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Over the holiday break, I was talking with a friend of the family about the history of science. Today, academics revolve around publication of results–and a publication record (and citation record) are important ways to measure research output of young scholars. (I’ll leave out the question of self-citation, dividing larger work into multiple small communications, impact factor, and other such things for now.)

But it’s interesting to consider the history of academic science. For example, in the Renaissance, I remember this story about the mathematician Gerolamo Cardano, who is credited at solving the general cubic equation (i.e., solving an equation like ax³ + bx² + cx + d = 0). The story starts with another professor, who solved a simpler form of “depressed cubic.”

From Journey Through Genius by William Dunham:

… academic appointments were by no means secure. Along with patronage and political influence, continued service depended on the ability to prevail in public challenges that could be issued from any quarter at any time. Mathematicians [...] always had to be ready to do scholarly battle with challengers. [...] Thus, a major new discovery was a powerful weapon. Should an opponent appear with a list of problems to be solved, del Ferro could counter with a list of depressed cubics. Even if del Ferro were stumped by some of his challenger’s problems, he cold feel confident that his cubics, … would guarantee the downfall of his unfortunate adversary.

The story gets a little more complicated, with one of del Ferro’s students challenging another professor, Tartaglia. Tartaglia figures out how to solve the cubic equations which he received, and solved all 30 challenge problems. Del Ferro’s student wasn’t as lucky and lost the challenge.

I’ll leave Cardano, Tartaglia and friends to other websites. Suffice to say, that solving certain types of mathematical problems was usually a sure-fire way to academic fame, if not necessarily fortune. Just hope that you don’t get someone like Tartaglia, who works out how to solve your special problems!

The key point is that there was little incentive to publish results, because a secure grasp of one topic could be the difference in maintaining your academic position and prestige.

Today, the situation is different. People “publish or perish.”

But the more things change, the more they stay the same, I think. Because there’s still a strong impulse to a specialization. If you can solve one type of problem that no one else can, or have a unique technique, then you can still easily secure grants, publications, etc.

Or is this too pessimistic a view? Is there strong incentive to share beyond modern scientific ethics? Is what I describe necessarily a bad thing?