It was some time before Descartes responded to Elizabeth’s letter. Possibly he was pondering how best to approach her. But in the end he evidently decided to take her at her word, because, through an intermediary, he sent her a math problem.
And not just any math problem: a lulu, one of those that had stumped mathematicians from the beginning of recorded time, one that had never before been solved. Except that Descartes had just solved it.
It’s called the kissing circles problem. There are three tangent circles (that is, all touching each other). Solve for a fourth circle that touches all of the other three.
He didn’t expect her to answer it. In fact, he almost immediately regretted sending it to her. “For the rest, I have much remorse for proposing the problem of the three circles to Madame the princess of Bohemia, because it is so difficult that it seems to me that an angel who had only the algebra taught her by [her math tutor] would not be able to solve it without a miracle,” he wrote on October 21 to the friend he had used to forward the puzzle in the first place. He knew that by sending it he’d been showing off a bit—he probably couldn’t resist—but it was also the gesture of respect that she had asked for. Mathematics was the measure by which Descartes judged the world. Those who grasped its principles and appreciated its beauty he held in high regard and counted among his intimate friends; those who did not were simply not taken as seriously.
And then she solved it.
It wasn’t an elegant answer, like Descartes’s, that solved for all possibilities, but she’d managed to work out a specific case. Princess Elizabeth herself was aware of this defect but decided to send her answer along anyway, “as a young angler might show an old fisherman his catch… For I know perfectly well that in my solution, there was nothing clear enough to result in a theorem,” she admitted in a letter of November 21, 1643. This problem, and Descartes’s solution (which was shown to her only afterward), “taught me more than I would have learned in six months with my tutor. I am very indebted to you… there are few things that I would not do to obtain the effects of your good will, which is infinitely esteemed by your very affectionate friend at your service, Elizabeth,” she concluded.
It was the turning point in their relationship. From a rocky start—condescension on his part, pride and frustration on hers—there now developed a warmth and closeness that rivaled physical intimacy. Descartes eventually took her step by step through his own solution to the kissing circles and used her queries to sharpen and refine his theories concerning the mind and the soul. “I have never met anyone who could so thoroughly understand all that is contained in my writings,” he enthused. “For there are many, even among the best and most highly instructed minds, who find them obscure, and I observe that almost all those who understand readily those things that pertain to mathematics are not capable of comprehending those that belong to metaphysics, and I can say with truth that I have met none except your Highness to whom both are equally easy.” He dedicated his next work, The Principles of Philosophy, published the following year, to her, and the inscription was so obviously heartfelt that it prompted comment. “Bless the good man!” the chatty French doctor said of Descartes. “He thinks only one man and one woman capable of entering into his doctrines, the physician Regius and the Princess of Bohemia.”
As for Princess Elizabeth, it would not be an exaggeration to say that the friendship she shared with Descartes—a friendship of ideas and analysis, a melding of minds and souls so different from the shallow pretense of her daily existence—was the most precious relationship in her life. To have secured the regard and affection of such a man, to have earned it through her own efforts, to be esteemed for who she was on the inside and not for her title, breeding, or connections—this was a source of great solace. There was no question of physical intimacy between a middle-aged Catholic philosopher and a Protestant princess twenty-three years his junior whose virginity might yet secure her an appropriate husband, but what they had together was more than most marriages could boast and that can only be described, without irony, as metaphysical love.
It was well for Princess Elizabeth that she managed to forge this intimacy with Descartes when she did, that she had someone she could trust to turn to during periods of sorrow or hardship. For life at her mother’s court at The Hague, never easy for her even in the good times, was about to become extremely challenging.
WHILE PRINCESS ELIZABETH WAS wrestling with algebra and geometry, the rest of Europe continued its armed struggles over religion and power. In the winter of 1642 again occurred one of those seminal events that resounded through the theater of war and that caused the dancers to pause momentarily in their steps. It was a loss not on the battlefield but in a quiet bedroom in Paris. There, on December 4, 1642, the architect of the French entrance into the German war, the man who had successfully, almost single-handedly, guided the kingdom through nearly two decades of serpentine political turmoil, Cardinal Richelieu, died at the age of fifty-seven.
He’d been sick for a long time, getting steadily weaker, as was true also of his sovereign, Louis XIII. The previous June both men had been so ill that the only way they could meet were in rooms that contained a bed for each to lie upon. By November Richelieu was coughing blood, and his physicians knew his end was near. “I pray God to condemn me, if I have had any other aim than the welfare of God and the State,” the cardinal was reported to have avowed just before his demise. At the time of his death, France, once apprehensive of being crushed between all-dominant Spain and the Empire, stood as the ascendant power in Europe. In nearly every direction—to the north, south, and east—the French had wrested territory away from the Habsburgs and pushed back their borders as a result of Richelieu’s tactics.
“A great politician has departed!” mourned Louis XIII when he was informed of the cardinal’s passing. Less than six months later, he too was dead, and the future of France—and, by extension, Europe—was left to his widow, the queen mother, Anne of Austria, who was regent for her two young sons, four-year-old Louis XIV and his younger brother, two-year-old Philippe, duke of Orléans.
But of course it was not France that occupied the thoughts and prayers of the queen of Bohemia’s court at The Hague at this time. It was to England and the civil war between Charles I and Parliament that the family’s anxious eyes were turned. They were right to worry. Charles’s war effort, feeble from the start, would likely have collapsed with the first battle were it not for the industry of one man whose exploits and expertise were so vital to the royal cause that they were analogous to possessing a secret weapon (or perhaps, more aptly, employing a ringer)—the king’s twenty-four-year-old nephew, Rupert.
THE ENERGETIC RUPERT’S EFFECT on his uncle’s military affairs was immediate and electric. No sooner had he and Maurice (who had accompanied his older brother to England to serve as his right-hand man) rendezvoused with Charles at Nottingham for the inauspicious planting of the royal standard, than Rupert, used to continental warfare and shocked by the overall lack of supplies and general ineptitude of the king’s troops, began to take over. The first order of business was obviously to train the cavalry they already had and then use them to secure additional men and armaments. This Rupert did so quickly that Charles made him not simply commander of the King’s Horse but general of the whole army. “That brave Prince and hopeful soldier, Rupert, though a young man, had in martial affairs some experience, and a good skill, and was of such intrepid courage and activity, that—clean contrary to former practice, when the King had great armies, but no commanders forward to fight—he ranged and disciplined that small body of men [Rupert had only 800 cavalry to begin with]—of so great virtue is the personal courage and example of one great commander. And indeed to do him right, he put the spirit into the King’s army that all men seemed resolved,” observed a member of Charles’s circle.
Having whipped his small team of men into shape in record time, Rupert, along with his white poodle, Boye, who was so intelligent that the oppos
ition Parliamentarian soldiers believed the dog to be possessed by the devil, conducted a whirlwind tour through the countryside.* All those years of English lessons his mother had insisted on came in handy, as is evident in the letter he sent to the mayor of Leicester in advance of his arrival, which was typical of his approach. With great decorum, in the king’s name, he asked for £2,000, promising that it would be repaid at a more convenient period; signed the note “Your friend, Rupert”; and then added a postscript: “If any disaffected persons with you shall refuse themselves, or persuade you to neglect the command, I shall tomorrow appear before your town in such a posture, with horse, foot, and cannon, as shall make you know it is more safe to obey than to resist his Majesty’s command.” In this way, Charles’s 800 ragtag cavalry troops grew to 3,000 well-supplied horsemen in a single month.
As a result of his high spirits, military expertise, and seemingly limitless energy, Rupert very soon became the public face of the royal army to the rest of the kingdom, and particularly the enemy. The stories of his escapades were legion. It was said that he could travel fifty miles in a single day through hostile territory, win a battle, take prisoners, and be back at base camp by dinner. Once, interrupted at shaving by an enemy attack, he simply shrugged into his shirt, leaped onto his horse, and routed the opposition before returning calmly to his washbasin. A Puritan soldier reported that Rupert, out on a surveillance mission, met an apple peddler on the road near the enemy camp, bought the man’s entire stock on the spot, exchanged his coat and horse for the apple seller’s costume and cart, and arranged to meet him again later in the day. The prince then drove the cart to the heath where the Parliamentarian soldiers were stationed, sold them the apples, counted the number of their forces, perused the quality of their artillery, and then returned to the peddler. He rewarded the man with a golden coin and instructed him to go back to the opposition troops “and ask the commanders how they liked the fruit which Prince Rupert did, in his own person, but this morning sell them.”*
Rupert’s innovative methods, while condoned on the Continent (whose inhabitants had been at war for over two decades and who were therefore much more inured to intimidation), were considered highly unorthodox by his English victims. “The two young Princes, Rupert especially, the elder and fiercer of the two, flew with great fury through divers counties… whereupon the Parliament declared him and his brothers ‘traitors,’” affirmed a chronicler of the period.
Unfortunately, her younger sons’ highly public intervention in English affairs, so necessary to her brother’s war effort, put great stress on the queen of Bohemia and her court. Since his ascension to the throne, Charles I had been helping to support his sister and her family with an annual stipend of £12,000—not sufficient for grandeur but enough to cover basic expenses and keep food on the table. But with the advent of the civil war, Parliament held the purse strings, and its members declined to support the mother of the commander of His Majesty’s forces. Instead, through Puritan spies, they put the court at The Hague under surveillance.
This dilemma appears to have been anticipated by Karl Ludwig (whom Charles had also supported financially) and had in fact been at least partly responsible for his leaving England when he did. But despite Karl Ludwig’s attempts at neutrality, no money was forthcoming. The court at The Hague entered a period of increasing austerity. “We were at times obliged to make even richer repasts than that of Cleopatra, and often had nothing at our court but pearls and diamonds to eat,” Sophia recalled. To help cut expenses, the queen of Bohemia once again sent her two youngest sons, twenty-year-old Edward and sixteen-year-old Philip, to live with relatives in France, taking the risk that, with the reviled Cardinal Richelieu safely in the grave, there would be no plots against them.
She was right—in a way. Under the new regime, the queen of Bohemia’s younger sons were perfectly safe from the threat of espionage, prison cells, and sword thrusts. But not, as it turned out, from Cupid’s arrows.
LIKE HIS OLDER BROTHER Rupert, Edward had grown into a very attractive young man. He had long, flowing dark locks, a little pencil mustache, and a muscular body. He spoke French to perfection, having spent much of his later childhood and adolescence in France. He knew the manners and customs of Paris better than those of Holland. He liked the fashionable pleasures of the capital, which were much more sophisticated and entertaining than life at The Hague, but, alas, he had not the financial means to pursue them as fully as he would have liked. Still, as a nephew of the queen of England, herself a member of the French royal family and aunt to the boy sovereign Louis XIV, Edward managed to get around a little, and was invited to dinners. At one of these soirees he met a force of nature by the name of Anna de Gonzaga.
Anna was born in 1616, which made her nearly eight years Edward’s senior. She was both highly political and notoriously passionate and was as a result in possession of a reputation sorely in need of rehabilitation. The second daughter of the count of Mantua, Anna had been raised in a French convent where she and a younger sister were enjoined to take the veil by their father, who wanted to put all his resources into obtaining an advantageous marriage for his beautiful eldest daughter, Marie.* But the count of Mantua died before he could force his middle daughter to say her vows, and at twenty-one, Anna exchanged the nunnery for the French court. There, she met Henri, duke of Guise,† with whom she fell instantly, hopelessly, recklessly in love. “M. de Guise had the figure, the attitude and the manners of a Roman hero,” she sighed in her memoirs. Henri reciprocated her passion and shortly thereafter seduced her, promising her marriage in a letter signed in blood. His mother tried to put a stop to it by using her influence to promote him to archbishop of Rheims, a position he accepted. His new life in the Church did not, however, get in the way of his torrid affair with Anna, although it did come in handy, as he was able to bully a priest into marrying them secretly in a private chapel with no witnesses. Anna was so infatuated that she disguised herself as a man in order to follow her lover wherever he went, and she referred to herself as the duchess of Guise in letters to friends. It therefore came as something of a shock when Henri suddenly eloped with a French countess, whom he (legitimately) married in Brussels. By 1643, Anna was back in Paris, devastated and seriously on the rebound, when she met Edward.
She was wealthy in her own right but wanted respectability and a title; he was young, penniless, and malleable. He never had a chance.* “This princess,” reported another lady of the French court, “did not despise the conquests of her eyes, which were in truth very beautiful; but besides that advantage, she had that which was of more value, I mean wit, address, capacity for conducting an intrigue, and a singular facility in finding expedients for succeeding in what she undertook.” But of course Anna was a Catholic and Edward was a Protestant, and this wouldn’t do—to have the marriage accepted by French society, he would have to convert. As a matter of fact, it would be much to Anna’s credit if she could get the son of the queen of Bohemia, who was widely recognized as one of the staunchest Protestants in Europe, to accept the Catholic faith, and this may have contributed something to his allure. Edward weighed the advantages of a marriage to Anna—a brilliant life in Paris, money, a worldly, fascinating wife—against those of his religion—poverty, rootlessness, a mother he barely knew, and the generally uncertain existence that could be expected by the middle son of a deposed king—and took the deal.
They were married in April of 1645 and afterward Edward very publicly converted to Catholicism, accepting Communion at the hands of a popular priest in Paris. Anna was given the credit for this coup, and her career at court was assured. She and Edward set up housekeeping in Paris as the prince and princess of Palatine, where they were accorded honors and a status comparable to those assigned to foreign dignitaries, and Edward would go on to watch his wife become a political force in France. “She had so much intelligence, and a talent so peculiar for business, that no one in the world ever succeeded better than she did,” a French statesman co
ncurred.
Edward and his new wife, Anna de Gonzaga
The news of Edward’s conversion and marriage fell upon the family court at The Hague like one of the ten plagues called upon the pharaoh by Moses in the Bible. His mother would have preferred that he take out his dagger and plunge it into her breast than to suffer the humiliation of having raised a traitor to the Protestant cause. Karl Ludwig, who had gone back to England, not to support his uncle’s cause, but to personally assure Parliament of his goodwill and lobby for the reinstatement of his income, was equally incensed, as Edward’s rejection of Protestantism played directly into Puritan fears that Charles I would call on Catholic forces to invade the kingdom. Moreover, as the nominal head of the family, Karl Ludwig should have been consulted before his brother entered into a marital alliance. To prevent further damage, he immediately ordered his youngest brother, Philip, to leave Paris, “where were only to be found either Atheists or hypocrites,” as he scornfully avowed, and return to the vigilant orthodoxy of The Hague.
Princess Elizabeth was, if possible, even more distressed than the rest of the family by what she considered to be a betrayal on Edward’s part. The sensational tidbit was picked up by the Dutch papers, and as might have been expected, they had a great deal of fun with it. The princess was used to adversity, even tragedy, but had always been firm in the family’s cause and clearly took her religion very seriously. The very public nature of the scandal mortified her. So used to turning to Descartes was she that, despite his being a devout Catholic who could not help but rejoice at Edward’s conversion, she poured out her heart to him. After first apologizing for not having answered an earlier letter as promptly as usual, “It is with shame that I confess the cause, since it has overthrown all that your lessons seemed to have established in my mind,” she continued, distraught. “I believed that a strong resolution only to seek happiness in the things which depend on my will would render me less sensitive to those which came from without, before the folly of one of my brothers made me feel my weakness. For it has disturbed the health of my body and the tranquility of my soul more than all the misfortunes which have yet happened to me.* If you take the trouble to read the gazette you must be aware that he has fallen into the hands of a certain sort of people who have more hatred to our family than love of their own worship, and has allowed himself to be taken in their snares to change his religion and become a Roman Catholic, without making the least pretence which could impose on the most credulous that he was following his conscience. And I must see one whom I loved with as much tenderness as I know how to feel, abandoned to the scorn of the world and the loss of his own soul (according to my creed).” Then, as if suddenly remembering that Descartes was a Catholic, she added quickly, “If you had not more charity than bigotry it would be an impertinence to speak to you of this matter, and if I were not in the habit of telling you all my faults as the person most able to correct them.”
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