# Is there any mathematical proof or logical reasoning for Newton's laws of motion? [duplicate]

Newtons laws of motion:

1.An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

2.The acceleration of an object depends on the mass of the object and the amount of force applied.

3.Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

What exactly did Newton do to prove his statements? Did he give a mathematical proof or was it experimentally based? Why did so many people accept that his statements will always hold true?

I am so sorry if my question offends you. It's just that I don't know much about the history.

• They can be essentially derived from Neother's theorem using the homogeneity of space (which leads to conservation of momentum, which logically requires those 3 laws to be true) Dec 5, 2021 at 3:12
• I'm pretty sure Isaak Newton didn't derive his laws of motion from Neother's Theorem. Dec 5, 2021 at 3:30
• Dec 5, 2021 at 3:50
• “Why did so many people...” Isn’t there a History of Science SE? Dec 5, 2021 at 5:35