Author: Michael Nielsen

Do outstanding minds differ from ordinary minds in any special way? I don’t believe that there is anything basically different in a genius, except for having an unusual combination of abilities, none very special by itself.

– From “Why people think computers can’t’”, an essay by Marvin Minsky

Certain kinds of talent are extremely evident in mathematically-oriented pursuits, such as theoretical physics. Solving simple mathematical problems (“Prove that any set of 51 numbers in the range 1 to 100 must contain two numbers with no common factor” [*]) is an important part of doing research in the mathematical sciences.

Some people will solve the problem just posed effortlessly and instantaneously. A smaller group of people can do the same even with much more complex problems. Other people will struggle with the problem, requiring several minutes or more of laborious thought to convince themselves of the truth of the statement.

It can be rather depressing to meet someone who is clearly much faster than you at this type of problem-solving. Some promising students give up and change fields for something less mathematically demanding, or leave science altogether.

In my opinion, this is a pity. Such mathematical quickness is, unfortunately, both easy to spot, and idolized within the culture of the mathematical sciences. People frequently comment on how “bright” another person is, and mathematical quickness seems to play a major role in forming such assessments.

Yet, such quickness does not seem especially important to make a creative contribution. As Minsky’s comment indicates, a whole plethora of skills and attributes are involved in making such creative contributions. It is more important to be reasonably competent across that entire range of skills and attributes than it is to be extremely talented in just one or a few ways.

[*] I believe I first heard this problem in a biography of the mathematician Paul Erdos.

Undergraduate education in physics is mostly concentrated on learning certain basic facts about physics, and technical skills that enable one to solve problems in physics. While both these are essential facets of doing research, many other equally essential skills are neglected, or ignored completely.

Why is this the case? In some small part it may be because not all people taking physics degrees necessarily hope to do research one day. However, to an extent far greater than in almost any other subject, an undergraduate degree in physics is, at least nominally, focused on the task of preparing people for research.

At the PhD level, it is interesting that while there is certainly a focus on doing research and getting research results, relatively few supervisors seem to engage in much active discussion of how research ought to be pursued. If a student is lucky they may see a particular research style modeled, through interactions with their supervisor and other more senior scientists.

Such modeling is potentially quite valuable, especially if a student is exposed to a wide range of research styles. However, what works for one person may not work for others; this may be especially true when one is inexperienced and lacks confidence, while another is very experienced and has considerable confidence. Furthermore, each individual needs to develop their own style, suited to their own unique combination of talents.

Many students fail even to see such modeling. A remarkably common attitude is that students either “have it”, or “don’t”, when it comes to research skills. This sells students lumped into either category short. It is true that some beginning PhD students are exceptionally well equipped to do the tasks required of a PhD student. Such students may complete their PhD much more rapidly than usual, with apparently astounding success. However, such students may also plateau – they may never move beyond this level, stagnating instead of growing into a new set of skills beyond that required of a PhD student. Similarly, other beginning students may be very well equipped in some ways, but lacking in certain essential skills that result in them being placed into the “don’t” category. It is interesting to wonder how such students might benefit from learning some basic research skills.

I believe that there are many ways in which the learning of research skills can be integrated into both the undergraduate and postgraduate curricula. Rather than drafting such a list to be placed here, I’ll leave the construction of such a list as a topic for discussion, and for future posts.

Topics for further thought:

• Why are research skills so seldom taught, or even discussed, at either the undergraduate or graduate levels?
• How significant a factor in research success is the process of thinking about how one does research, discussing it with others, and looking for lessons from history?
• How can the learning of research skills be integrated into the undergraduate and graduate curricula?