and Truth. Publisher
(b) Goethe, Johann. (1832). Faust (translator: Bayard Taylor) (pgs. 230-31). Houghton, Mifflin & Co., 1883.
8. Froude, James A. (1848). “Faust in the German Puppet-Show”, Fraser’s Magazine, 37:32-40, Jan.
9. (a) Simrock, Karl. (1846). Doctor Johannes Faust: Elevators Puppetry into Four (Doctor Johannes Faust: Puppenspiel in vier aufzügen). H.L. Pronner.
(b) Froude, James A. (1848). “Faust in the German Puppet-Show”, Fraser’s Magazine, 37:32-40, Jan.
10. Clegg, Brian. (2003). The First Scientist: a Life of Roger Bacon. Da Capo Press.
11. Charles, Daniel. (2005). Master Mind: the Rise and Fall of Fritz Haber, the Nobel Laureate who Launched the Age of Chemical Warfare. Harper Collins Publishers.

External links
Faustian – Dictionary.com.

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