$e^{iθ}$

Once one sees the series expansions of $\cos θ$, $\sin θ$, and $e^x$, it's easy to see why
$e^{iθ} = \cos θ + i\sin θ$,
and from there, why
$e^{iπ} + 1 = 0$
which I always thought appeared mystical.

However, I'm not satisfied; I'd like to understand it at a visual level. Also, I'd like to understand how to derive the related Taylor/Maclaurin series.

I learned Gaussian integers ($m + ni, | m, n ∈ ℤ$) and proved an equilateral triangle cannot have all vertices at Gaussian integers.

Maxwell's religious views

Maxwell's mindset seems to be that faraway stars are composed of molecules exactly the same as we find on Earth (which he would know through spectroscopy). Only created objects stay the same, whereas natural objects continually change. Therefore, the universe was created by a Creator. Therefore God.

http://www.victorianweb.org/science/maxwell/molecules.html

Einstein's religious views

1923: "My comprehension of God comes from the deeply felt conviction of a superior intelligence that reveals itself in the knowable world. In common terms, one can describe it as pantheistic."

1929: "I believe in Spinoza's God who reveals himself in the harmony all that exists, but not a God who concerns himself with the fate and actions of human beings."

1931: "It is very difficult to elucidate this cosmic religious feeling to anyone who is entirely without it. The religious geniuses of all ages have been distinguished by this kind of religious feeling, which knows no dogma and no God conceived in man's image; so that there can be no church whose central teachings are based on it. In my view, it is the most important function of art and science to awaken this feeling and keep it alive in those who are receptive to it."

1934: "You will hardly find one among the profounder sort of scientific minds without a religious feeling of his own. But it is different from the religiosity of the naive man. For the latter, God is a being from whose care one hopes to benefit and whose punishment one fears; a sublimation of a feeling similar to that of a child for its father."

Date unknown by me: "In every true searcher of nature, there is a kind of religious reverence, for he finds it impossible to imagine that he is the first to have thought out the exceedingly delicate threads that connect his perceptions."

Date unknown by me: "A contemporary has said, not unjustly, that in this materialistic age of ours the serious scientific workers are the only profoundly religious people."

Einstein's activism

Einstein was active in civil rights, including equality for gays, but particularly for African Americans. Of course the FBI noted such suspicious behavior as Einstein signing a fundraising appeal for the NAACP.

A conservative columnist, Jimmy Tarantino, wrote, "Red-fronting Einstein should be deported. The Senate Internal Security Committee would most likely discover that Einstein's Commie connections have been so wide and vast in scope that it may be safer to deport him to his native Europe. Who needs this Einstein? Not the American people, and that's for sure."

the return of vacuum tubes?

Qubits deteriorate easily. One of the mainstream areas of research into how to preserve them is with the use of vacuum tubes.

QM foundation discussion banned; no-cloning theorem

According to HarvardX: EMC2x The Einstein Revolution:

The principal physics journal in the United States, Physical Review, for a time more or less banned discussion of the foundations of quantum mechanics. [hyperbole?]

Also, I've now heard of the no-cloning theorem which states it is impossible to create an identical copy of an arbitrary unknown quantum state. (1982) Supposedly it's comparable in importance to the uncertainty principle.

Bohr vs Einstein

(Taking Kaiser's article at face value)

Einstein and Bohr had very different styles that were reflected in their approach to QM (quantum mechanics). (In fact, there were a series of Bohr-Einstein debates about the nature of QM.)

Bohr valued plain language, community, and teamwork.
Einstein valued visualization supplemented with math, and solitary thought.

Bohr was content with descriptions and wasn't bothered by QM stopping with probability.
Einstein valued axioms and wanted underlying principles that led to QM's uncertainty.

Source: David Kaiser's "Bringing the Human Actors Back On Stage: The Personal Context of the Einstein-Bohr Debate". 

Big Bang Theory linked to divine creation

The Big Bang Theory was originally seen as supportive or quasi-supportive of religion by both religious factions and by skeptical scientists.

So we have Pope Pius embracing Big Bang Theory saying:

"it would seem that present-day science has succeeded in bearing witness to the august instant of the primordial Fiat Lux, when, along with matter, there burst forth from nothing a sea of light and radiation. What, then, is the importance of modern science in the argument for the existence of God based on change in the universe? With exact and detailed research into the large-scale and small-scale worlds it has considerably broadened and deepened the empirical foundation on which the argument rests. Thus, with that concreteness which is characteristic of physical proofs, it has confirmed the contingency of the universe and also the well-founded deduction as to the epoch when the world came forth from the hands of the Creator. Hence, creation took place. We say, therefore, there is a Creator. Therefore, God exists.”

And we have Fred Hoyle (leading astronomer) arguing for the competing Steady State Theory, writing

"for it is against the spirit of scientific inquiry to regard observable effects as arising from causes unknown to science, and this is in principle what creation-in-the-past implies."

Source: HarvardX: EMC2x The Einstein Revolution

Physicist assassin

Einstein and his friend Friedrich Adler both applied for the chair of the University of Zurich’s physics department. Adler told the university that if they had the chance to hire Einstein, they should hire Einstein instead of himself.

Adler soon turned his attention to politics, as he hated Austria’s support of WWI. This lead Adler to assassinate the Minister-President of Austria. Adler’s father tried to save his son by arguing Friedrich was insane, but Friedrich instead argued his political position, and I presume he appeared quite sane while doing so. Einstein wrote to help but stopped short of saying Adler was insane.

From prison Adler delighted that he could think about physics again, and wrote to Einstein describing what he thought was a flaw in relativity. Adler’s father seized on this as further evidence his son was insane (because he dared to argue with Einstein)! The father wrote to leading physicists for confirmation of this. The physicists were in a bind because they could see Adler made a normal mistake, but not an insane one.

Adler was sentenced to death. Turbulent times lead to an offer of amnesty for all political prisoners in exchange for an apology, but Adler refused to apologize. Eventually Adler’s sentence was commuted.

Hubble discovered that other galaxies existed

I knew Edwin Hubble for discovering galaxy redshifts (1929), showing the universe was expanding. What I did not know was that just 6 years prior, it wasn't known that other galaxies even existed! It was Hubble who proved some there were galaxies beyond our own. This had long been suspected, yet it had not been the prevailing view.

Source: https://en.wikipedia.org/wiki/Edwin_Hubble