Nature And Numbers

Georg Glaeser
Arts and Society, Cross-Disciplinary Strategies
2019S, Lecture and Discussion (VOD), 2.0 semester hours, course number S02613


This lecture is about mathematics in connection with other sciences, especially with biology and physics. The driving force behind the development of mathematics may be found in human nature: As a species, we seem to be uniquely interested in finding rational explanations for regular or repetitive phenomena in order to be able to predict them. Nature is never perfect -- otherwise, human beings would not exist as they do today (this statement could be taken as a joke, but it relates to the imperfect reality of biological evolution). Nature is a pragmatic mechanism and accepts many supposedly imperfect solutions, which emerge by means of selection or random chance, insofar as they improve an organism’s reproductive success. If they are advantageous or better than existing ones, nature is always ready to accept new forms. This holds equally true for th edevelopment of life as for the emergence of shapes and patterns.

Since this is not an ordinary math lecture and only limited mathematical training can be expected, we will “derive” certain important relations purely on the basisof common sense. A geometrically insightful sketch is usually preferred to mathematical abstraction. The  strictly mathematical way of phrasing ideas is avoided, since this is usually a major obstacle for “non-mathematiticians” to understand the intrinsical ideas of theorems.

Here are two exemplaric questions that can be answered by means of rather simple mathematical considerations:

* Why is there an upper limit for the size of insects,and a lower limit for the size of warm-blooded animals?The answer follows from an important theoremabout similar objects.

* Why do rainbows exist? Why does the sun appearas a glowing red fireball even after it has, from apurely physical point of view, already disappearedbehind the horizon? The answers areto be found in the refraction and total reflection of light.



* G. Glaeser: "Nature and Numbers. A Mathematical Photo Shooting" aus der Edition Angewandte (de Gruyter)

* G. Glaeser: "Math Tools - 500+ Applications in Science and Arts" (Springer, 2017).

* Ian Stewart: "The Beauty of Numbers in Nature: Mathematical patterns and principles from the natural world", Ivy Press, 2017

Examination Modalities

It is expected that the students participate in at least 80% of the lectures and contribute actively to the progress of knowledge transfer by scrutinzing the presented problems.

At the beginning of  each lecture, there will be a short repetition in written form where the participants should show that they have understood the discussed topics.

Additionally, it is expected that the students work through each lecture on their own , as if they were asekd to explain the contents to other persons.

At the end of the lecture series, there is a final written exam (1 hour) plus a 10-minute individual examination talk. 


Who is allowed to join your course?

CDS students, students of other departments at Angewandte.

Students from other faculties or universities will be given a place on the course subject to room capacities.

Maximum number of participants: 20.

Location: Hintere Zollamtsstraße 17 (HIZO), 4th floor, "lecture room"


Key Words

Nature, math, geometry, physics, biology


06 March 2019, 09:15–12:45
20 March 2019, 09:15–12:45
03 April 2019, 09:15–12:45
10 April 2019, 09:15–12:45
02 May 2019, 09:15–12:45
08 May 2019, 09:00–12:45
22 May 2019, 09:00–12:45
29 May 2019, 09:15–11:00

Course Enrolment

Until 04 March 2019, 23:59
Via online registration
via email:

co-registration: possible (3.0 ECTS)

Individual courses: possible (3.0 ECTS)