Emilie du Châtelet (1706-1749) was an important person during the Enlightenment. She made great contributions to physics and math. She worked hard to connect theory and practical uses in science. Here are some of her notable achievements:

1. Translation and Commentary: Du Châtelet translated Isaac Newton's "Principia Mathematica" into French. She also added her own helpful notes. Finished in 1756, this version is still considered the main French translation today. Her work made complicated scientific ideas easier for many people to understand across Europe.

2. Energy Conservation: Du Châtelet worked on the "principle of conservation of energy." She came up with the formula for kinetic energy, which is the energy of moving objects. It says that kinetic energy depends on the mass of the object and the speed at which it is moving. The formula is:

   $KE = \frac{1}{2} mv^2$

   In this formula, $m$ is the mass and $v$ is the speed. This idea became really important for future discoveries in science.

3. Critique of Descartes: Du Châtelet disagreed with the ideas of another thinker, Descartes. She believed that movement wasn't just about force but also included energy. This was a new way of thinking for her time.

4. Promoting Female Scholarship: As one of the few female scientists in the 18th century, Du Châtelet not only helped advance science but also inspired future women scholars.

Even though she hasn’t always received recognition, her work shows how important women have been in science. Back then, only about 20% of people involved in scientific discussions were women. Du Châtelet has made a lasting impact and is recognized as a key figure in the development of modern science.