“God created the natural numbers; all else is the work of man.” This remark, one of the more famous quotations in the history of mathematics, is attributed to Leopold Kronecker, brilliant 19th century German mathematician. Since it seems to minimize God and exalt man, this quotation is likely to alienate the Christian, at least when he first hears it. Indeed, that was my reaction, and as a matter of fact I still do not like the sound of it out of context because the impression it leaves seems contrary to the emphasis of Scripture. Not knowing the full intent or motives of the author, I believe we should be careful not to be critical of Kronecker by reading into this statement all kinds of anti-Christian thoughts or bias. Tn fact it appears that he had the opposite of anti-Christian bias, according to E. T. Bell, noted mathematics historian. “Among other things Kronecker imbibed from Werner was a liberal draught of Christian theology, for which he acquired a lifelong enthusiasm. With what looks like his usual caution, Kronecker did not embrace the Christian faith till practically on his deathbed when,…, he permitted himself to be converted from Judaism to evangelical Christianity in his sixty-eighth year.”1
Kronecker in effect said that there is creation by the mind of man in the world of mathematics. Now there are some Christians, even in Christian education, who feel that we should not use that terminology in reference to man. They are jealous for the glory of God, emphasizing the Creator-creature relationship against various forms of heresy. Thus they say that creation is a uniquely divine activity, and consequently we should not speak of such activity by man the creature. Now is this a sound Christian position?
Surely we would agree that only God creates ex nihilo, i.e., in the original, primary sense; but is this the only sense in which God creates? Is there no sense in which we may properly speak of creation by man? Is it contrary to Scripture and must we therefore refrain from saying that man creates?
Biblical Usage
It is helpful to consider Biblical usage in this connection. The Hebrew word bara’, which is usually translated by some form of the verb “create,” means to shape and is used in many places in addition to Genesis 1:1, always of divine activity. However it is very clear that it does not always refer to what is usually thought of as the original ex nihilo creation. Genesis 1:27 uses the word in reference to woman in whose creation material was used. Many times individuals are referred to as created by God, obviously referring to their conception, formation or birth (Ezekiel 21:30; 28:13, 15; Malachi 2:10; Ecclesiastes 12:1). This word bara’ is applied not only to what we might call secondary creation (in which material is used), but also to a product of God’s activity which came via human agency in a natural way. either the meaning of the word nor its contextual usage restricts it to original ex nihilo creation.
The Hebrew word yatsar is usually translated “form,” and is used of activity by man as well as God. It too is used of God’s activity which is not ex nihilo creation, and furthermore has the same meaning as bara’ in the parallelism of Isaiah 43:1, 7. It is used of the human activity of the potter with clay, the carver of wood, and quite significantly of the forming of thought (even though evil) in Psalm 94:20. The significance of this is that the results of such action need not be physical objects, but can be ideas in the mind.
Another Hebrew word, ‘asah, has many meanings but is often translated “make,” and is used of both God and men many times. In Genesis 1:7, 16, 25, 26 it is clearly used as a synonym for bara’. Moreover, in Isaiah 45:7 it is used in parallelism with bara’ as is also the verb yatsar. In Genesis 5:1 it occurs in parallelism as a synonym of bata’. Referring to men it is used of making the cherubim, a candlestick, images, a coat, and many other things.
There is nothing sacrosanct about the English word “create” and there is no reason to restrict it to translate only the verb bara’. In view of the incomplete evidence above, other verbs could just as properly be translated by “create.” Furthermore there is no Scriptural reason not to use the word “create” of the similar activity of men. Yes, there is a real and proper sense in which we can refer to creation by man. He brings into existence things which did not previously exist as such. He brings to the knowledge of mankind new thoughts. He forms ideas and products not previously known to men. (We must remember that God is said to create that which actually came into being through human activity in a very natural way.)
Man’s Creative Activity
Man’s creative activity often involves the discovery of things built into the nature of the universe by God. Can we also refer to the products of man’s creation as the creation of God, or is God’s role minimized or neglected when we speak of creation by man, as is suggested by Kronecker’s statement out of context? Ultimately in a broad and general sense we can speak of the products of man’s creation as the creation of God. We speak, after all, of the world as it now is as being created by God when as a matter of fact is many respects its present form is the result of man s work. God has made man, his mind and his faculties, with all their potential. God is absolutely sovereign and omniscient as the Creator and controller of the universe. He does not learn from man. For example, God did not learn nor become aware of new mathematics when man created it. In the broadest sense, God is the author of all and can be said to be the Creator of mathematics (and other things) without denying man’s creativity directly. Men should be properly commended for creative activity, and God should be praised thereby. We can give credit to creative men and still say to God, “How great thou art!”
There is, then, a good and proper sense in which we speak of human creative activity in a way which is quite consistent with the Scriptural view of the Triune God. As for Kronecker’s statement, we ned not and in fact should not discard it, even though it may have a crass sound to the Christian who believes “soli Deo gloria.” Many people involved in mathematics interpret his statement to mean that the mind of man is naturally endowed with the ability to comprehend the concept of what we often call the counting numbers (namely, [1, 2, 3, 4, 5, 6, 7 , …]), while other number systems are the result of the creativity of man. Mathematically speaking there is a basically important truth set forth in the Kronecker statement. It is that beginning with these counting numbers (or natural numbers) it is possible for the mathematician to construct other number systems; from the naturals the mathematician can construct the integers (namely, [… –4, –3, –2, –1, 0, 1, 2, 3, 4, …], what the layman usually thinks of as positive whole numbers, negative whole numbers and zero}; from the integers he can go to the rationals (what the layman usually thinks of as all possible fractions, i.e., with numerator being an integer and denominator a non-zero integrity; from the rationals he goes to the real numbers; from the reals he can move to the complex numbers and beyond. In the rigorous construction of these other number systems beginning with the naturals, there is genuine human creativity. Obviously creativity by man pervades not only mathematics, but science, literature, music, art, indeed all of culture. It is not insignificant that Bell says of Kronecker, “Music he declared when he was an old man, is the finest of all the fine arts, with the possible exception of mathematics, which he likened to poetry…”2
Christian Education is Creative
We should not speak of human creativity reluctantly; we should not simply be willing to use the language. Rather we should strongly encourage it and do all in our power to develop it in ourselves and others. This should be an integral part of good education. In fact it must be such an integral part for if it is lacking then the education by my definition is not good, at least not good enough. Certainly, if anyone should promote and encourage man’s creative activity, it should be the Christian. Especially this should be the case in Christian education, for such education must be good education; indeed it must strive to be the best education, and it cannot approach this goal without a good emphasis upon creativity in the students.
It is a tragic shame and disgrace that so much of what has been called Christian education has not been like this, but rather has overemphasized a unidirectional communication of a body of knowledge from teacher to student. The teacher gives, the student receives. Sadly it has been too often the case that such so-called Christian education has (like much of the church) failed to distinguish between true conservativism and dead traditionalism, and has continued to teach “like the good old days” with the authoritarian schoolmaster-type pedagogue communicating a vast collection of facts to quiet and (hopefully) receptive students. No doubt this has been a consequence (but not a necessary one) of Ii he Christi an view of Scripture and a body of absolute truth to be proclaimed and received. This type of stilted and boring education need not be, and should not be in Christian education. A proper emphasis upon human creativity (student creativity, to be specific) is perfectly consistent with the Christian view of God and truth. In fact it is not only consistent; something is wrong if it is missing. If we have a sound view of Christianity and man’s creative activity in relation to it, then this should permeate our entire Christian educational process and methodology.
1. E. T. Bell, Men of Mathematics, New York, 1937, p. 467.
2. Ibid, p. 468.
Mr. Verno, a graduate of Westminster Seminary, is professor of mathematics at Westchester College, Pennsylvania.
Kronecker in effect said that there is creation by the mind of man in the world of mathematics. Now there are some Christians, even in Christian education, who feel that we should not use that terminology in reference to man. They are jealous for the glory of God, emphasizing the Creator-creature relationship against various forms of heresy. Thus they say that creation is a uniquely divine activity, and consequently we should not speak of such activity by man the creature. Now is this a sound Christian position?
Surely we would agree that only God creates ex nihilo, i.e., in the original, primary sense; but is this the only sense in which God creates? Is there no sense in which we may properly speak of creation by man? Is it contrary to Scripture and must we therefore refrain from saying that man creates?
Biblical Usage
It is helpful to consider Biblical usage in this connection. The Hebrew word bara’, which is usually translated by some form of the verb “create,” means to shape and is used in many places in addition to Genesis 1:1, always of divine activity. However it is very clear that it does not always refer to what is usually thought of as the original ex nihilo creation. Genesis 1:27 uses the word in reference to woman in whose creation material was used. Many times individuals are referred to as created by God, obviously referring to their conception, formation or birth (Ezekiel 21:30; 28:13, 15; Malachi 2:10; Ecclesiastes 12:1). This word bara’ is applied not only to what we might call secondary creation (in which material is used), but also to a product of God’s activity which came via human agency in a natural way. either the meaning of the word nor its contextual usage restricts it to original ex nihilo creation.
The Hebrew word yatsar is usually translated “form,” and is used of activity by man as well as God. It too is used of God’s activity which is not ex nihilo creation, and furthermore has the same meaning as bara’ in the parallelism of Isaiah 43:1, 7. It is used of the human activity of the potter with clay, the carver of wood, and quite significantly of the forming of thought (even though evil) in Psalm 94:20. The significance of this is that the results of such action need not be physical objects, but can be ideas in the mind.
Another Hebrew word, ‘asah, has many meanings but is often translated “make,” and is used of both God and men many times. In Genesis 1:7, 16, 25, 26 it is clearly used as a synonym for bara’. Moreover, in Isaiah 45:7 it is used in parallelism with bara’ as is also the verb yatsar. In Genesis 5:1 it occurs in parallelism as a synonym of bata’. Referring to men it is used of making the cherubim, a candlestick, images, a coat, and many other things.
There is nothing sacrosanct about the English word “create” and there is no reason to restrict it to translate only the verb bara’. In view of the incomplete evidence above, other verbs could just as properly be translated by “create.” Furthermore there is no Scriptural reason not to use the word “create” of the similar activity of men. Yes, there is a real and proper sense in which we can refer to creation by man. He brings into existence things which did not previously exist as such. He brings to the knowledge of mankind new thoughts. He forms ideas and products not previously known to men. (We must remember that God is said to create that which actually came into being through human activity in a very natural way.)
Man’s Creative Activity
Man’s creative activity often involves the discovery of things built into the nature of the universe by God. Can we also refer to the products of man’s creation as the creation of God, or is God’s role minimized or neglected when we speak of creation by man, as is suggested by Kronecker’s statement out of context? Ultimately in a broad and general sense we can speak of the products of man’s creation as the creation of God. We speak, after all, of the world as it now is as being created by God when as a matter of fact is many respects its present form is the result of man s work. God has made man, his mind and his faculties, with all their potential. God is absolutely sovereign and omniscient as the Creator and controller of the universe. He does not learn from man. For example, God did not learn nor become aware of new mathematics when man created it. In the broadest sense, God is the author of all and can be said to be the Creator of mathematics (and other things) without denying man’s creativity directly. Men should be properly commended for creative activity, and God should be praised thereby. We can give credit to creative men and still say to God, “How great thou art!”
There is, then, a good and proper sense in which we speak of human creative activity in a way which is quite consistent with the Scriptural view of the Triune God. As for Kronecker’s statement, we ned not and in fact should not discard it, even though it may have a crass sound to the Christian who believes “soli Deo gloria.” Many people involved in mathematics interpret his statement to mean that the mind of man is naturally endowed with the ability to comprehend the concept of what we often call the counting numbers (namely, [1, 2, 3, 4, 5, 6, 7 , …]), while other number systems are the result of the creativity of man. Mathematically speaking there is a basically important truth set forth in the Kronecker statement. It is that beginning with these counting numbers (or natural numbers) it is possible for the mathematician to construct other number systems; from the naturals the mathematician can construct the integers (namely, [… –4, –3, –2, –1, 0, 1, 2, 3, 4, …], what the layman usually thinks of as positive whole numbers, negative whole numbers and zero}; from the integers he can go to the rationals (what the layman usually thinks of as all possible fractions, i.e., with numerator being an integer and denominator a non-zero integrity; from the rationals he goes to the real numbers; from the reals he can move to the complex numbers and beyond. In the rigorous construction of these other number systems beginning with the naturals, there is genuine human creativity. Obviously creativity by man pervades not only mathematics, but science, literature, music, art, indeed all of culture. It is not insignificant that Bell says of Kronecker, “Music he declared when he was an old man, is the finest of all the fine arts, with the possible exception of mathematics, which he likened to poetry…”2
Christian Education is Creative
We should not speak of human creativity reluctantly; we should not simply be willing to use the language. Rather we should strongly encourage it and do all in our power to develop it in ourselves and others. This should be an integral part of good education. In fact it must be such an integral part for if it is lacking then the education by my definition is not good, at least not good enough. Certainly, if anyone should promote and encourage man’s creative activity, it should be the Christian. Especially this should be the case in Christian education, for such education must be good education; indeed it must strive to be the best education, and it cannot approach this goal without a good emphasis upon creativity in the students.
It is a tragic shame and disgrace that so much of what has been called Christian education has not been like this, but rather has overemphasized a unidirectional communication of a body of knowledge from teacher to student. The teacher gives, the student receives. Sadly it has been too often the case that such so-called Christian education has (like much of the church) failed to distinguish between true conservativism and dead traditionalism, and has continued to teach “like the good old days” with the authoritarian schoolmaster-type pedagogue communicating a vast collection of facts to quiet and (hopefully) receptive students. No doubt this has been a consequence (but not a necessary one) of Ii he Christi an view of Scripture and a body of absolute truth to be proclaimed and received. This type of stilted and boring education need not be, and should not be in Christian education. A proper emphasis upon human creativity (student creativity, to be specific) is perfectly consistent with the Christian view of God and truth. In fact it is not only consistent; something is wrong if it is missing. If we have a sound view of Christianity and man’s creative activity in relation to it, then this should permeate our entire Christian educational process and methodology.
1. E. T. Bell, Men of Mathematics, New York, 1937, p. 467.
2. Ibid, p. 468.
Mr. Verno, a graduate of Westminster Seminary, is professor of mathematics at Westchester College, Pennsylvania.