Ramanujan & Hardy

(3 Minute Read. 4Aug2021)

Bust of Ramanujan
Birla Industrial & Technological Museum
Kolkata, India

Recently I have been reading about Srinivasa Ramanujan (1887–1920), the brilliant Indian mathematician of a century ago. The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel tells the story of his life.

One of Ramanujan’s discoveries that is still in use today involves the mathematical constant represented by the Greek letter Pi (π) which is the ratio of a circle’s circumference to its diameter (C = πD). The number π turns up in many formulas throughout mathematics and physics.

π is an irrational number. Irrational means that it is not the ratio of two integers. Its decimal expansion never ends and never endlessly repeats. The rational number 22 / 7 approximates π to two decimals (3.14), but it is not equal to π.
245850922 / 78256779 is a rational approximation to π that is accurate to 15 decimals (3.141592653589793).
π = 3.14159265358979323846264338327950288419716939937510. . .

π is also a transcendental number. This means that it is not the solution of any polynomial equation with rational coefficients. The square root of two (√2) is an example of an irrational number that is not transcendental because it is a solution of the polynomial equation X² – 2 = 0.

Ramanujan discovered this infinite series which can be used to calculate approximations to π:

Ramanujan’s series for π converges extremely rapidly. It is the basis for some of today’s fastest algorithms that calculate approximations to π.

Using only the first term of the series (k=0) gives the π approximation 9801√2/4412 = 3.141592. . . which is accurate to six decimal places. Using just the first two terms of the series (k=0,1) gives the approximation 3.14159265358979. . . which is accurate to 14 decimal places.

Mathematicians have worked for 100 years studying and proving Ramanujan’s numerous results. Some are still unproven.

Sadly, Ramanujan did not know the Great Mathematician whose deep mathematical truths he so amazingly discovered. He was an orthodox Hindu and grew up in a family that prayed to stone idols. He credited his mathematical insights to his family goddess, Namagiri Thayar. He said she sent him visions of scrolls with complex mathematical formulas.

Ramanujan’s mentor at Cambridge University was the mathematician G. H. Hardy (1877–1947). Hardy was probably the premier British mathematician of his time.

In the epilogue of The Man Who Knew Infinity (page 367), Kanigel reports these five New Year’s resolutions that Hardy made one year, probably in the 1930s.
1. Prove the Riemann hypothesis.
2. Find an argument for the non-existence of God which shall convince the general public.
3. Be the first man at the top of Mount Everest.
4. Be proclaimed the first president of the USSR, of Great Britain, and Germany.
5. Murder Mussolini.

Hardy accomplished none of these goals. The Riemann hypothesis is still an open question today. It is probably the most important unsolved problem in mathematics.

Apparently Hardy never considered where his ability to think and reason and discover wondrous mathematical truths came from. Where did his brilliant mind come from?

Hardy was a self-proclaimed lifelong atheist. He refused to even enter chapels for funerals or college functions.

Yet Hardy was not a true atheist. His games with God were a well-known standing joke.

When walking with friends past a church, Hardy would maneuver to keep them between him and the church. Hardy’s idea was that walking too near a church might tempt God to strike him dead with a lightning bolt.

If God does not exist as Hardy claimed to believe, then there is no need for this stratagem by Hardy.

On one occasion before returning by boat from a trip abroad, he mailed a postcard to a colleague stating that he had proved the Riemann hypothesis. He thought this was insurance against the boat sinking because God would not allow him the fame of having solved such a famous problem.

Of course such “insurance” presupposes the existence of God.

According to this Scripture passage from the Apostle Paul, Hardy knew there was a God.
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God, or give thanks; but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools. (Romans 1:18-22)

Both Ramanujan and Hardy were brilliant mathematicians, some of the best mathematical minds ever. But intellectual brilliance, which is itself a gift of the Great Creator, does not necessarily help one grasp spiritual truth.
For the word of the cross is to those who are perishing foolishness, but to us who are being saved it is the power of God. For it is written, “I WILL DESTROY THE WISDOM OF THE WISE, AND THE CLEVERNESS OF THE CLEVER I WILL SET ASIDE.” Where is the wise man? Where is the scribe? Where is the debater of this age? Has not God made foolish the wisdom of the world? For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe. . . but we preach Christ crucified, to Jews a stumbling block, and to Gentiles foolishness, but to those who are the called, both Jews and Greeks, Christ the power of God and the wisdom of God. Because the foolishness of God is wiser than men, and the weakness of God is stronger than men. . . But God has chosen the foolish things of the world to shame the wise, and God has chosen the weak things of the world to shame the things which are strong.
(1 Corinthians 1:18-21,23-25,27)

Questions to Ponder

1. Are you missing God’s truth in some area because of intellectual pride?
2. What can you say to give credit to the Great Creator for your successes in a winsome way?

Share your thoughts on these questions in the comments below. It could encourage or help another reader.

For Christ and His Kingdom. Soli Deo Gloria. Alere Flammam Veritatis.

Read the sequel:
π in the Bible

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©William T. Pelletier, Ph.D.
“contending earnestly for the faith”
“destroying speculations against the knowledge of God”
“for the defense of the gospel”
(Jude 1:3; 2 Cor 10:5; Phil 1:16)
Wednesday August 4, 2021 A.D.

The sum of Thy word is truth, and every one of Thy righteous ordinances is everlasting. (Psalms 119:160)

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