Final answer:
The person in question who lived from 1623 to 1662 and has made significant contributions to mathematics, science, and philosophy is Blaise Pascal (Option 4). His work in hydrodynamics, mathematics, and religious philosophy makes him a prominent figure of his time.
Step-by-step explanation:
The individual who lived from 1623 to 1662 and was a renowned mathematician, scientist, philosopher, and Christian thinker is Blaise Pascal. Option 4 is the correct answer. His contributions spanned various fields, including the invention of an early mechanical calculator, experimentation with fluids which led to the formulation of Pascal's law in hydrodynamics, and his famous wager argument related to faith in God. He was not only a figure in mathematics and physics but also a significant contributor to the philosophy of religion.
Rene Descartes, Isaac Newton, and Galileo Galilei were other seminal figures in the development of modern science and mathematics. However, their lifespans do not align with the dates provided. Galileo Galilei (1564-1642) was an earlier pioneer of modern science, especially known for his use of the telescope and contributions to astronomy. Isaac Newton (1643-1727) is renowned for his laws of motion and gravity, which formed a foundation for classical mechanics.