Appendix B: Check Your Understanding of the Theistic View of Mathematics

“For from Him all things come, through Him all things live, and for Him all things exist. Glory to Him forever! Amen.” Mathematics comes from Him, lives through Him, and exists for Him.

“For the invisible things of Him from the creation of the world are clearly seen, being understood by the things which are made, even His eternal power and Godhead, so they are without excuse.” Since mathematics is the language fabric of the creation, it clearly reflects His eternal power and Godhead (infinity).

“But we all, with unveiled face, beholding as in a glass the glory of the Lord, are changed into the same image, from glory to glory, even as by the spirit of the Lord.” As we behold the glory of God reflected in mathematics, the Holy Spirit conforms us, from one degree of glory to another, to the image of Jesus Christ.

“Beloved, now we are the sons of God, and it doth not yet appear what we shall be, but we know that when He shall appear, we shall be like Him, for we shall see Him as He is.” When we see Christ face to face we shall be like Him. Now, as we behold His reflected glory in mathematics, we should be becoming like Him.

“For whom He did foreknow He did also predestinate to become conformed to the image of His Son, that He might be the firstborn among many brethren.” We take part in fulfilling our destiny as Christians when we behold God’s glory reflected in mathematics.

“He is the reflection of God’s glory and the perfect representation of His being, and continues to uphold the universe by His mighty word.” The only universal language ever discovered is mathematics.

Mathematics, an entity which always exists in the mind of God, is for us the universal expression of His creative and sustaining word of power.

The nature of mathematics is to reveal God; the purpose is to glorify God.

The two basic reasons to study mathematics are to behold the glory of God reflected there, and to implement His command to subdue and replenish the earth, and to take dominion over it.

The two characteristics of mathematics are its unity and its application to nature.

Christians become like Christ by beholding His glory; His glory is reflected in mathematics.

“So then faith cometh by hearing, and hearing by the word of God.” The spiritual sight (faith) we need to behold God’s glory reflected in mathematics comes from the word of God.

What are the assumptions? What are the consequences of the assumptions? Are the consequences realistic? (Can you live with them?) Or: What are the assumptions? What are the facts? What are the conclusions?

Two attributes are infinity and power.

One example is infinitely many infinite sets of infinite decimals between infinitely many pairs of infinite decimals on the infinite number line.

One example is solving equations simultaneously; God has given us a mechanism which searches through an infinite set of possible solutions and quickly picks the right ones, or indicates that there are none. Another example is a rocket to the moon, not possible without mathematics.

Some unifying ideas are: sets, vectors, and functions. We expect this unity because mathematics is an entity which comes from one person, God.

We know (by faith we understand) because we assume the Bible is true, and the Bible states that everything came from God.

Two values are: to be sure we are dealing with true mathematics and not some human’s vain imagination, and to learn to carry out God’s command to subdue and replenish the earth and take dominion over it.

The basic value of studying mathematics is that we are conformed to the image of Christ by the power of the Holy Spirit as we see the glory of God reflected in what we are studying.

Mathematics is an abstraction (or model) of nature, which man obviously did not invent. So many different people in different parts of the world at different times contributed to mathematical thought that we would expect it to be fragmented and disjointed; instead, there is unity and universality. Simultaneous discoveries of the same concept indicate there is something there which man searches out but does not invent. Applications to nature which come from purely cerebral activity indicate that mathematics is the language of the cosmos.

It demonstrates the unity between geometry and algebra which we expect to find because they both are the thinking of God.

If it is truly mathematics, it will be an abstraction (model) from the physical creation, or it will be an application to the physical creation.

We sometimes wait many years after an idea surfaces before we see the application.

Remind him how dangerous it is to refer to God’s thinking as “junk,” and refer him to Numbers 19 and 20 above.

Mathematics is the “glass”
Romans 1:20

We look for the revelation of God’s glory implicitly in mathematics; not for an object lesson. Also, it is dangerous to say that anything is “like God.”

Riemann, Kronecker, Cauchy, Pascal, Newton, Hermite, Cayley, Cantor, Euler.

No, neither can it be proved that mathematics is the thinking of man. We assume it came from God, and we are gratified that the consequences of this assumption are realistic.

Mathematics has unity and has applications to nature, neither of which are true of art.

Mathematics is the entity which originated in the mind of God; it is the language of the universe. “Mathematical” refers to a logical process; each statement is inferred from the previous one. Mathematics is always mathematical, but a mathematical (valid) display may or may not be mathematics (truth).

Some people have tried to argue that mathematics is only a man-made game (God not needed) by presenting a logically valid argument from an unrealistic major premise to a ridiculous conclusion. The truth of a conclusion depends not only on a valid argument, but also on the truth of the major premise (assumption).