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Brook Taylor (1685-1731) was one of the earliest advancers of the field of calculus. He is perhaps best known for the theorem and mathematical series named after him, as well as his mathematical coverage of the theory of the transverse vibrations of strings.

Brook was born into an aristocratic family in Middlesex, England, the grandson of a prominent member of Oliver Cromwell's Assembly. His family was on the fringes of nobility and were financially well off; as a result, young Brook received an excellent well-rounded education. Brook Taylor, besides his mathematical talents, was also an accomplished musician and painter.

Brook entered Cambridge in 1703 with a good grounding in classics and mathematics, and his interests quickly led toward mathematics. He graduated with letters in mathematics in 1709 and a paper already written, although it wouldn't see publication until 1714.

In 1712, Taylor was elected to the Royal Society, mostly based on his expertise as it was known to other Society members (through private discussions and letters) rather than on his published results. In 1714, he finally published his first paper, a mechanics paper which discussed the problem of the center of oscillation in a body.

In 1715 Taylor published a book (Methodus Incrementorum Directa et Inversa) which contained his famous theorem, which essentially states that any function can be described by expanded powers of it. Here is roughly what it looks like:

```                           h^2
f(x+h) = f(x) + h*f'(x) + ----- * f"(x) + ....
2!
```

This series of functions is also often known as the Taylor series. It is one of the fundamental principles of multidimensional calculus and is perhaps the work that Taylor is best remembered for.

This book also discussed his well known theory of the transverse vibrations of strings, which basically states that the number of half vibrations in a second can be numerically described by the following:

```(DP/LN)^(1/pi)
where
D = length of a second's pendulum (in simple harmonic motion)
L = length of the string
N = weight of string
P = weight which stretches it
```

This equation helped to describe a physical phenomenon that had baffled mathematicians and physicists for years.

Taylor eventually served as Secretary of the Royal Society for four years and would publish many more papers, eventually retiring in 1723 in poor health. He died in 1731 in London, leaving behind several momentous achievements in calculus and mathematical physics.

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