Prof. Dr. Tobias Friedrich

What is Science

Autor: Timo Kötzing

A question to start with: What are we doing here, anyway?

We will discuss the following aspects of "What is Science".

  1. Definition and origin of the word
  2. The demarcation problem: What is Science and what is not?
  3. Pólya: The mathematical method
  4. What are indicators of good science?
  5. How do we choose a project to work on?
  6. Why do we sometimes do seemingly useless science?

1. What Do We Think of as Science?

Many people, when asked what comes to mind when thinking about "science" and "scientist", think about people in white lab coats, some kind of experiments, maybe something about going to space. A good example for that is the picture the UC Berkeley uses for their page on "What is science". In fact, this focus on experimental science is ingrained into the Anglo-Saxon understanding of "Science", as the following definition shows.

English Wikipedia on "Science"
Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

This strict dependence on experimental data is also embodied in the concept of "the scientific method", defined as follows.

English Wiktionary on "Scientific Method"
A method of discovering knowledge about the natural world based in making falsifiable predictions (hypotheses), testing them empirically, and developing theories that match known data from repeatable physical experimentation.

This is in contrast with the German understanding of the word "Wissenschaft" (a typical translation of "science"), as given by the following quote.

German Wiktionary on "Wissenschaft"
Science is the epitome of the totality of human knowledge, insight and experiences of an epoch of time that is systematically expanded, collected, preserved, taught, and transmitted (made a tradition).

Original: Die Wissenschaft ist der Inbegriff der Gesamtheit des menschlichen Wissens, der Erkenntnisse und der Erfahrungen einer Zeitepoche, welches systematisch erweitert, gesammelt, aufbewahrt, gelehrt und tradiert wird.

The origin of the word "Wissenschaft" is, on the other hand, again empirical.

German Wiktionary on "Wissen"
Althochdeutsch "wissan" = "gesehen haben" (= to have seen)

2. The Demarcation Problem

The philosophy of science contains a long debate about the so-called "demarcation problem", the problem of deciding whether something is science or not.

The demarcation problem tries to draw the line between what is good scientific practice and what is not, mostly focusing on empirical science. For the remainder we will focus on mathematical science.

3. Pólya: The mathematical method

In 1945, George Pólya published the book How to solve it, in which he details a method for how mathematicians attack and solve a problem. His four step method mirrors the four steps of the scientific method. The four steps are the following.

  1. Understand the problem. Look at the problem from different angles.
  2. Devise a plan. What tools should be used? In what way? What lemmas should I try to prove?
  3. Carry out the plan. This is the craft of mathematics: there is not much creativity necessary to do the manipulations required by the plan.
  4. Review/extend. Reflect on the proof. Are there unnecessary steps? Unused assumptions? Can the statement be generalized and still proven by the same proof? What can we learn from how this proof worked out?

Steps 2 and 3 are the most visible ones when actually doing math (and we frequently fall back from Step 3 to Step 2 when the plan fails).

Step 1 is sometimes forgotten, especially whenever this step comes essentially for free (because similar problems are known and well-understood). But especially when attacking a problem that seems a bit more elusive or is just in an area which we do not know so well, this step is very useful as a preparation for finding a proof. Here a literature review can be helpful, or proving small auxiliary statements in the vicinity of our problem.

Steps 4 is also some times forgotten, after the proof is finally found one wants to savor the moment. On the other hand, Step 4 gives the most benefit for the least effort: we might be able to strengthen the result without having to find a new proof. We can gain insights from our own proof without having to add new creative ideas. We can learn for future proofs at very little expense.

4. Indicators of Good Science

What do we see as indicators of good scientific work? We can make a long list of angles that scientific work is judged under, below I give a (subjective) list in clusters. The first cluster is about science increasing our understanding (of phenomena), while the second one deals with science as a means to control the world. The third cluster is about how science can be checked to deliver on its promise; the fourth is about virtues of scientific work for the scientific endeavor itself (how the work helps science). The fifth cluster concerns depth, criteria for why a given work is not just a small step. Finally, the sixth cluster is about aesthetics, or how scientist feel about the work as a value in itself.

  • Understanding: explanation (of a phenomenon), new perspective, insightful, making a connection.
  • Control: usability, applicability, profitability.
  • Quality control: soundness, completeness, replicability, refutability.
  • Inner-scientific angles: originality, improving state of the art, tradition, bridges a gap (between areas), novel technique, initiates a new field, has a community.
  • Depth: difficulty, complexity, answers open question.
  • Aesthetics: beauty, simplicity, elegance, simple to state, surprise, interestingness.

It is important to know that there is no general agreement on which criteria are to be used in what way to decide on the quality of scientific work. In fact, different communities have different "tastes", even when they work on the same problems with the same methods. There is no "right" and "wrong" to this, but inside any scientific community there is typically some kind of basic agreement on how to evaluate scientific work. Thus, knowing the agreement of a community is vital for being recognized by this community. Still, different reviewers might feel different about these points, so that very different judgments can be given for the very same work.

5. Project Choice

When thinking about what project to choose (implicitly assuming that we have more ideas for projects than time to work on these projects), we typically think about "how much gain for how much pain" kind of trade-offs. Where is the scientific (or personal) advancement best, given the efforts required? A second angle for project choice is to consider the variance: something will go wrong, how bad can it be? Or, similarly, how good can it be if all stars align?

  • Price: challenge level, resources required, technique-problem fit, I know the methods, it's a nail for my hammer ("because I can").
  • Gain: challenge level, importance of the result, popularity of the area, possible insights into the area I actually care for.
  • Variance: scoopability, expandability (range of possible problems to work on).
  • Personal: I can team up with people I want to team up with, I care for the topic, I am associated with this topic, I have always worked on these problems.

The personal criteria are very important, though not for science. They are important because science is carried out by human beings, and we are mostly self-driven in our research. The price/gain trade-off is seldom overlooked and a core to many considerations for what direction to chose. But it is equally important to be aware of the possible outcomes of the project. Will it succeed one way or another? Are there always some changes to the question so that some (publishable) answer will be found? If everything turns out too easy, can we extend the questions suitably? In other words, can I make sure that I have something to show for in the end?

6. Why Do We Do Seemingly Useless Science?

Some science seems to follow no purpose directly. The criteria for good science seem to point out that some work is rather unnecessary. Why do we still feel that there is some virtue here? Some possible answers are the following.

  • Uncertainty: the future is unknown and the science might become useful, we are searching in the dark and the results we find might turn out useful.
  • Pure understanding: enthusiasm for insights, expanding human knowledge.
  • Structural: constructing a web of knowledge.

What did we learn?

  1. Science is hard to define and hard to judge for quality.
  2. Criteria for good science take many angles.
  3. The personal reasons for what science to pursue are yet different.
Being aware of the different angles discussed here (and probably adding some more from own experience) can help navigating a scientific career as well as focusing on actually helping science.


I want to thank Thomas Bläsius for a helpful discussion on how to handle a large amount of criteria usefully. Also, Karen Seidel and Martin Krejca provided much appreciated feedback regarding this web page.