Professor Andrew Knoll is one of the world's leading paleontologists and works at Harvard University. He has numerous awards and achievements to his credit including Paleontological Society Medal, the Wollaston Medal of the Geological Society (London), the Moore Medal of the Society for Sedimentary Geology, the Oparin Medal of the International Society for the Study of the Origin of Life, and both the Walcott and Thompson medals of the US National Academy of Sciences.
Professor Knoll has done extensive research on the early life on earth, specifically the first 3 billion years, which is the focus of one of his more significant books.
He was also a member of the NASA Mars Rover project team, using his skills and knowledge of early evolutionary life to support this significant endeavour.
Professor Knoll kindly gave some time to answer a few questions about is use and application of maths in his work.
Here is what he had to say:
1. Describe what maths lessons were like for you at school.
I grew up in US schools much influenced by Sputnik. The “new math” taught in primary schools was heavy on Venn diagrams, number sets and the like. Thankfully, we still learned basic arithmetic and, as we got older, algebra and geometry.
2. Was the maths that you learnt at school useful to you later in life?
Beyond a basic understanding of numbers and what they mean, the maths I learned in school provided a framework for the calculus and statistics I learned later at university. And THOSE I use every day.
3. How good do you need to be at mental arithmetic to do calculations in your head?
One of the great skills that many people (including scientists) need to learn is how to approximate an answer. To make a quick evaluation of a problem, you commonly don’t need to calculate the precise answer, but rather need to know whether the answer is close to ten, close to one hundred, or close to one thousand. Thus, quick, approximate mental arithmetic is truly useful.
4. Mathematics teaches us that you can put two things together to make a new thing. Is this important in what you do?
In a sense, yes. Commonly, I would like to know the relationship between two sets of data, say, body length and weight. If I plot length on the X axis and weight on the Y axis of a graph, the spread of points on the graph really does make a “new thing.” For example, in the case mentioned, it may tell us about how the organisms in question grow.
5. Mathematics is about finding patterns. Do you need to look for patterns, or exceptions to patterns, in your research?
I do research in geology and paleontology and I spend my life looking for patterns. Mathematical pattern may show how the chemistry of sediments changes along a depth gradient, or how biological diversity increased through time.
6. Mathematics also teaches us about balance and equality. Is this idea useful in your research?
Balance and equality are important -- I’m not sure how I would apply either to my research.
6. Mathematics helps us to represent quantities and measurements numerically. Do you do this in your work?
All the time. We describe fossils, using numbers to describe length, width, and many other features., And we characterize the chemistry of ancient sedimentary rocks, again using numbers of indicate how much carbon, or calcium, or iron is present in a sample.
7. Is estimation good enough or do you need to measure things accurately?
As I noted earlier, estimation is a useful skill. But sometimes I really need make precise measurements or do exact calculations. In a sense, estimation is the quick and dirty, whereas precise measurements and calculations enable the final product.
9. How do you use statistics to analyse your results?
Again, nearly every day. As a paleontologist, I commonly need to know whether two fossil populations are different or not, and statistics allows me to draw this kind of conclusion.
10. Do you have any other insights to offer into how you use maths in your work?
What a great line to end on - "Mathematics is simply the language of science."
Thanks you so much Professor Knoll for your support of the Maths in Science project.