Math and the Bible

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The Bible was the inspiration for set theory and other breakthroughs in math. The New Testament gave infinity a theological basis that led to an acceptance of it by the secular world, after philosophers had rejected it. The greatest mathematicians, including Bernard Riemann, Georg Cantor, Kurt Gödel, and John von Neumann, were avid readers of the Bible.

Enormous potential exists for additional mathematical discoveries based on insights gleaned from the Bible.

Infinity

The concept of infinity was hotly disputed, and rejected, by Greek mathematicians and philosophers.[1] Aristotle and Pythagoras, for example, both rejected the existence of actual infinity.[2]

The concept of infinity has two daughter concepts: eternity and immortality.

Infinite Time, or Eternity

The full concept of infinite time, or eternity, is unique to the New Testament, which references it often:[3]

Gospels
  • Matthew
    • Matthew 6:19-21: ("Lay not up for yourselves treasures upon the earth, where moth and rust consume, and where thieves break through and steal: but lay up for yourselves treasures in heaven, where neither moth nor rust doth consume, and where thieves do not break through nor steal: for where thy treasure is, there will thy heart be also.")
    • Matthew 13:24-30, 36-43, 49-50: ([P]arables illustrating the nature of the Kingdom of God.)
    • Matthew 18:8-9: ("And if thy hand or thy foot causeth thee to stumble, cut it off, and cast it from thee: it is good for thee to enter into life maimed or halt, rather than having two hands or two feet to be cast into the eternal fire. And if thine eye causeth thee to stumble, pluck it out, and cast it from thee: it is good for thee to enter into life with one eye, rather than having two eyes to be cast into the hell of fire.")
      • Mark 9:43-50: (Humility and brotherly love enjoined. [contains doublet of Matthew 18:8-9])
    • Matthew 24:3-35: (Christ foretells the destruction of the temple, the persecution of his disciples and the signs of His second coming; 24:35: "Heaven and earth shall pass away, but my words shall not pass away.")
      • Mark 13:3-33: (Doublet: Our Lord foretells the destruction of Jerusalem, and his second coming; and exhorts to watchfulness.)
      • Luke 21:5-33: (Doublet: Prophecy of Christ's second coming.)
    • Matthew 25:31-46: (Description of the final judgment; 25:46: "And these shall go away into eternal punishment: but the righteous into eternal life." [eternal punishment in addition to eternal life[4]].)
  • Mark
    • Mark 10:17-31: (Inquiry of a rich man; our Lord's answer, and following discourse.)
  • Luke
    • Luke 10:25-37: (Reply to a question by a lawyer; parable of the good Samaritan.)
  • John
    • John 1:1-3: ("In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made through him; and without him was not anything made that hath been made.")
    • John 6:37-40:
      • ("All that which the Father giveth me shall come unto me; and him that cometh to me I will in no wise cast out
      • For I am come down from heaven, not to do mine own will, but the will of him that sent me.
      • And this is the will of him that sent me, that of all that which he hath given me I should lose nothing, but should raise it up at the last day.
      • For this is the will of my Father, that every one that beholdeth the Son, and believeth on him, should have eternal life; and I will raise him up at the last day.")
    • John 6:68: (Eternal life:[4] "Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life.")
    • John 8:51: ("Verily, verily, I say unto you, If a man keep my word, he shall never see death.")
    • John 10:24-30:
      • ("The Jews therefore came round about him, and said unto him, How long dost thou hold us in suspense? If thou art the Christ, tell us plainly.
      • Jesus answered them, I told you, and ye believe not: the works that I do in my Father's name, these bear witness of me.
      • But ye believe not, because ye are not of my sheep.
      • My sheep hear my voice, and I know them,
      • And they follow me: and I give unto them eternal life; and they shall never perish, and no one shall snatch them out of my hand.
      • My Father, who hath given [them] unto me, is greater than all; and no one is able to snatch [them] out of the Father's hand.
      • I and the Father are one.")
    • John 11:23-27:
      • ("Jesus saith unto her, Thy brother shall rise again.
      • Martha saith unto him, I know that he shall rise again in the resurrection at the last day.
      • Jesus said unto her, I am the resurrection, and the life: he that believeth on me, though he die, yet shall he live;
      • and whosoever liveth and believeth on me shall never die. Believest thou this?
      • She saith unto him, Yea, Lord: I have believed that thou art the Christ, the Son of God, [even] he that cometh into the world.")
    • John 17:1-3: (Eternal life[4]: "These things spake Jesus; and lifting up his eyes to heaven, he said, Father, the hour is come; glorify thy Son, that the son may glorify thee: even as thou gavest him authority over all flesh, that to all whom thou hast given him, he should give eternal life. And this is life eternal, that they should know thee the only true God, and him whom thou didst send, [even] Jesus Christ.")

Pauline letters
  • Romans 6: (The results of the Gospel; the believer made holy by his union with Christ, who frees him from the power of sin. 6:23: "For the wages of sin is death; but the free gift of God is eternal life in Christ Jesus our Lord.")
  • 1 Corinthians 15:34-58: (The Christian doctrine of the resurrection of the dead.)
  • 2 Corinthians 4:12-5:10: (The motives, responsibilities, trials and supports of the apostolic ministry; 5:1: "For we know that if the earthly house of our tabernacle be dissolved, we have a building from God, a house not made with hands, eternal, in the heavens.")
  • Galatians 6:8: ("For he that soweth unto his own flesh shall of the flesh reap corruption; but he that soweth unto the Spirit shall of the Spirit reap eternal life.")
  • Colossians 1:16-17: ("[F]or in him were all things created, in the heavens and upon the earth, things visible and things invisible, whether thrones or dominions or principalities or powers; all things have been created through him, and unto him; and he is before all things, and in him all things consist.")
  • 1 Timothy 1:17: ("Now unto the King eternal, immortal, invisible, the only God, [be] honor and glory forever and ever. Amen.")
  • 1 Timothy 6:12: (Eternal life[4]: "Fight the good fight of the faith, lay hold on the life eternal, whereunto thou wast called, and didst confess the good confession in the sight of many witnesses.")
  • Titus 1:2: ("[I]n hope of eternal life, which God, who cannot lie, promised before times eternal;...")

Other letters from apostles and prophets
  • Hebrews 1:10-12: ("And, Thou, Lord, in the beginning didst lay the foundation of the earth, and the heavens are the works of thy hands: they shall perish; but thou continuest: and they all shall wax old as doth a garment; and as a mantle shalt thou roll them up, as a garment, and they shall be changed: but thou art the same, and thy years shall not fail.")
  • Hebrews 5:9: (Eternal salvation:[4] "[A]nd having been made perfect, he became unto all them that obey him the author of eternal salvation;...")
  • Hebrews 6:2: (Eternal judgment:[4] "[O]f the teaching of baptisms, and of laying on of hands, and of resurrection of the dead, and of eternal judgment.")
  • Hebrews 9:14: (Eternal Spirit:[4] "[H]ow much more shall the blood of Christ, who through the eternal Spirit offered himself without blemish unto God, cleanse your conscience from dead works to serve the living God?")
  • Hebrews 13:7-8: ("Remember them that had the rule over you, men that spake unto you the word of God; and considering the issue of their life, imitate their faith. Jesus Christ [is] the same yesterday and to-day, [yea] and for ever.")
  • 1 Peter 1:3-7, 22-25: (The wonders of redemption; Exhortations to a course of life corresponding to the blessings of the Christian state.)
  • 1 Peter 5:10: ("And the God of all grace, who called you unto his eternal glory in Christ, after that ye have suffered a little while, shall himself perfect, establish, strengthen you.")
  • 2 Peter 3:1-13: (The certainty of the Lord's coming established against the denials of profane scoffers.)
  • 1 John 1:2: (Eternal life:[4]"[A]nd the life was manifested, and we have seen, and bear witness, and declare unto you the life, the eternal [life], which was with the Father, and was manifested unto us;...")
  • 1 John 2:16-17: ("For all that is in the world, the lust of the flesh and the lust of the eyes and the vain glory of life, is not of the Father, but is of the world. And the world passeth away, and the lust thereof: but he that doeth the will of God abideth for ever.")
  • 1 John 2:25: (Eternal life[4] "And this is the promise which he promised us, [even] the life eternal.")
  • 1 John 3:15: (Eternal life[4] "Whosoever hateth his brother is a murderer: and ye know that no murderer hath eternal life abiding in him.")
  • 1 John 5:11-12: ("And the witness is this, that God gave unto us eternal life, and this life is in his Son. He that hath the Son hath the life; he that hath not the Son of God hath not the life.")
  • 2 John 1-2: ("The elder unto the elect lady and her children, whom I love in truth; and not I only, but also all they that know the truth; for the truth's sake which abideth in us, and it shall be with us for ever:")
  • Jude 5-8:
    • ("Now I desire to put you in remembrance, though ye know all things once for all, that the Lord, having saved a people out of the land of Egypt, afterward destroyed them that believed not.
    • And angels that kept not their own principality, but left their proper habitation, he hath kept in everlasting bonds under darkness unto the judgment of the great day.
    • Even as Sodom and Gomorrah, and the cities about them, having in like manner with these given themselves over to fornication and gone after strange flesh, are set forth as an example, suffering the punishment of eternal fire.")
    • ("Yet in like manner these also in their dreamings defile the flesh, and set at nought dominion, and rail at dignities.")
  • Jude 21: (Eternal life:[4] "keep yourselves in the love of God, looking for the mercy of our Lord Jesus Christ unto eternal life.")

Prophecy
  • Revelation 1:17-18: ("And when I saw him, I fell at his feet as one dead. And he laid his right hand upon me, saying, Fear not; I am the first and the last, and the Living one; and I was dead, and behold, I am alive for evermore, and I have the keys of death and of Hades.")
  • Revelation 2:7-11:
    • ("He that hath an ear, let him hear what the Spirit saith to the churches. To him that overcometh, to him will I give to eat of the tree of life, which is in the Paradise of God.
    • And to the angel of the church in Smyrna write: These things saith the first and the last, who was dead, and lived [again]:
    • I know thy tribulation, and thy poverty (but thou art rich), and the blasphemy of them that say they are Jews, and they art not, but are a synagogue of Satan.
    • Fear not the things which thou art about to suffer: behold, the devil is about to cast some of you into prison, that ye may be tried; and ye shall have tribulation ten days. Be thou faithful unto death, and I will give thee the crown of life.
    • He that hath an ear, let him hear what the Spirit saith to the churches. He that overcometh shall not be hurt of the second death.")
  • Revelation 3:5: "He that overcometh shall thus be arrayed in white garments; and I will in no wise blot his name out of the book of life, and I will confess his name before my Father, and before his angels."
  • Revelation 10:5-6 ("And the angel that I saw standing upon the sea and upon the earth lifted up his right hand to heaven, and sware by him that liveth for ever and ever, who created the heaven and the things that are therein, and the earth and the things that are therein, and the sea and the things that are therein, that there shall be delay no longer:...")
  • Revelation 20-22: (Christ's victories and reign—Satan bound; the first resurrection, and millennial kingdom...Satan loosed; his last battle and defeat; the final judgment. Vision of the new creation and the New Jerusalem. Concluding admonitions, warnings and promises.)

To a much lesser extent, and with a narrower meaning, there are a few references to eternity in the Old Testament.

Old Testament
  • Job 38:1-13: (Jehovah's address to Job.)
  • Psalms 9:5-8:
    • ("Thou hast rebuked the nations, thou hast destroyed the wicked; Thou hast blotted out their name for ever and ever.
    • The enemy are come to an end, they are desolate for ever; And the cities which thou hast overthrown, the very remembrance of them is perished.
    • But Jehovah sitteth [as king] for ever: He hath prepared his throne for judgment;
    • And he will judge the world in righteousness, He will minister judgment to the peoples in uprightness.")
  • Psalms 16:10-11: ("For thou wilt not leave my soul to Sheol; neither wilt thou suffer thy holy one to see corruption. Thou wilt show me the path of life: In thy presence is fulness of joy; in thy right hand there are pleasures for evermore.")
  • Psalms 33:10-11: ("Jehovah bringeth the counsel of the nations to nought; He maketh the thoughts of the peoples to be of no effect. The counsel of Jehovah standeth fast for ever, The thoughts of his heart to all generations.")
  • Psalms 48:8,14: ("As we have heard, so have we seen in the city of Jehovah of hosts, in the city of our God: God will establish it for ever.... For this God is our God for ever and ever: He will be our guide [even] unto death.")
  • Psalms 73:24-28:
    • ("Thou wilt guide me with thy counsel, and afterward receive me to glory.
    • Whom have I in heaven [but thee]? And there is none upon earth that I desire besides thee.
    • My flesh and my heart faileth; [But] God is the strength of my heart and my portion for ever.
    • For, lo, they that are far from thee shall perish: Thou hast destroyed all them that play the harlot, [departing] from thee.
    • But it is good for me to draw near unto God: I have made the Lord Jehovah my refuge, that I may tell of all thy works.")
  • Psalms 90:2: "Before the mountains were brought forth, or ever thou hadst formed the earth and the world, even from everlasting to everlasting, thou art God."
  • Psalms 102:25-26: ("Of old didst thou lay the foundation of the earth; and the heavens are the work of thy hands. They shall perish, but thou shalt endure; yea, all of them shall wax old like a garment; as a vesture shalt thou change them, and they shall be changed:...")
  • Psalms 104:5-6: ("Who laid the foundations of the earth, that it should not be moved for ever. Thou coveredst it with the deep as with a vesture; the waters stood above the mountains.")
  • Psalms 119:160: "The sum of thy word is truth; And every one of thy righteous ordinances [endureth] for ever."
  • Psalms 146:5-6: ("Happy is he that hath the God of Jacob for his help, whose hope is in Jehovah his God: who made heaven and earth, the sea, and all that in them is; who keepeth truth for ever;...")
  • Proverbs 8:22-29: (Wisdom described and commended; her promises and warnings.)
  • Lamentations 5:19: "Thou, O Jehovah, abidest for ever; thy throne is from generation to generation."
  • Daniel 7:18: "But the saints of the Most High shall receive the kingdom, and possess the kingdom for ever, even for ever and ever."

Apocrypha (TJB)
  • Ecclesiasticus 42:21: "He has imposed an order on the magnificent works of his wisdom, he is from everlasting to everlasting,..."
  • 2 Maccabees 7:23: "'It is the creator of the world, ordaining the process of man's birth and presiding over the origin of all things, who in his mercy will most surely give you back both breath and life, seeing that you now despise your own existence for the sake of his laws.'"
  • Wisdom 3-5: (The destinies of good and bad men compared; better be barren than have godless children; the premature death of the virtuous man; virtuous men and godless at the judgement. TJB)
  • Wisdom 7:24-26
    • ("[F]or Wisdom is quicker to move than any motion; she is so pure, she pervades and permeates all things.")
    • ("She is a breath of the power of God, pure emanation of the glory of the almighty; hence nothing impure can find a way into her.
    • She is a reflection of the eternal light, untarnished mirror of God's active power, image of his goodness.")

Ancient Greek philosophers did not accept, and indeed often rejected, the notion of a full eternity. Plato was one of the first even to consider the possibility of eternity, but he thought that time was limited to the existence of the material universe (the heavens).[5]

Infinite Nature of God

The word "infinite" is mentioned three times in the text of the King James Version (Job 22:5; Ps 147:5; Nah 3:9), and once in an explanatory footnote (Nah 2:9), all in the Old Testament.[6]

Modern understanding of the full nature of infinity is based on the work of devout Christian Georg Cantor, who studied infinity as a way to understand God better. Several teachings of Jesus (and his faithful contemporaries) explain that infinity is the real nature of God:

  • Matthew 3:9 ("and do not presume to tell yourselves, 'We have Abraham for our father', because, I tell you, God can raise children of Abraham from these stones." [John the Baptist] TJB)
    • Luke 3:8 ("and do not think of telling yourselves, "We have Abraham for our father" because, I tell you, God can raise children for Abraham from these stones." TJB)
  • Matthew 19:26 ("Jesus gazed at them. 'For men' he told them 'this is impossible; for God everything is possible'" TJB)
    • Mark 10:27 ("Jesus gazed at them. 'For men', he said 'it is impossible, but not for God: because everything is possible for God.'" TJB)
    • Luke 1:37 ("For nothing will be impossible with God." [Gabriel] NAS)
  • Matthew 20:1-16 (Parable of the Vineyard Workers)
  • Luke 15:11-32 (Parable of the Prodigal Son)
  • Romans 8:35-39
    • ("Who shall separate us from the love of Christ? shall tribulation, or anguish, or persecution, or famine, or nakedness, or peril, or sword?
    • Even as it is written, For thy sake we are killed all the day long; We were accounted as sheep for the slaughter.
    • Nay, in all these things we are more than conquerors through him that loved us.
    • "For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth,
    • nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord." ASV)
  • 1 Corinthians 1:17-2:16 (Correction of party spirit; Paul's manner of preaching defended)
  • Philippians 3:7-21 (Cautions and counsels; and exhortation to the cultivation of every Christian grace)
  • Colossians 2:2-3: ("It is all to bind you together in love and to stir your minds, so that your understanding may come to full development, until you really know God's secret in which all the jewels of wisdom and knowledge are hidden." TJB)
  • Hebrews 4:13 ("No created thing can hide from him; everything is uncovered and open to the eyes of the one to whom we must give account of ourselves." TJB)
  • 1 John 3:1-3: ("Think of the love that the Father has lavished on us, by letting us be called God's children; and that is what we are. Because the world refused to acknowledge him, therefore it does not acknowledge us. My dear people, we are already the children of God, but what we are to be in the future has not yet been revealed; all we know is, that when it is revealed we shall be like him because we shall see him as he really is. Surely everyone who entertains this hope must purify himself, must try to be as pure as Christ." TJB)
  • Revelation 19:6 ("And I seemed to hear the voices of a huge crowd, like the sound of the ocean or the great roar of thunder, answering, 'Alleluia! The reign of the Lord our God Almighty has begun;...'" TJB) The Biblical title given to God of "Almighty" extends into the New Testament.

(add to list)

Infinite Nature of Jesus

In addition, the concept of infinity is set forth in Hebrews in explaining that Jesus is infinitely superior to angels:[7]

  • John
    • John 8:58 ("Jesus replied: 'I tell you most solemnly, before Abraham ever was, I Am.'" TJB) The Biblical name given to God by Himself and told to Moses ("I Am") extends into the New Testament and portrays God's first essence to be His existence. Thus the naming indicates that if He exists at all in this unique way, He also exists in a way that is essential to existence itself (that is, essential to other things that actually exist, but that don't exist as a result of their first essence and must depend on something else, ultimately, whose first nature is to exist, for existence) as drawn from virtually unlimited possible existences.
    • John 13:31-17:26 (Discourse after Last Supper)
  • Colossians 1:13-20: (Prayer for the fruitfulness and growth in the knowledge of Christ; whose dignity and work are the great subjects of the apostle's ministry.)
  • Hebrews 1:4 ("having become as much superior to angels as the name he has inherited is more excellent than theirs", ESV)

Coherence of Math

Several references exist in the Bible for the concept that mathematics is coherent, inerrant, and unchanging logic, as made possible by God:[8]

  • Hebrews 13:8 ("Jesus Christ is the same yesterday and today and forever.")

Old Testament References to Infinity

There are far fewer references to infinity in the Old Testament than in the New. Here are Old Testament references:[9]

  • Genesis 18:14 ("Is anything too difficult for the Lord? At the appointed time I will return to you, at this time next year, and Sarah shall have a son.")
  • Exodus
    • 3:14: (And God said to Moses, "I AM WHO I AM"; and He said, "Thus you shall say to the sons of Israel, 'I AM has sent me to you.'")
    • 15:18: ("The Lord shall reign forever and ever.")
  • Job
    • 11:7-9: ("Can you discover the depths of God? Can you discover the limits of the Almighty? They are high as the heavens, what can you do? Deeper than Sheol, what can you know? Its measure is longer than the earth, And broader than the sea.")
  • Isaiah 40:28: Do you not know? Have you not heard? The Everlasting God, the LORD, the Creator of the ends of the earth Does not become weary or tired His understanding is inscrutable.
  • Jeremiah 23:24: "Can a man hide himself in hiding places So I do not see him?" declares the LORD "Do I not fill the heavens and the earth?" declares the LORD.
  • Psalm 113:4-6: The LORD is high above all nations; His glory is above the heavens. Who is like the LORD our God, Who is enthroned on high, Who humbles Himself to behold The things that are in heaven and in the earth?
  • Psalm 145:3: Great is the LORD, and highly to be praised, And His greatness is unsearchable.
  • Psalm 147:5: Great is our Lord and abundant in strength; His understanding is infinite.
  • 1 Kings 8:27: "But will God indeed dwell on the earth? Behold, heaven and the highest heaven cannot contain You, how much less this house which I have built!
  • 2 Chronicles 2:6: "But who is able to build a house for Him, for the heavens and the highest heavens cannot contain Him? So who am I, that I should build a house for Him, except to burn incense before Him?
  • 2 Chronicles 6:18: "But will God indeed dwell with mankind on the earth? Behold, heaven and the highest heaven cannot contain You; how much less this house which I have built.

Apocrypha References to Infinity

  • Judith 16:13-17:
'I will sing a new song to my God./Lord, you are great, you are glorious,
Wonderfully strong, unconquerable/May your whole creation serve you!
For you spoke and things came into being,
you sent your breath and they were put together,
and no one can resist your voice.
'Should mountains topple/to mingle with the waves,
should rocks melt/like wax before your face,
to those who fear you,/you would still be merciful.
'A little thing indeed/is a sweetly smelling sacrifice,
still less the fat/burned for you in holocaust;
but whoever fears the Lord/is great for ever.
'Woe to the nations/who rise against my race!
The Lord Almighty/will punish them on judgement day.
He will send fire and worms in their flesh/and they shall weep with pain for evermore.'
  • Esther 13:9-12 (Prayer of Mordecai [portion])
  • 2 Maccabees 8:18 ("'They may put their trust in their weapons and their exploits,' he said 'but our confidence is in almighty God, who is able with a nod to overthrow both those marching on us and the whole world with them.'")
  • Wisdom 11:17-26 (God's forbearance with Egypt and the forbearance explained)
  • Wisdom 12:12-18 (God's forbearance with Canaan explained)
  • Wisdom 16:20-29 (God's dietary and spiritual providence)
  • Ecclesiasticus 15:18-19
For vast is the wisdom of the Lord;/he is almighty and all-seeing.
His eyes are on those who fear them,/he notes every action of man.
  • Ecclesiasticus 16:17-20[10]
Say not: 'I am hidden from God,/And in the height who will remember me?
I shall not be noticed among so illustrious a people,
And what is my soul among the mass of the spirits of all the children of men?'
Behold the heavens and the heavens of the heavens,
And the deep, and the earth;/When He treadeth upon them they stand firm,
And when he visiteth them they tremble.
Yea, the bottoms of the mountains, and the foundations of the world,
When He looketh upon them they tremble greatly.
'In truth, unto me He will not have respect: And as for my ways, who will mark them?
17:15, 17, 19-20 (The divine judge)
23:18-20
39:19-21
42:18-21

References

  1. http://descmath.com/diag/ancients.html
  2. [1] In modern times, such ideas are formalized by the mathematical school of Intuitionism, founded by Luitzen Brouwer.
  3. Multiple references:
    • Bible quotations from American Standard Bible (1901).
    • Biblical paragraphing and capitalized section description by The Religious Tract Society (1861). The Annotated Paragraph Bible, vol. 2.
  4. 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 Non-Annotated Paragraph Bible summary description of verse.
  5. Revisionism tries to credit ancient Greek philosophers for eternity, even though in though in fact they rejected the full concept:
    Concepts of eternity have developed in a way that is, as a matter of fact, closely connected to the development of the concept of God in Western thought, beginning with ancient Greek philosophers;

    Stanford Encyclopedia of Philosophy

    Aristotle believed <need more here, with citations>, and influenced Christian thinkers like Boethius.

  6. http://classic.net.bible.org/dictionary.php?word=Infinite
  7. Biblical quotations are from TJB,ASV,ESV.
  8. Quotations are from ESV.
  9. https://bible.knowing-jesus.com/topics/God, -Infinite - Biblical quotations are from New American Standard Bible.
  10. Transl. R.H. Charles, 1913.

See also