Who discovered momentum? I read some text about momentum in Wikipedia, but I didn't find any information who discovered momentum. Is the momentum a philosophic principle?
 A: Although it builds on related earlier ideas, Jean Buridan's notion of impetus is very close to the modern notion of momentum. Here is what he had to say on the matter:

...after leaving the arm of the thrower, the projectile would be moved by an *impetus* given to it by the thrower and would continue to be moved as long as the impetus remained stronger than the resistance, and would be of infinite duration were it not diminished and corrupted by a contrary force resisting it or by something inclining it to a contrary motion

He was very close to defining $p=mv$. Quoting from wikipedia:

Buridan further held that the impetus of a body increased with the speed with which it was set in motion, and with its quantity of matter. 
The answer to your question is a function of how fuzzy you make the notion of momentum. For some range of fuzziness, Buridan is your answer.
A: Pretty sure it was Newton who formulated it mathematically via $F = ma$. But, Wikipedia has a brief timeline of people who thought about it in one form or another.
A: Comments:


*

*Buridan's speculations are interesting and probably contributed to the definition of momentum. Descarte's contribution was probably definitive, but it appears not to have been widely accepted. Newton reports in the Principia that the Royal Society had appointed a committee of enquiry into the matter (which, incidentally, included the architect Sir Christopher Wren). Newton appears to have accepted the report of this committee.

*Newton did not write down the equation F=ma - it was first written down by Euler several decades later. Nor did Newton provide in his published work either a definition or a formula for his "quantity of motion", which is commonly interpreted to be his term for "momentum".  

*The real importance of momentum is that it is a conserved quantity (under the right circumstances). That is why it is so useful. The equation F=ma is a set of second order ordinary differential equations, one for each degree of freedom of the system, This means that, in principle, we need to perform two integrations for each degree of freedom to arrive at the answer. Conservation laws are a way to avoid the first integration by means of a rule of thumb, hence they are sometimes called a "first integral" of the equations. The same is true of energy and of angular momentum. These concepts provide shortcuts to the integration.

*The real importance of energy, momentum and angular momentum is only made evident when one considers moving the physical apparatus by translation, rotation or by performing the same experiment at different times. If the system always displays the same behaviour as before it was moved in either space or time, then its momentum (translations), angular momentum (rotation) and energy (time translation) are conserved. 

*The concepts of mechanics, like those of all other branches of knowledge, were discovered piecemeal, over long periods of time, and through the efforts of very many investigators. Further, the significance of these concepts were not always immediately understood. This is especially true of the concept of momentum. 

*There is nothing "fishy" about physics or the concepts of physics. The difference between the velocity dependence of energy and momentum is easily understood when considering the process of integration of NII. You get another perspective on this same topic by looking at the conservation laws from the point of view of Lagrangian mechanics and Hamiltonian mechanics. 

*The fact that Lagrangian mechanics uses L=T-V rather than the total energy is closely related to the analogous topic in Thermodynamics. L is an energy, just like the total energy. The energy appropriate to a given formulation depends on the nature of the variables that are used in its description. Lagrangian mechanics uses position and velocity as the independent variables. The appropriate energy to extremise under these circumstances is T-V. Consider it to the the "free energy" of the system. Hamiltonian mechanics works with momentum and position as its variables. The appropriate energy to extremise here is the total energy. This is analogous to using the internal energy, the Helmholtz free energy, the enthalpy or the Gibbs free energy in thermodynamics. Routhian mechanics, which uses some velocity and some momentum variables (and so is intermediate between Lagrangian and Hamiltonian mechanics) uses Routhian functions which are the appropriate free energy for those combinations of variables. 

*On the whole, I found most of the above comments interesting and helpful. My thanks to their various authors. It is not useful in a discussion of this kind to make derogatory remarks or slanderous generalisations like "Physicists are unwilling to admit something is fishy". Apart from not being useful, this kind of sentiment can only brand you as disaffectioned (or possibly even loony). Uninformed value judgements like "Energy has a physical meaning (it exists in nature), but momentum is completely made up" are also not helpful. They display ignorance and smug complacency in that ignorance. Both energy and momentum are "made up". They are elements of a mathematical model that we have found successful in describing nature. Further, momentum is as "real" in nature as is energy, as you would find out were you to apply brakes on an icy road. The conservation of momentum as you continue to move with uniform motion in a straight line is very real, as is the destruction of that momentum (force!) when you hit a solid barrier. 
A: Rene Descartes formulated momentum when he was living in Holland.  He was looking to describe mathematically how objects move.  He began with the idea that motion was a conserved property of the universe.  He used collisions to test that idea.  The first mathematical expression was the product of mass and speed.  This seemed to work well for elastic collisions but failed utterly in inelastic collisions.  A student of his offered an observation and Descartes used it to add a directional aspect to speed.  In other words, Descartes tried the product of mass and velocity only to find that it worked well.
Newton took Descartes' work further and from it he developed his Laws of Motion.  Add those laws together and it produces the Law of Conservation of Momentum.  This is where Descartes began.
Energy came much later and its introduction posed a question no one has ever asked openly?  Why are there 2 mathematical forms for moving objects that use the same variables?  One of these, momentum, increases directly with velocity and the other does not [kinetic energy].  This does not make any sense.  Have someone try to explain this and they will only wind up confusing you.  The only answer they can give is that is the way it is based on the mathematics.  Physicists are unwilling to admit something is fishy.
A: At the time of Newton, there was still confusion about the difference between Kinetic Energy and Momentum. 
So, the question should not be "who discovered momentum" - as the inertia of a moving object has been known for a long time. The real discovery was that there are two different types of inertia. I think that this was first sorted out by 
Willem 's Gravesande and Émilie du Châtelet.
There's a recent and good book about the life of Voltaire and Émilie du Châtelet:  Passionate Minds: The Great Love Affair of the Enlightenment.
A: Jean Buridan (1295-1358) discovered impetus, the measure of which is called momentum. In fact, there is one recent physics textbook that defines an SI unit of momentum as the Buridan (1 B = 1 kg m/s).
Buridan wrote:

This impetus would endure forever [ad infinitum] if it were not diminished and corrupted by an opposed resistance or by something tending to an opposed motion.

This sounds very much like Newton's 1st Law, which is really contained implicitly in his 2nd Law, $F=\dot{p}$.
