The Discourse on the Method is a philosophical and mathematical treatise published by René Descartes in 1637. Its full name is Discourse on the Method of Rightly Conducting the Reason, and Searching for Truth in the Sciences (French title: Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences). The Discourse on Method is best known as the source of the famous quotation "Je pense, donc je suis" ("I think, therefore I am"), which occurs in Part IV of the work. (The similar statement in Latin, Cogito ergo sum, is found in §7 of Principles of Philosophy.) In addition, in one of its appendices, La Géométrie, is contained Descartes' first introduction of the Cartesian coordinate system.
The Discourse on the Method is one of the most influential works in the history of modern science. It is a method which gives a solid platform from which all modern natural sciences could evolve. In this work, Descartes tackles the problem of skepticism which had been revived from the ancients such as Sextus Empiricus by authors such as Michel de Montaigne. Descartes modified it to account for a truth that he found to be incontrovertible. Descartes started his line of reasoning by doubting everything, so as to assess the world from a fresh perspective, clear of any preconceived notions.
The book was originally published in Leiden in French, together with his works "Dioptrique, Météores e Géométrie". Later, it was translated into Latin and published in 1656 in Amsterdam.
Together with Meditations on First Philosophy (Meditationes de Prima Philosophia), Principles of Philosophy (Principia philosophiae) and Rules for the Direction of the Mind (Regulae ad directionem ingenii), it forms the base of the Epistemology known as Cartesianism.

Organization
"Good sense is mankind's most equitably divided endowment. . .the differences of opinion are not due to difference in intelligence, but merely to the fact that we use different approaches and consider different things. For it is not enough to have a good mind: one must use it well."
In the "building metaphor" laid forth by Descartes, opinions and our own thoughts are the ground upon which our later perceptions are built. Descartes remarks on the sedentary nature of ideas and opinions, saying "I firmly believed that in this way I should much better succeed in the conduct of my life, than if I built only upon old foundations, and leaned upon principles which, in my youth, I had taken upon trust." In other words, the core principle is that one must not seek to build on old foundations of knowledge, but should look for other fertile land to build knowledge upon.

How to think correctly

The Method of Science
The following quote from Discourse on Method presents the four precepts that characterize the Method itself:
1. "The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.
2. The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
3. The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
4. And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted."
By clear and distinct he suggests the evidence of the senses.
The enumerations have in time developed into many forms. He suggested drawing boxes on a paper, and connecting them. This idea has led to a multitude of graphic thinking aids that we use today.

The four precepts
The following three maxims were adopted by Descartes so that he could effectively function in the "real world" while experimenting with his method of radical doubt. They formed a rudimentary belief system from which to act before he developed a new system based on the truths he discovered using his method.
Descartes uses the analogy of tearing down the house to its foundation in order to build a secure edifice (He even extends the analogy to move next door into a house of morality, while his own house is being rebuilt). The foundation he reveals appears to have three parts.

Obey the laws and customs of my country and religion
Be as firm and resolute in my actions as I was able
Endeavor always to conquer myself rather than fortune, and change my desires rather than the order of the world, and in general, accustom myself to the persuasion that, except our own thoughts, there is nothing absolutely in our power; so that when we have done our best in things external to us, all wherein we fail of success is to be held, as regards us, absolutely impossible. Proof of God and the Soul
Here he describes how he in other writings discusses the idea of laws of nature, of the sun and stars, the idea of the moon being the cause of ebb and flood, on gravitation, going to examine light and fire, and goes on to medicine, the motion of the blood in the heart and arteries. He describes that these motions seem to be totally independent of what we think, and concludes that our bodies are separate from our soul.
He does not seem to distinguish between mind, spirit and soul, which are identified as our faculty for rational thinking.Hence the term "I am thinking , therefore I am." All three of these words (particularly "mind" and "soul") can be identified by the single French term âme.

Experiments
One of the practical methods was to order the objects in different ways on paper to make them easy to see clearly. This became the basis of the Cartesian coordinate system, the Histogram, modern mathematical heuristics, and Analytic geometry. These ideas, among other methods of science, influenced Isaac Newton and Gottfried Leibniz in their development of calculus.
The most important influence, however, was the first precept, which states, in Descartes words,"[To]never to accept anything for true which I did not clearly know to be such". This new idea of skepticism influenced many to start finding out things for themselves rather than relying solely on authority. The idea as such may have been the starting point for the development of modern science.
This skepticism not only influenced the "hard" sciences, but is considered the start of modern philosophy. Later philosophers adopted Descartes's doubt with great fervor. Most prominently, David Hume doubted the concept of causality and was unable to "clearly know" it to be true.