## Quotes on mathematics

These quotes on mathematics will help you to explore its nature, form links with other WOKs and AOKs, and provide discussion points for TOK lessons. They will also support you as you address knowledge questions within your TOK essay and TOK presentation.

### Consideration points

- What do the quotes suggest about the nature of mathematics as an area of knowledge?
- What do they suggest about the purpose of the mathematics?
- Are the quotes consistent, or do they clash about the role it plays as an area of knowledge, and its relationship with others WOKs and AOKs?
- Can you think of other ways of knowing and areas of knowledge that these quotes relate to?
- How many of these thinkers are you familiar with? Research the ones you haven’t come across before – and, indeed, the ones you think you already know. Click on the names to take you to the corresponding Wikipedia article, although this should only be used as a starting point for your research.

Finally, how would you use the quotes to construct a typical IB Diploma TOK essay title? Look at , and see if you can compose something similar (and think about how you’d go about structuring it)

### 1. The nature and purpose of mathematics

Mathematics is the most beautiful and most powerful creation of the human spirit.

**Stefan Banach**

The essence of mathematics lies in its freedom.

**Georg Cantor**

The mathematics is not there till we put it there.

**Arthur Eddington**

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

**Albert Einstein**

Pure mathematics is, in its way, the poetry of logical ideas.

**Albert Einstein**

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

**Albert Einstein**

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

**Bertrand Russell**

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

**Bertrand Russell**

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza’s God, it won’t love us in return.

**Bertrand Russell**

### 2. Mathematics and intuition

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.

**Richard Courant**

**3. Mathematics and language**

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics.

**Brian Greene**

Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it’s supposed to talk about but is always spreading around.

**Howard Nemerov**

Logic and mathematics are nothing but specialised linguistic structures.

**Jean Piaget**

You can not apply mathematics as long as words still becloud reality.

**Hermann Weyl**

### 4. Mathematics and reason

Mathematics allows for no hypocrisy and no vagueness.

**Stendhal**

Mathematics is the music of reason.

**James Joseph Sylvester**

### 5. Mathematics and the arts

Film is one of the three universal languages, the other two: mathematics and music.

**Frank Capra**

But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.

**Marston Morse**

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

**Bertrand Russell**

### 6. Mathematics and ethics

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.

**Daniel Dennett**

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

**David Hilbert**

### 6. Mathematics and the natural sciences

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

**E. T. Bell**

### 7. Mathematics and religion

God used beautiful mathematics in creating the world.

**Paul Dirac**

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

**Andre Weil**

**Cite this page as:**Dunn, Michael.

*Quotes on mathematics*(18th September 2013). theoryofknowledge.net. http://www.theoryofknowledge.net/areas-of-knowledge/mathematics/quotes-on-mathematics/ Last accessed: 19th March 2018