A Quote by Leonhard Euler
To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
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If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
Science is Christian, not when it condemns itself to the letter of things, but when, in the infinitely little, it discovers as many mysteries and as much depth and power as in the infinitely great
Science is Christian, not when it condemns itself to the letter of things, but when, in the infinitely little, it discovers as many mysteries and as much depth and power as in the infinitely great.
A quantity which is increased or decreased by an infinitely small quantity is neither increased nor decreased.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
It is commonly, but erroneously, believed that it is easy to ask questions. A fool, it is said, can ask questions that a wise man cannot answer. The fact is that a wise man can answer many questions that a fool cannot ask.
Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.
It is astonishing how much the word infinitely is misused: everything is infinitely more beautiful, infinitely better, etc. The concept must have something pleasing about it, or its misuse could not have become so general.
So what are the effects of increasing minimum wages? Any Econ 101 student can tell you the answer: The higher wage reduces the quantity of labor demanded, and hence leads to unemployment.
...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
Throughout my political career, I've believed in the concept of home rule. Some call it local control. Whichever phrase you use, the concept is the same - the best decisions are those made closest to those who will be impacted by the decisions.
What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!
I believe the calculation of the quantity of probability might be improved to a very useful and pleasant speculation, and applied to a great many events which are accidental, besides those of games; only these cases would be infinitely more confused, as depending on chances which the most part of men are ignorant of.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
If you had a system that could read all the pages and understand the context, instead of just throwing back 26 million pages to answer your query, it could actually answer the question. You could ask a real question and get an answer as if you were talking to a person who read all those millions and billions of pages, understood them, and synthesized all that information.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
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