Mydorge was born in Paris to one of the wealthiest families in France. He was educated at the Jesuit College of La Flèche and subsequently trained as a lawyer, before embarking on a legal and administrative career. After serving as conseiller to the court of the Grand Châtelet, he became treasurer of the généralité of Amiens, the collector general being a direct agent of the king. Mydorge's chosen employment allowed him sufficient time to combine public office with the life of a savant. Residing in what remained of the ancient Palais des Tournelles, he first met Descartes around 1625, becoming one of his most faithful friends and helping to establish his reputation in Paris. The mathematician Claude Hardy, a leading figure in the scientific circles around Mersenne, Roberval, and Étienne Pascal, lodged with him while he was producing his edition of Euclid's Elements.

Mydorge shared with Descartes a strong interest in optics and the nature of vision. It is well known that in order to promote his friend's investigations on these topics, he commissioned the production of innumerable parabolic, hyperbolic, oval, and elliptic lenses, reputedly spending in excess of 100,000 écus on optical instruments over the years. Both men were interested particularly in refraction, and when Descartes, independently of Snell, discovered the law of refraction, he persuaded Mydorge to have a hyperbolic glass made in order to test his discovery. It is possible that Mydorge contributed to the results that Descartes achieved, although his approach to refraction differed fundamentally from the law published in Dioptrics, which employs the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

Mydorge's first major work was the Examen du livre des Récréations mathématiques, published in 1630. As the title suggest, it was a work on recreational mathematics and was effectively a critique of Laurechon's book on the theme. However, it was through his work on conic sections that Mydorge made the greatest scientific impact. His motivation for these studies came from his investigations on catoptrics, the optics of mirrors. While employing ancient techniques in dealing with conics, he achieved considerable success in simplifying the proofs of Apollonius.