By Kareem Carr

I feel that we are rapidly approaching a future where the maxim, ‘Cheaters only cheat themselves’, obtains. I have, of late, come to understand, perhaps only in small part, the prodigious resources open to the modern mathematical learner. Blogs, forums, online chats, question-and-answer sites, tutorial services, online lectures (by both Ivy League professors and guys in their basements) and large data repositories abound. Thousands of books are available online either in part or in whole. The lines between cheating and information gathering are blurring. I think we are fast approaching a point where, in order to personally advance, even the most conscientious student must be fully self-aware of where he is crossing the line between just the right amount of help and too much help. Otherwise, he could easily undermine himself and his efforts.

Yet, I can’t help but be overjoyed with the spread of mathematics. This is surely a liberation and democratization of mathematical teaching and knowledge.

Why now? What has stimulated this flourishing? Grant me some latitude to advance a theory. I have been doing some research on the occurrence of mathematical talent. From the sources that I’ve gathered, a few things become clear. Mathematical talent occurs in clusters: families, communities, social groups and countries. It often requires social contact with other mathematically inclined people to flourish. Paradoxically, it requires a tremendous amount of personal drive. However, drive is not always enough. If it were not so, we would not need universities as learning institutions for mathematicians.

The internet allows people who have drive, even if they are born in a circumstance which is poor in mathematical resources to connect with others around the world.

I still predict that internet fostered-talent will appear in clusters. However, at least the doors are a little more open.

But I’ve gone off on a tangent. What about cheating? I feel the role of the educator might be changing. Once, a few could control the flow of information. That is changing. A homework model that is based on limited availability of information to the student, i.e. the student not being able to find the answer if he or she so chose, might not last. It has been difficult for most systems which have relied in the past on information asymmetry such as travel agencies, scientific journals, and the encyclopedia and dictionary market. So perhaps, it will be difficult for formal education to adapt also. However, gradually, solutions are being developed and approaches are being adapted. So, perhaps teaching will change too to encompass the new possibilities.