Series

Christian Mathematicians – Leibniz

joshwilkerson14 Comments

By Steve Bishop

(Disclaimer: The views expressed by guest authors do not necessarily reflect those of GodandMath.com. Guest articles are sought after for the purpose of bringing more diverse viewpoints to the topics of mathematics and theology. The point is to foster discussion. To this end respectful and constructive comments are highly encouraged.)

Gottfried Wilhelm Leibniz (1646-1716) was born in Leipzig. He was a rationalist in that he thought that all knowledge was based on logic. As Herbert Breger in ‘God and Mathematics in Leibniz’s Thought’ in Mathematics and the Divine ed. Teun Koetsier and Luc Bergmans (Elsevier, 2005) puts it:

Leibniz believed in the God of Christianity and he also had an extraordinarily high esteem for reason and its capabilities.

Mathematics Developed

Leibniz discovered calculus at the same time as Newton. This raises an interesting question: why did they discover it at the same time? where there any cultural influences that shaped their thoughts?

The notation we use for differential and integral calculus – dx and the elongated ‘s’ are Leibniz’s. He also gave us the terms ‘function’ and ‘coordinates’ as well as the symbols = for ‘equals’ and x for ‘product’.

Theology and Apologetics

He also devoted much time and energy to theology and apologetics.

In 1709 he attempted to improve the ontological argument for God and in 1710 His Theodicy, or “Vindication of the Justice of God“, was published.  It attempted to justify the existence of God with the existence of evil.

Leibniz also attempted to provide a proof for God’s existence. He wrote, “The first question which should rightly be asked is this: why is there something rather than nothing?”

George MacDonald Ross in Leibniz Oxford University Press (Past Masters)  1984 writes:

Leibniz’s solution had two parts. The first was to admit that the universe was indeed imperfect, but to point out that its imperfection was logically necessary in order to preserve its distinctness from God, the only perfect being. God could not be blamed for failing to contravene the laws of logic. The other part of his answer was to say that, although the universe was not perfect, it was the best possible – it was as perfect as it could be without collapsing back into God himself. Consequently, to blame God for creating this universe as he did would be tantamount to saying that he should not have created anything at all.

His argument has been framed as follows:

  1. Every existing thing has an explanation of its existence, either in the necessity of its own nature or in an external cause.
  2. If the universe has an explanation of its existence, that explanation is God.
  3. The universe exists.
  4. Therefore, the universe has an explanation of its existence (from 1, 3)
  5. Therefore, the explanation of the existence of the universe is God (from 2, 4)

He maintained that that if God did not exist, not only nothing else would exist, but there would be nothing possible either.

Resources for the study of Leiniz are available here http://www.philosophypages.com/ph/leib.html

Previous Entries in this Series:

Christian Mathematicians – Euler

Steve Bishop is the compiler of A Bibliography for a Christian Approach to Mathematics and the author of several articles on the relationship between faith and math. Look for future posts from him in this series on Christian Mathematicians.

Christian Mathematicians – Euler

joshwilkerson16 Comments

By Steve Bishop

(Disclaimer: The views expressed by guest authors do not necessarily reflect those of GodandMath.com. Guest articles are sought after for the purpose of bringing more diverse viewpoints to the topics of mathematics and theology. The point is to foster discussion. To this end respectful and constructive comments are highly encouraged.)

 

Leonhard Euler (1707-1783)

 

Euler was a committed Christian and, apparently, a biblical literalist as well as being (arguably) one of the greatest mathematicians ever – he was certainly the most prolific (apart from perhaps Paul Erdos).

According to one website (condensed from E T Bell’s Men of Mathematics):

Euler remained a Christian all of his life and often read to his family from the Bible. One story about his religion during his stay in Russia involved the atheistic philosopher Diderot. Diderot had been invited to the court by Catherine the Great, but then annoyed her by trying to convert everyone to atheism. Catherine asked Euler for help, and he informed Diderot, who was ignorant of mathematics, that he would present in court an algebraic proof of the existence of God, if Diderot wanted to hear it. Diderot was interested, and, according to De Morgan, Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: “Sir, (a + bn) / n = x , hence God exists; reply! ” Diderot had no reply, and the court broke into laughter. Diderot immediately returned to France.

Leonhard was born into a Calvinist family and his father, Paul, was a minister in the church as was his grandfather. Euler’s father wanted him to follow him into the church. However, being a good Calvinist he realised that one could serve God through mathematics as well as theology and seeing his son’s ability in and passion for mathematics allowing him to pursue mathematics.

Euler always held an interest in theology as well as mathematics. For him mathematics gave insight into God’s good creation.

Eulogy of Euler by Nicolas Fuss:

He was entirely imbued with respect for religion and his piety was sincere and his devotion was full of fervor. He fulfilled with the greatest detail all the duties of a Christian. He loved everyone, and if he felt stirrings of indignations it was against those enemies of religion, especially against the declared apostles of atheism that he made a stand in the defense of the Revelation against the objections of atheists in a work which was published in Berlin in 1747.

Dan Graves in his Scientists of Faith has this to say of Euler:

Euler retained his firm Calvinist beliefs throughout life, holding daily prayer and worship in his home and sometimes preaching.

Euler was one of the first inventors of the number game Suduko. Though he called it Latin squares.

He introduced the letter e to represent the base of natural logs, f(x) to denote functions,and made countless contributions to number theory and graph theory, most notably he showed that the Koinisberg bridge problem was unsolvable.

His name is associated with angles, approximation, circles, cycle, criterion, graphs, operator’s, polynomials, pseudo primes, … and Euler’s identity: said to be the most beautiful formula in the world.

And let’s not forget:

V – E + F = 2

Euler was able to serve his God through his mathematics.

Also on Euler:

Steve Bishop is the compiler of A Bibliography for a Christian Approach to Mathematics and the author of several articles on the relationship between faith and math. Look for future posts from him in this series on Christian Mathematicians.

Beyond Practicality

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Here is a link to the presentation I am giving at the 2012 Joint Mathematics Meetings in Boston:

If you would like to read the full paper, you can do so here:

Beyond Practicality: George Berkeley and the Need for Philosophical Integration in Mathematics