Quotes of All Topics . Occasions . Authors
As for my studies in school, I was a solid student. I was strong in English and Latin, but I got lost anytime the subject included math. I wish I had paid more attention to biology and science in general, subjects that came to interest me as an adult. I could have gotten better marks, but I never took a book home, never did homework.
What makes it possible to learn advanced math fairly quickly is that the human brain is capable of learning to follow a given set of rules without understanding them, and apply them in an intelligent and useful fashion. Given sufficient practice, the brain eventually discovers (or creates) meaning in what began as a meaningless game.
I was always told that I was good in mathematics, and I guess my grades and standardized test scores supported that. My worst subjects were those that generally involved a lot of reading - English and history. So, having good test scores in math and mediocre ones in reading, I was naturally advised to major in engineering in college.
How do we fill the need for technology workers, people who have computer skills and math and science skills? How do we get a more diverse science workforce? These are all issues - I would look at these documents that were from the '50s and '60s and '70s, and you'd swear they were written two weeks ago because the issues are the same.
We need to eliminate the existing hierarchy of subjects. Elevating some disciplines over others only reinforces outmoded assumptions of industrialism and offends the principle of diversity. The arts, sciences, humanities, physical education, languages and maths all have equal and central contributions to make to a student's education.
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.
Elodin proved a difficult man to find. He had an office in Hollows, but never seemed to use it. When I visited Ledgers and Lists, I discovered he only taught one class: Unlikely Maths. However, this was less than helpful in tracking him down, as according to the ledger, the time of the class was 'now' and the location was 'everywhere.
No wonder that Churchill described this effort [the British codebreakers working at Bletchley Park] as "Britian"s secret weapon," a weapon far more effective than the buzz bombs and the rockets that Werner von Braun designed for a German victory, a weapon absolutely decisive, in the judgement of many, in winning the war for the Allies.
My high school career was undistinguished except for math and science. However, having barely been admitted to Rice University, I found that I enjoyed the courses and the elation of success and graduated with honors in physics. I did a senior thesis with C.F. Squire, building a regulator for a magnet for use in low-temperature physics.
I was very disruptive. I was horrible. I didn't learn like all the other kids. I had to sometimes take my tests out in the hallways because I couldn't focus. But, my teachers would come see me in the plays and were like 'I don't understand how you can focus and be in the moment in a play and you go into math class and you can't focus.'
I exclusively attended public school... And I can honestly say that on the day of my graduation, if you had given me a pop quiz on history, science, or math, I would have in no way been able to pass it - despite the fact that I completely understood it at the time that it had been 'taught' to me, and had even made a good 'grade' on it.
It is a profoundly erroneous truism, repeated by all copy books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.
The real irony is that the view of infinity as some forbidden zone or road to insanity - which view was very old and powerful and haunted math for 2000+ years - is precisely what Cantor's own work overturned. Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting.
The interaction between math and physics is a two-way process, with each of the two subjects drawing from and inspiring the other. At different times, one of them may take the lead in developing a particular idea, only to yield to the other subject as focus shifts. But altogether, the two interact in a virtuous circle of mutual influence.
Phyllis explained to him, trying to give of her deeper self, 'Don't you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It's music, hanging there in the middle of space, meaning nothing but itself, and so moving...'
I was never a class clown or anything like that, but I do remember being in the first grade and my teacher, Mr. Chad, told the class one day that we were going to do some exercises. He meant math exercises, but I stood up and started doing jumping jacks. To this day, I don't know what possessed me to do that, but all my friends cracked up.
I was taught to do math and read at the same time. So you're six years old, you're reading 'Snow White and the Seven Dwarfs' and it becomes rapidly obvious that there are only two kinds of men in the world: dwarves and Prince Charmings. And the odds are seven is to one against your finding the prince. That's why little girls don't do math.
The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.
A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
Mindset changes are not happening from change in legislation. Like desegregation. We legally got rid of legal segregation, but schools are still segregated. You can demand people have better math understanding, but it depends how you interpret math understanding, and what you want it for, and if you think everybody can and should have that.
The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few primarily those who are independently motivated and who will learn under any conditions.
Especially girls, but any kids exposed to music programs and arts programs do much better on their tests. They have a better chance of going to college. They can focus better. You know, we're not just automatons learning how to work machines and do engineering and math and science. All of that's great, but you've got to build a whole person.
Let's be clear about what Common Core is. It spells out what students should know at the end of each grade. The goal is to ensure that our students are sound in math and literacy and that our schools have some basic consistency nationwide. But the standards do not dictate a national curriculum, and teachers are not told how or what to teach.
There was a survey done a few years ago that affected me greatly. it was discovered that intelligent people either estimate their intelligence accurately or slightly underestimate themselves, but stupid people overestimate their intelligence and by huge margins. (And these were things like straight up math tests, not controversial IQ tests.)
I know we can all remember the days of sitting in algebra class asking ourselves, 'why will I need algebra or chemistry in the future?' The answer was and still remains that advanced math and science classes help high school students develop their analytical and cognitive skills and better prepare them to compete in college and the workplace.
California is the highest-tax state in the nation and has been for a long time. It has the highest-paid teachers in the nation, by far - $400 a month more than New Jersey - and yet California is the third lowest state on test scores for fourth and eighth grade English and math in the nation, and has been at the low level for a long, long time.
Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.
Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy - it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.
All I wanted to do was put together one of the best home maths systems in the world, and that's what we've done. I've loved numbers since I was two or three, and I get really excited about them. Now, I'm allowing myself to get excited about things. If you're doing it for a TV network or any major corporation, you have to put a lid on it a little.
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
If we possessed a thorough knowledge of all the parts of the seed of any animal (e.g. man), we could from that alone, be reasons entirely mathematical and certain, deduce the whole conformation and figure of each of its members, and, conversely if we knew several peculiarities of this conformation, we would from those deduce the nature of its seed.
It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.
If you've never programmed a computer, you should. There's nothing like it in the whole world. When you program a computer, it does exactly what you tell it to do. It's like designing a machine — any machine, like a car, like a faucet, like a gas-hinge for a door — using math and instructions. It's awesome in the truest sense: it can fill you with awe.
You know, students who major in elementary education - they're going to be grade school teachers - they have the highest rates of math anxiety of any college major. And they bring that into the classroom. So you find students being introduced to math concepts by teachers who may have not only a lack of training but also a lack of enthusiasm about math.
In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.
What makes screenplays difficult are the things that require the most discipline and care and are just not seen by most people. I'm talking about movement - screenwriting is related to math and music, and if you zig here, you know you have to zag there. It's like the descriptions for a piece of music - you go fast or slow or with feeling. It's the same.
People think they don’t understand math, but it’s all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he won’t be able to tell you. But if you rephrase the question: what is better, 2 bottles of vodka for 3 people or 3 bottles of vodka for 5 people, he will tell you right away: 2 bottles for 3 people, of course.
Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians' stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
It has been proven time and time again in countless studies that students who actively participate in arts education are twice as likely to read for pleasure, have strengthened problem-solving and critical thinking skills, are four times more likely to be recognized for academic achievement, four times more likely to participate in a math and science fair.
...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.
You're sure your new roommate won't be like the last one who wore tinfoil socks and had a tendency to occasionally urinate in the refrigerator. You're sure you'll pass Math 106 this time around. You're determined to actually join some clubs this year and not just sit around in your dorm eating spray cheese from a can and watching youtube videos about cats.
The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.
This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.
Analysis of President Bush's tax plan has revealed that several elaborate tricks and gimmicks were used to make it look like a $1.35 trillion cut, but in reality it's going to be closer to costing $1.8 trillion. Critics claim it's math so fuzzy, you have to squint to see our nation's future of subsistence farming and post-apocalyptic roving motorcycle gangs.
The skylines lit up at dead of night, the air-conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.
I was never very good at math and science, to be honest, so it's fun to play a character that is so scientific and mathematical, and whose brain functions at such a high pace. The biggest difference is that Maura is very linear in her thinking and very logical. I'm not quite like that. I'm much more laid back and not quite so type A. That's the big difference.
So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.
The most important steps that I followed were studying math and science in school. I was always interested in physics and astronomy and chemistry and I continued to study those subjects through high school and college on into graduate school. That's what prepared me for being an astronaut; it actually gave me the qualifications to be selected to be an astronaut.