Some mathematical constants appear consistently in nature. What does this tell us about mathematical knowledge?

Why does mathematical modeling work so well for practical purposes?

Does the fact that Leibniz and Newton came across the calculus at similar times support the argument that mathematics exists prior to its discovery?

So essentially, is mathematics invented or discovered?

Minor Knowledge Question

What does the dispute between Newton and Leibniz tell us about human emotion and mathematical discovery?

**A Theoretical Examination of Mathematics**

By: Ashton, Niharika, and Ramya

The fact that mathematical models are so accurate at predicting natural phenomena supports that fact that math is innate and part of the natural world

The Fibonacci sequence is a sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21...) in which each number is formed by the addition of the two previous numbers.

The fact that the Fibonacci sequence and mathematical constants existed in nature prior to discovery supports the idea that mathematics was discovered, not invented. This leads to the idea that there are other undiscovered mathematical laws that govern nature.

Minor Knowledge Question

Throughout time we have discovered patterns in nature that can be explained through mathematics.

Fibonacci Sequence

These numbers are seen throughout nature in the number of leaves on a plant, the number of petals on a flower, the number of seeds in plant, etc. The numbers can also be put together to form a spiral, which is seen in the formation of plants and animals.

Throughout the discovery of geometry and calculus, we have seen the repetition of mathematical constants that we have given names such as pi and e.

These values already existed, we just gave them a name.

Mathematical Constants

Knowledge Question:

This is a controversy that is still discussed by mathematicians today. Newton discovered the beginnings of calculus, but decided to withhold from publishing it. A few years later, Leibniz also discovered some main tenants of calculus, but went right ahead and published them. It is interesting that they both discovered calculus independently of one another.

This example can be used to support the assertion that mathematics is discovered. It is highly unlikely that two different individuals could just accidentally invent the same subject around the same time.

Conclusion

Bibliography

Parveen, Nikhat. "Fibonacci in Nature." Fibonacci in Nature. UGA, n.d. Web. 31 Oct. 2013.

Lienhard, John H. "No. 1952: Constants of Nature." No. 1952:. The Engines of Our Ingenuity, 2004. Web. 31 Oct. 2013.

"Tok Maths Resources." IB Maths ToK IGCSE and IB Resources. IB Math Resources, 2011. Web. 31 Oct. 2013.

Raussen, Martin, and Vicente Munoz. "Newsletter of the European Mathematical Society." EMS. European Mathematical Society, June 2008. Web. 30 Oct. 2013.

Loy, Jim. "Newton vs. Leibniz." Newton vs. Leibniz. N.p., 2002. Web. 31 Oct. 2013.

Albert Einstein pondered, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”

Most of us take it for granted that math works—that scientists can devise formulas to describe subatomic events or that engineers can calculate paths for spacecraft. The creation theory and discovery theory, we believe, are both inadequate to describe the certainty and innate nature of math.