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.
- 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 previous TOK essay titles, 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.
The essence of mathematics lies in its freedom.
The mathematics is not there till we put it there.
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.
Pure mathematics is, in its way, the poetry of logical ideas.
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.
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.
Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
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.
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.
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.
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.
Logic and mathematics are nothing but specialised linguistic structures.
You can not apply mathematics as long as words still becloud reality.
4. Mathematics and reason
5. Mathematics and the arts
Film is one of the three universal languages, the other two: mathematics and music.
But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.
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.
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.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
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