Grothendieck has revolutionized the notion of mathematical space, as Einstein did in physics. He invented a new geometry, in which « the arithmetic world and the world of continuous quantities are now one ».
To combine the discontinuous and the continuous, the numbers and the quantities, to make them unite intimately, Grothendieck conceived the metaphor of their « marriages ». This marriage of paper had to be followed by proper consumption, in order to ensure the generation of new mathematical beings.
« For the expected ‘brides’,’of numbers and greatness’, it was like a decidedly narrow bed, where only one of the future spouses (i.e., the bride) could at least find a place to nestle as best as they could, but never both at the same time! The « new principle » that remained to be found, to consume the marriage promised by favourable fairies, was also that this spacious « bed » that the future spouses were missing, without anyone having only noticed it until then. This « double bed » appeared (as if by a magic wand…) with the idea of topos. » i
Grothendieck, the greatest mathematical thinker of the 20th century, explained a revolutionary breakthrough using a matrimonial metaphor, and all that follows.
Indeed, the metaphor of « marriage » has always been used to translate difficult ideas into philosophical contexts.
Two thousand years ago, the Jewish philosopher Philo of Alexandria used this same metaphor to present the « mystery of the divine generation ». To translate the idea of « divine generation » into Greek, Philo uses the word τελετή (‘telete’).
This mystery is composed of three elements. There are the two initial « causes » of the generation and their final product.
The two causes are God and Wisdom (who is « the bride of God », – remaining « virgin »)ii.
Wisdom is Virginity itself. Philo relies on the authority of the prophet Isaiah, who affirms that God unites himself with Virginity in itself.iii
Philo specifies elsewhere: « God and Wisdom are the father and mother of the world ».iv
In the Christian tradition, there are similar metaphors, derived from Jewish ideas, but transposed into the « union » of Christ and the Church.
A 16th century Christian cabalist, Guillaume Postel, uses the metaphor of the love of the male and female to describe this union:
« For as there is love of the male to the female, by which she is bound, so there is love and bond of the female to the male by which she is bound. This is the mystery of the most wonderful secret of the Church’s authority over God and Heaven, as well as over God and Heaven on Church by which Jesus meant it: Whatever you bind on earth will be bound to Heaven. »v
Teresa of Avila, a contemporary of Guillaume Postel, speaks through experience of « perfect union with God, called spiritual marriage »:
« God and the soul are one, like crystal and the ray of sunlight that penetrates it, like coal and fire, like the light of the stars and the light of the sun (…) To give an idea of what it receives from God in this divine cellar of union, the soul is content to say these words (and I do not see that it could better say to express something of them):
From my Beloved I drank.
For as the wine that we drink spreads and penetrates into all the limbs and veins of the body, so this communication of God spreads to the whole soul (…) The Bride speaks of it in these terms in the book of Songs: ‘My soul has become liquefied as soon as the Bridegroom has spoken’. »vi
Therese of Avila speaks of the Bride « burning with the desire to finally reach the kiss of union with the Bridegroom », quoting the Song of Songs: « There you shall teach me ».
The Song of Songs has incestuous resonances:
« Oh, what a brother to me, breastfed in my mother’s womb! Meeting you outside, I could kiss you, without people despising me. I’ll drive you, I’ll introduce you to my mother’s house, you’ll teach me! I’ll make you drink a fragrant wine, my pomegranate liqueur. »vii
This spicy passage was strangely interpreted by S. François de Sales:
« And these are the tastes that will come, these are the ecstasies, these are the summits of the powers; so that the sacred wife asks for pillows to sleep. »viii
Metaphors! Metaphors! Where do you lead us to?
iRécoltes et Semailles, §2.13 Les topos — ou le lit à deux places
iiPhilo of Alexandria. De Cherubim
iii Is. 66, 6-9
iv De Ebrietate, 30
v Guillaume Postel (1510-1581). Interprétation du Candélabre de Moïse (Venise 1548).« Car comme il y a amour du masle à la femelle, par laquelle elle est liée, aussi y a-t-il amour et lien de la femelle au masle par lequel il est lyé. Cecy est le mistère du très merveilleux secret de l’authorité de l’Eglise sur Dieu et sur le Ciel, comme de Dieu et du Ciel sur icelle par lequel Jésus l’a voulu dire : Ce que vous lierez sur la terre sera lyé au Ciel. »
viTeresa of Avila (1515-1582). The Interior Castle
viiiFrançois de Sales. Œuvres complètes. p. 706