Ernst Kummer. Image source: https://rjlipton.files.wordpress.com/2016/01/ernst-eduard-kummer2.jpgPeople often think that being good at quickly adding or multiplying numbers is a sign of being a mathematical genius. The truth is that mathematics has little to do with numbers, and more to do with spotting patterns and proving results. Indeed, evaluating complicated calculations quickly has practically no mathematical value whatsoever, so much so that nowadays we let calculators and computers perform this tedious work for us.
Nevertheless, it is true that mathematicians are good at performing quick number calculations. However, one mathematician who is an exception to this rule is Ernst Kummer, a German mathematician who introduced ideal numbers – a concept later extended by Richard Dedekind.
By doing so, Kummer managed to partially prove a taxing claim made by Pierre de Fermat, nowadays known as Fermat’s Last Theorem. This result was only successfully proved completely in 1994 by Sir Andrew Wiles, for which he received the Abel prize last year.
However, Kummer’s arithmetic was very poor. Once, in class, he needed the product 7x9. He could not remember it, so he asked the class to help him. One mischievous student told him that the answer is 61. Another student interjected “no, the correct answer is 69”. Eventually, he figured out that the correct answer is 63 by using the following method: 61 is a prime number, 65 is divisible by 5, 67 is a prime number, 69 is too large, so it must be 63.
This shows that even the best of mathematicians may not be as good with multiplying numbers as you think!