Uniformly at Random

What is mathematics for?

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A while back, Underwood Dudley wrote this essay in the Notices of the American Mathematical Society.  His main point (which many may well disagree with) is that mathematics is very seldom useful in the workplace.  His concluding paragraph summarizes his argument:

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.”

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Written by uncudh

August 24, 2010 at 10:27 pm

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Romantic mathematics

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Here is a short quotation from the excellent book Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, by Amir Alexander:

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.

Written by uncudh

June 26, 2010 at 12:00 pm

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Enough of science and of art

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From Coleridge and Wordsworth’s Lyrical Ballads:

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.

Written by uncudh

April 1, 2010 at 12:58 pm

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Jane Austen in togas

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Another noteworthy quotation from Heather:

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.

Written by uncudh

February 26, 2010 at 6:13 pm

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Linguistic conservatism in Latin

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Peter Heather makes some interesting remarks on the education of Roman aristocrats and the resulting effect on the Latin language:

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).

Written by uncudh

February 21, 2010 at 12:26 pm

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There is no such thing as the Byzantine Empire

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The preface of J. B. Bury’s A History of the Later Roman Empire from Arcadius to Irene begins as follows:

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.

Written by uncudh

February 21, 2010 at 12:09 pm

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The Loves of the Triangles

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One of the most bizarre poems in the English language is surely “The Loves of the Triangles”, which is a parody of an almost equally bizarre poem, “The Loves of the Plants“, by Erasmus Darwin.  The following excerpt describes the erotic tendencies of the different conic sections: parabolas, hyperbolas, and ellipses.  I imagine that if parents knew just how dirty geometry can be, we would not be allowed to teach the subject in high schools!

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.

Written by uncudh

December 14, 2009 at 11:32 pm

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