The Housekeeper and the ProfessorBook - 2009
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"Someone once wrote that worrying is the hardest thing about being a parent."
"So who was it? Who discovered zero?" "An Indian mathematician; we don't know his name. The ancient Greeks thought there was no need to count something that was nothing. And since it was nothing, they held that it was impossible to express it as a figure. So someone had to overcome this reasonable assumption, someone had to figure out how to express nothing as a number. This unknown man from India made nonexistence exist. Extraordinary, don't you think?"
"But the most marvelous thing about zero is not that it's a sign or a measurement, but that it's a real number all by itself. It's the number that's one less than 1, the smallest of the natural numbers. Despite what the Greeks might have thought, zero doesn't disturb the rules of calculation; on the contrary, it brings greater order to them..."
Of course, lots of mathematical discoveries have practical applications, no matter how esoteric they may seem. Research on ellipses made it possible to determine the orbits of the planets, and Einstein used non-Euclidean geometry to describe the form of the universe. Even prime numbers were used during the war to create codes—to cite a regrettable example. But those things aren't the goal of mathematics. The only goal is to discover the truth." The Professor always said the word truth in the same tone as the word mathematics.
"For all natural numbers greater than 3, there exist no integers x, y, and z, such that: x^n + y^n = z^n.
If you added 1 to e elevated to the power of π times i, you got 0: e^πi + 1 = 0.
Though there was no circle in evidence, π had descended from somewhere to join hands with e. There they rested, slumped against each other, and it only remained for a human being to add 1, and the world suddenly changed. Everything resolved into nothing, zero.
"I'll show you one more thing about perfect numbers," he said, swinging the branch and drawing his legs under the bench to make more room on the ground. "You can express them as the sum of consecutive natural numbers." 6 = 1 + 2 + 3; 28 = 1 + 2 + 3 + 4 + 5 + 6 + 7; 496 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31
Two is the only even prime. It's the leadoff batter for the infinite team of prime numbers after it.
And, the sum of the prime factors of 714 equals the sum of the prime factors of 715: 714 = 2 × 3 × 7 × 17; 715 = 5 × 11 × 13; 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29. A pair of consecutive whole numbers with these properties is quite rare. There are only 26 such pairs up to 20,000. This one is the Ruth-Aaron pair. Just like prime numbers, they are more rare as the numbers get larger. And 5 and 6 are the smallest pair.
"The truly correct proof is one that strikes a harmonious balance between strength and flexibility. There are plenty of proofs that are technically correct but are messy and inelegant or counterintuitive. But it's not something you can put into words—explaining why a formula is beautiful is like trying to explain why the stars are beautiful."
The sum of the factors of 220 is 284, and the sum of the factors of 284 is 220. They're called 'amicable numbers,' and they're extremely rare. Fermat and Descartes were only able to find one pair each.
the sums of the divisors of numbers other than perfect numbers are either greater or less than the numbers themselves. When the sum is greater, it's called an 'abundant number,' and when it's less, it's a 'deficient number.' Marvelous names, don't you think? The divisors of 18 is 1 + 2 + 3 + 6 + 9 = 21, so it's an abundant number. But 14 is deficient: 1 + 2 + 7 = 10."
"If n is a natural number, then any prime can be expressed as either 4n + 1 or 4n - 1. It's always one or the other." "All of those numbers, those infinite primes, can all be divided into two groups?" "Take 13, for example ..." "That would be 4 × 3 + 1," Root said. "That's right. And 19?" "4 × 5 - 1." "Exactly!" The Professor nodded. "And there's more to it: the numbers in the first group can always be expressed as the sum of two squares, but those in the second can never be." "So, 13 = 2^2 + 3^2."
He had a special feeling for what he called the "correct miscalculation," for he believed that mistakes were often as revealing as the right answers.
"It's sometimes called the 'Queen of Mathematics,' " he said, after taking a sip of his coffee. "Noble and beautiful, like a queen, but cruel as a demon. In other words, I studied the whole numbers we all know, 1, 2, 3, 4, 5, 6, 7 ... and the relationships between them."
... 28=1+2+3+4+5+6+7 ... The subtle formula for the Artin conjecture and the plain line of the factors for the number 28 blended seemlessly, surrounding us where we sat on the bench. The figures became stitches in the elaborate pattern women in the dirt. I sat utterly still, afraid I might accidentally erase part of the design. It seemed as though the secret of the universe had miraculously appeared right here at our feet, as though God's notebook had opened under our bench... p46
Math has proven the existence of God because it is absolute and without contradiction; but the devil must exist as well, because we cannot prove it.
“The Professor never really seemed to care whether we figured out the right answer to a problem. He preferred our wild, desperate guesses to silence, and he was even more delighted when those guesses led to new problems that took us beyond the original one. He had a special feeling for what he called the "correct miscalculation," for he believed that mistakes were often as revealing as the right answers.”
“Soon after I began working for the Professor, I realized that he talked about numbers whenever he was unsure of what to say or do. Numbers were also his way of reaching out to the world. They were safe, a source of comfort.”
“Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley.”
SummaryAdd a Summary
He is a brilliant math Professor with a peculiar problem--ever since a traumatic head injury, he has lived with only eighty minutes of short-term memory. She is an astute young Housekeeper, with a ten-year-old son, who is hired to care for him. And every morning, as the Professor and the Housekeeper are introduced to each other anew, a strange and beautiful relationship blossoms between them. Though he cannot hold memories for long (his brain is like a tape that begins to erase itself every eighty minutes), the Professor’s mind is still alive with elegant equations from the past. And the numbers, in all of their articulate order, reveal a sheltering and poetic world to both the Housekeeper and her young son. The Professor is capable of discovering connections between the simplest of quantities--like the Housekeeper’s shoe size--and the universe at large, drawing their lives ever closer and more profoundly together, even as his memory slips away. The Housekeeper and the Professor is an enchanting story about what it means to live in the present, and about the curious equations that can create a family
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