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“Calculus and Science: A Legacy of Christian Theology”
Calculus is a mathematical discipline that is essential to modern science, and it is also
important in other fields of study such as economics and decision theory. Calculus and
science were conceived and birthed in the midst of the theological discussions of the 16th
and 17th centuries. Such theological discussions were the direct result of the
unprecedented dissemination of the Bible that occurred in Western Europe at that time.
Well-known mathematician and physicist Freeman Dyson wrote, “Western science grew
out of Christian theology. It is probably not an accident that modern science grew
explosively in Christian Europe and left the rest of the world behind.”
With the availability of the Bible, great thinkers focused much attention on the ancient
notion of the “two books.” One, the book of revelation or Bible, reveals God’s mind and
will to mankind. The other, the book of nature,
exhibits the wisdom and acts of the Creator. Both
“books” must be totally consistent because they
y = 2x2-10x
have the same author, who is God—the source of
everything. Galileo, the “father of modern science,”
placed great emphasis on this latter point.
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70
60
50
40
Another important thinker of this period was the
17th century theologian and philosopher Descartes.
Descartes attempted to develop a logical
methodology that could be applied to both “books.”
His methodology was particularly applicable to
what we now call the scientific method.
y
y = 2x2
30
20
10
0
-10
y = 2x2+10x
-20
-10
-8
-6
-4
-2
0
x
2
4
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8
10
Examples of Function Graphs
Descartes also made important contributions to
mathematics such as the idea of Cartesian coordinates, which allows one to represent
relationships between variables as pictures referred to as graphs. Such relationships are
called functions, and calculus provides us with very useful ways of relating functions to
one another. Function graphs played a significant role in the later development of
calculus. Consequently, graphing skills are now important to learning calculus.
Two important names from the second half of the 17th century are Leibnitz (from
Germany) and Newton (from England). In their day, both men were rival intellectuals
who contributed greatly to the theological debates of the time. In spite of many
differences of opinion, both men also recognized the authority of the Bible—and are also
PATRICK HENRY COLLEGE PREPARATORY ACADEMY
Phone: 540-338-8290 · Email: [email protected] · Website: www.phcprep.org
Here’s your Patrick Henry College Prep Academy
Free Download from
AP Calculus AB
Enjoy this reading from our course…
credited with revolutionary ideas
in science and mathematics.
Leibnitz and Newton are
recognized as the co-inventors of
calculus, although it is the method
and nomenclature of Leibnitz that
has persisted to the present day.
Function y = 1x
Let ∆x and ∆y be small variations in x and y
∆y =
∆y
x2
-∆x
+ x∆x
dy
-1
-1
limit ∆x = dx = limit x2 + x∆x = 2
x
∆x 0
∆x 0
differentials
derivative of y
Leibnitz’s approach was based on
the concept of the
Leibnitz’s Differential Method Example
“infinitesimal”—which is an
arbitrarily small variation in the
value of a variable. From this point, Leibnitz developed differential and integral
calculus—and we follow this same basic methodology today. The word, “calculus” is
Latin for small stones that were used for counting and calculating in ancient times. Thus,
the word “calculus” is a very appropriate name for this powerful and far-reaching
mathematical discipline based on the differential concept.
If you would like to know more about the AP Calculus AB course,
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