1.** Daniel Bernoulli**

Daniel Bernoulli was a Swiss mathematician and physicist born in Groningen in 1700 into a family of outstanding mathematicians and died in 1782 at age 85. His father Johann (one of the early developers of calculus) had a nephew (Jacob, who was the first to discover the theory of probability), three sons and grandsons who were all great mathematicians. Among them, the most prominent mathematician was his second oldest son Daniel. Johann wanted his son Daniel to study biology and medicine, but not mathematics. Thus, Daniel initially specialized in mathematical biology. Daniel and Leonhard Euler were close friends, and he won the Grand Prize of the Paris Academy about ten times. Daniel Bernoulli has made outstanding achievements in the history of mathematics, he made key contributions in statistics and the theory of equations, developed partial differential equations, discovered and proved an important theorem about trochoids, preceded Fourier in the use of Fourier series, developed a theory of economic risk. However, Daniel is more famous for his important discoveries in mathematical physics and is sometimes called the “Founder of Mathematical Physics”; he created the Bernoulli Principle underlying air flight and the concept that heat is merely molecules of random kinetic energy.

2. **Alexis Claude Clairaut**

The reputation built by the Bernoulli’s and Euler was so high that it almost made it easy to neglect the contributions of other important mathematicians in the field of mathematical physics. In some situations, Euler made an error in his contributions in physics due to rejections of Newton’s theories by some Europeanist in favor of the contradictory theories of Descartes and Leibniz. Other great mathematicians of the mid-18th century that made significant contributions are Alexis Clairaut and d’Alembert.

Alexis Clairaut was a French mathematician, astronomer, and geophysicist born in 1713. Alexis was a prominent Newtonian and a prodigy, at an early age (10 years), he started studying calculus. At age 13, he delivered a math paper and became the youngest person ever elected to the Paris Academy of Sciences. He contributed significantly to differential equations and mathematical physics and developed the idea of skew curves–the earliest precursors of spatial curvature.

As a Newtonian, Alexis supported Newton against the Continental schools and also assisted Newton in translating his work into the French language. Newton’s theory gave different predictions about the earth’s shape (whether the poles were pointy or flattened); Alexis participated in Maupertuis’ expedition to Lapland to measure the polar regions. Their results confirmed Newton theory about the earth’s shape; at high latitudes, the poles appeared to be flattened. Alexis worked on ellipsoid’s theories and the three-body problem, e.g., the moon’s orbit. The moon’s orbit was a mathematical problem, many mathematicians found it very difficult to reconcile and observe the theory. However, Alexis Clairaut was able to resolve this theory by addressing the problem with a rigorous approach than others.

After Euler understood the solution developed by Clairaut, he described it as “the most important and profound discovery that has ever been made in mathematics.” Later on, Clairaut was acclaimed as “the new Thales’ when Halley’s Comet recurred as he foretold. Alexis Clairaut died in 1765.

3. **Jean-Baptiste le Rond d’Alembert**

Jean le Rond d’Alembert was born in France in 1717, he was named after a Parisian church where he was abandoned as a baby. d’Alembert played significant roles in the development of a mathematical technique used to clarify and augment Newton’s Laws of Motions. His D'Alembert's Principle made it possible to clarify Newton’s third law of motion and gave room to express challenges in dynamics with simple partial differential equations; he was able to reduce those equations to simple differential equations through his method of characteristics. He invented some techniques that are currently applied in today’s physics, such as the method of eigenvalues used to solve the resultant linear systems and also the Cauchy-Riemann equations.

D’Alembert was upfront in areas of complex variables and the notions of infinitesimals and limits. His papers on elastic collisions, dynamics, hydrodynamics, vibrating strings, the cause of winds, refraction, celestial motions, and others made his effort more recognized than his older rival, Daniel Bernoulli. d’Alembert must have been the first to describe time as a “fourth dimension.”

In addition, d’Alembert was able to prove that all polynomial has a complex root; currently, this is called the Fundamental Theorem of Algebra, and in France, it is called the D’Alembert-Gauss Theorem. In as much as Gauss was the first person to provide a complete strong proof, d’Alembert’s proof preceded and was almost complete than the proof attempted by Euler. He also made contributions in geometry (anticipated Monge’s Three Circle Theorem) and was the main creator of the major encyclopedia in his time. According to d’Alembert, "The imagination in a mathematician who creates makes no less difference than in a poet who invents." He died in 1783.

**About Author**

Hugh Beaulac is a brainiac who loves maths, physics, history, and programming. Studied at Georgia Institute of Technology and currently works as a content media specialist at MC2 STEM project