Professor George Whitesides of Harvard University is one of the most significant chemical scientists in the world today. He is well known for advances in NMR spectroscopy, nanotechnology and physical and organic chemistry. He has been the recipient of many prestigious awards for his work, including the AIC Gold Medal, the Priestly Medal, the National Medal of Science, the Benjamin Franklin Medal, the IRI medal, the Othmer Gold Medal and many other national and international awards.
Professor Whitesides is also a prolific writer and has produced hundreds of articles for scientific journals and magazines. He took time out of his very busy schedule to answer some questions for me about his experience with mathematics.
1. Describe what maths lessons were like for you at school.
I loved algebra, geometry, and calculus; I was not so fond of arithmetic and trigonometry. I prefer abstraction to numbers
2. Was the maths that you learnt at school useful to you later in life?
Absolutely. I’m a scientist, and I use mathematics all the time. Also geometry (and drafting) were very useful in developing the ability to visualize things in 3D.
3. How good do you need to be at mental arithmetic to do calculations in your head?
I can’t answer. I don’t think of myself as being good at mental arithmetic, but I estimate numbers all the time (in my head, on paper, wherever).
4. Mathematics teaches us that you can put two things together to make a new thing. Is this important in what you do?
Again, I’m not sure of the question. A combination of two things—in math, in physics, in art, in music—is often a new thing.
5. Mathematics is about finding patterns. Do you need to look for patterns, or exceptions to patterns, in your research?
Both. One tests for a pattern, and if that does not work, one tests for another pattern. Sometimes you don’t find one.
6. Mathematics also teaches us about balance and equality. Is this idea useful in your research?
If you mean here that “=” is equality and balance, of course. All the time.
7. Mathematics helps us to represent quantities and measurements numerically. Do you do this in your work?
8. Is estimation good enough or do you need to measure things accurately?
Both. Estimation helps to follow the course of experiments, to design them, and to look for trends. Accurate measurement and analysis is critical to quantitation of prediction, and for both confirming compatibility of result and prediction, and maybe more importantly for showing incompatibility of result and prediction.
9. How do you use statistics to analyse your results?
Constantly in some programs. Understanding what a number or a result means is absolutely crucial to any experimental program; statistical analysis is the best chance we have to answer that question. Statistics is a hard subject to get excited about until you actually care (for whatever reason) about the meaning of data. Simple questions like “Are these two numbers—with different numerical values—distinguishable or indistinguishable?” are core questions in science. If I had one subject that I wish were better taught (I don’t know how) to students who would go on to work with data in any form, it would be statistics.
10. Do you have any other insights to offer into how you use maths in your work?
There are areas of science that are purely qualitative, and for which math is not necessary, but not many. I, most scientists, and all engineers use math all the time. The more you know, the more you can do.
Thank you so much Professor Whitesides for your participation in the "Maths in Science" project. I certainly value your contribution.