Johann Heinrich Lambert Quotes

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.

There is no royal road to geometry.

Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

Where there is matter, there is geometry.

Plane geometry is sort of the key course where you learn about proving things and abstraction.

The ludicrous state of solid geometry made me pass over this branch.

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.

There are no sects in geometry.

Geometry is the only science that it hath pleased God hitherto to bestow on mankind.

To expect reason is where the fallacy lies.

No one is beat till he quits, no one is through till he stops. No matter how hard failure hits, no matter how often he drops, a fellow's not down till he lies in the dust and refuses to rise.

Math was my big interest when I was in prep school. I was considering taking math in college, and majoring in it.

We are convinced that the intelligent investor can derive satisfactory results from pricing of either type (market timing or fundamental analysis via price). We are equally sure that if he places his emphasis on timing, in the sense of forecasting, he will end up as a speculator and with a speculator's financial results." And "The speculator's primary interest lies in anticipating and profiting from market fluctuations. The investor's primary interest lies in acquiring and holding suitable securities at suitable prices.

I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.

With five feeble senses we pretend to comprehend the boundlessly complex cosmos, yet other beings with wider, stronger, or different range of senses might not only see very differently the things we see, but might see and study whole worlds of matter, energy, and life which lie close at hand yet can never be detected with the senses we have.

We wish to find the truth, no matter where it lies. But to find the truth we need imagination and skepticism both. We will not be afraid to speculate, but we will be careful to distinguish speculation from fact.

We have the right to lie, but not about the heart of the matter.

Gentlemen are not supposed to tell the truth about their sex lives, nor are ladies, for that matter. Of course Clinton lied - as would anybody in his position.

Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.

I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.