A Quote by Arthur Mattuck
Mathematics is the art of accurate reasoning on inaccurately-drawn figures... let that be our motto.
Related Quotes
Geometry is the art of correct reasoning from incorrectly drawn figures.
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.
... if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connection between the two is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.
As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.
Mathematics is not just a language. Mathematics is a language plus reasoning.
Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive.
One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music... In the same way, the symbolism of mathematics is merely its coded form, not its substance.
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!
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.
Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
the art of becoming 'rich', in the common sense, is not absolutely nor finally the art of accumulating much money for ourselves, but also of contriving that our neighbour shall have less. In accurate terms, it is 'the art of establishing the maximum inequality in your own favour'.
Geometry is the science of correct reasoning on incorrect figures.
Today, it is not only that our kings do not know mathematics, but our philosophers do not know mathematics and - to go a step further - our mathematicians do not know mathematics.
We are used to discounting the river-gods and dryads of the Greeks as poetical fancies, and even the chief figures in the classical Pantheon-Venus, Minerva, Mars, and the rest-as allegories. But, forgetting that they once carried as much sanctity as our saints and divinities, we refrain from applying the same reasoning to our own objects of worship.
What exactly is mathematics? Many have tried but nobody has
really succeeded in defining mathematics; it is always something
else. Roughly speaking, people know that it deals with numbers,
figures, with relations, operations, and that its formal procedures
involving axioms, proofs, lemmas, theorems have not changed
since the time of Archimedes.
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