What mathematics education is for is not for jobs. It is to teach the race to reason. It does not, heaven knows, always succeed, but it is the best method that we have. It is not the only road to the goal, but there is none better. Furthermore, it is worth teaching. Were I given to hyperbole I would say that mathematics is the most glorious creation of the human intellect, but I am not given to hyperbole so I will not say that. However, when I am before a bar of judgment, heavenly or otherwise, and asked to justify my life, I will draw myself up proudly and say, “I was one of the stewards of mathematics, and it came to no harm in my care.” I will not say, “I helped people get jobs.”

The iconic tale of the tragic romantic mathematician, it seems clear, was both novel and exclusive in the early nineteenth century—novel because it ran counter to the images that had prevailed only a few years earlier, when mathematicians were more likely to be viewed as simple natural men than as striving romantic heroes; exclusive because the new story was reserved, among the sciences, to mathematics alone.  Only mathematics came to be viewed as a quest for pure sublime truth, only mathematics was perceived as a creative art rather than a science, and only mathematicians became tragic romantic strivers in the manner of contemporary poets, painters, and musicians.  It can well be said that in the early nineteenth century mathematics took leave of the natural sciences, which had been its companions for millennia, and sought a place for itself instead with the creative arts.

THE TABLES TURNED; AN EVENING SCENE, ON THE SAME SUBJECT.

Up! up! my friend, and clear your looks,
Why all this toil and trouble?
Up! up! my friend, and quit your books,
Or surely you’ll grow double.

The sun above the mountain’s head,
A freshening lustre mellow,
Through all the long green fields has spread,
His first sweet evening yellow.

Books! ’tis a dull and endless strife,
Come, hear the woodland linnet,
How sweet his music; on my life
There’s more of wisdom in it.

And hark! how blithe the throstle sings!
And he is no mean preacher;
Come forth into the light of things,
Let Nature be your teacher.

She has a world of ready wealth,
Our minds and hearts to bless—
Spontaneous wisdom breathed by health,
Truth breathed by chearfulness.

One impulse from a vernal wood
May teach you more of man;
Of moral evil and of good,
Than all the sages can.

Sweet is the lore which nature brings;
Our meddling intellect
Misshapes the beauteous forms of things;
—We murder to dissect.

Enough of science and of art;
Close up these barren leaves;
Come forth, and bring with you a heart
That watches and receives.

The lifestyle of Symmachus and his friends provides a blueprint for that of the European gentry and nobility over much of the next sixteen hundred years.  Leisured, cultured and landed:  some extremely rich, some with just enough to get by in the expected manner, and everyone perfectly aware of who was who.  And all engaged in an intricate, elegant dance around the hope and expectation of the great wealth that marriage settlement and inheritance would bring.  Symmachus and his friends may have enjoyed editing Latin texts rather than painting watercolours and learning Italian, and their notions of such things as childhood and gender may have been rather different, but there is certainly a touch of Jane Austen in togas about the late Roman upper crust.

Frakking awesome.

The bedrock of the system was the intense study of a small number of literary texts under the guidance of an expert in language and literary interpretation, the grammarian.  This occupied the individual for seven or more years from about the age of eight, and concentrated on just four authors: Vergil, Cicero, Sallust and Terence.  [...]  Essentially, these texts were held to contain within them a canon of ‘correct’ language, and children were to learn that language—both the particular vocabulary and a complex grammar within which to employ it.  One thing this did was to  hold educated Latin in a kind of cultural [vise] preventing or at least significantly slowing down the normal processes of linguistic change.  It also had the effect of allowing instant identification.  As soon as a member of the Roman elite opened his mouth, it was obvious that he had learned ‘correct’ Latin.  It is as though a modern education system concentrated on the works of Shakespeare with the object of distinguishing the educated by their ability to speak Shakespearean English to one another (The Fall of the Roman Empire: A New History).

There is no period of history which has been so much obscured by incorrect and misleading titles as the period of the later Roman Empire. It is, I believe, more due to improper names than one might at first be disposed to admit, that the import of that period is so constantly misunderstood and its character so often misrepresented. For the first step towards grasping the history of those centuries through which the ancient evolved into the modern world is the comprehension of the fact that the old Roman Empire did not cease to exist until the year 1453. The line of Roman Emperors continued in unbroken succession from Octavius Augustus to Constantine Palaeologus.

And first, the fair PARABOLA behold,
Her timid arms, with virgin blush, unfold!
Though, on one focus fix’d, her eyes betray
A heart that glows with love’s resistless sway,
Though, climbing oft, she strive with bolder grace
Round his tall neck to clasp her fond embrace,
Still e’er she reach it from his polish’d side
Her trembling hands in devious Tangents glide.

Not thus HYPERBOLA:—with subtlest art
The blue-eyed wanton plays her changeful part;
Quick as her conjugated axes move
Through every posture of luxurious love,
Her sportive limbs with easiest grace expand;
Her charms unveil’d provoke the lover’s hand:—
Unveil’d except in many a filmy ray
Where light Asymptotes o’er her bosom play,
Nor touch her glowing skin, nor intercept the day.

Yet why, ELLIPSIS, at thy fate repine?
More lasting bliss, securer joys are thine.
Though to each fair his treacherous wish may stray,
Though each in turn, may seize a transient sway,
‘Tis thine with mild coercion to restrain,
Twine round his struggling heart, and bind with endless chain.

The full text can be found in The Poetry of the Anti-Jacobin, which is available for free download on Google Books.

I shall attack Chemistry, like a Shark.

Reminds me of this comic from xkcd.

My opinion is this—that deep Thinking is attainable only by a man of deep Feeling, and that all Truth is a species of Revelation.  The more I understand of Sir Isaac Newton’s works, the more boldly I dare to utter to my own mind & therefore to you, that I believe the Souls of 500 Sir Isaac Newtons would go to a making up of  a Shakespeare or a Milton . . . Newton was a mere materialist—Mind in his system is always passive—a Lazy Looker-on on an external World.  If the mind be not passive, if it be indeed made in God’s Image,  that too in the sublimest sense—the Image of the Creator—there is ground for suspicion, that any system build on the passiveness of the mind must be false, as a system.

These machines he had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with King Hiero’s desire and request, some little time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of the people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry, which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art. Archimedes, however, in writing to King Hiero, whose friend and near relation he was, had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labour and many men; and, loading her with many passengers and a full freight, sitting himself the while far off, with no great endeavour, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. These the king himself never made use of, because he spent almost all his life in a profound quiet and the highest affluence. But the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.

The manner of the death of Archimedes is quite famous, and is described by Plutarch (Marcellus):

But nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through. Others write that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was then at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate that, as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.