Mathematical Birthday Quotes

The ladies were quite uninterested; either because they did not care for mathematics, or preferred to ignore birthdays.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

Every now and then, I'm lucky enough to teach a kindergarten or first-grade class. Many of these children are natural-born scientists - although heavy on the wonder side, and light on skepticism. They're curious, intellectually vigorous. Provocative and insightful questions bubble out of them. They exhibit enormous enthusiasm. I'm asked follow-up questions. They've never heard of the notion of a 'dumb question'. But when I talk to high school seniors, I find something different. They memorize 'facts'. By and large, though, the joy of discovery, the life behind those facts has gone out of them. They've lost much of the wonder and gained very little skepticism. They're worried about asking 'dumb' questions; they are willing to accept inadequate answers, they don't pose follow-up questions, the room is awash with sidelong glances to judge, second-by-second, the approval of their peers. They come to class with their questions written out on pieces of paper, which they surreptitiously examine, waiting their turn and oblivious of whatever discussion their peers are at this moment engaged in. Something has happened between first and twelfth grade. And it's not just puberty. I'd guess that it's partly peer pressure not to excel - except in sports, partly that the society teaches short-term gratification, partly the impression that science or mathematics won't buy you a sports car, partly that so little is expected of students, and partly that there are few rewards or role-models for intelligent discussion of science and technology - or even for learning for it's own sake. Those few who remain interested are vilified as nerds or geeks or grinds. But there's something else. I find many adults are put off when young children pose scientific questions. 'Why is the Moon round?', the children ask. 'Why is grass green?', 'What is a dream?', 'How deep can you dig a hole?', 'When is the world's birthday?', 'Why do we have toes?'. Too many teachers and parents answer with irritation, or ridicule, or quickly move on to something else. 'What did you expect the Moon to be? Square?' Children soon recognize that somehow this kind of question annoys the grown-ups. A few more experiences like it, and another child has been lost to science.

Recently, two economists—Kelly Bedard and Elizabeth Dhuey—looked at the relationship between scores on what is called the Trends in International Mathematics and Science Study, or TIMSS (math and science tests given every four years to children in many countries around the world), and month of birth. They found that among fourth graders, the oldest children scored somewhere between four and twelve percentile points better than the youngest children. That, as Dhuey explains, is a “huge effect.” It means that if you take two intellectually equivalent fourth graders with birthdays at opposite ends of the cutoff date, the older student could score in the eightieth percentile, while the younger one could score in the sixty-eighth percentile.

prompting the United States in 1935 to join about twenty other countries that had already instituted a social insurance program. Social Security made moral sense. It made mathematical sense, too. At that time, just over half of men who reached their 21st birthday would also reach their 65th, the year at which most could begin to collect a supplemental income. Those who reached age 65 could count on about thirteen more years of life.32 And there were a lot of younger workers paying into the system to support that short retirement; at that time only about 7 percent of Americans were over the age of 65. As the economy began to boom again in the wake of World War II, there were forty-one workers paying into the system for every beneficiary. Those are the numbers that supported the system when its first beneficiary, a legal secretary from Vermont named Ida May Fuller, began collecting her checks. Fuller had worked for three years under Social Security and paid $24.75 into the system. She lived to the age of 100 and by the time of her death in 1975 had collected $22,888.92. At that point, the poverty rate among seniors had fallen to 15 percent, and it has continued to fall ever since, owing largely to social insurance.33 Now about three-quarters of Americans who reach the age of 21 also see 65. And changes to the laws that govern the US social insurance safety net have prompted many to retire—and begin collecting—earlier than that. New benefits have been added over the years. Of course, people are living longer, too; individuals who make it to the age of 65 can count on about twenty more years of life.34 And as just about every social insurance doomsdayer can tell you, the ratio of workers to beneficiaries is an unsustainable three to one.

Imagine that you get a car as a birthday present, with the key in the ignition, but you have never heard of cars before and have absolutely no information about how they work. Being an inquisitive person, you get inside and start messing with the various buttons, knobs and levers. Eventually, you figure out how to use it and get quite good at driving. But unbeknownst to you, somebody has removed the letter R by the gearshift and messed with the transmission so that you need to apply a crazy amount of force to shift into Reverse. This means that unless someone tells you, you’ll probably never figure out that the car can drive backwards as well. If asked to describe how the car worked, you’d incorrectly assert that, without exception, as long as the engine is running, the harder you push on the accelerator pedal, the faster the car moves forward. If in a parallel universe, the car had instead required huge force to shift into forward drive mode, you’d have concluded that this strange machine worked differently and only moved backwards. Our Universe is very much like this car. As illustrated in Figure 6.6, it has a bunch of “knobs” that control how it works: the laws according to which things move when you do various things to them and so forth—what we’re told in school are the laws of physics, including so-called constants of nature. Each setting of the knobs corresponds to one of the phases of space, so if there are 500 knobs with 10 possible settings each, there are 10500 different phases. When I was in high school, I was incorrectly taught that these laws and constants were always valid, and never changed either from place to place or from time to time. Why this mistake? Because an enormous amount of energy—much more than we have at our disposal—is required to change the settings of these knobs, just as the gearshift on that car, so we didn’t realize that the settings could be changed. Nor that there even were any settings to change: unlike gearshifts, nature’s knobs are well hidden. They come in the form of so-called high-mass fields and other obscure entities, and huge energy is required not only to alter them, but even to detect that they exist in the first place.