To cheer you up in difficult times, here is a wonderful thoughtful, entertaining, and provocative post by Igor Pak about conjectures. See also Shmuel Weinberger’s take on conjectures.
Conjecturesare a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and sizes. Some of them are famous, classical, general, important, inspirational, far-reaching, audacious, exiting or popular, while others are speculative, narrow, technical, imprecise, far-fetched, misleading or recreational. That’s a lot of beliefs about unproven claims, yet we persist in dispensing them, inadvertently revealing our experience, intuition and biases.
The conjectures also vary in attitude. Like a finish line ribbon they all appear equally vulnerable to an outsider, but in fact differ widely from race to race. Some are eminently reachable, the only question being who will get there first (think 100 meter dash). Others are barely on the horizon, requiring both great effort, variety of tools, and an extended time commitment (think ironman triathlon). The most celebrated third…
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Here is Mike Saks’ take on what a conjecture is: https://youtu.be/hYfeRtdj7cw?t=7m32s
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My view about conjectures is the same as about one’s other scientific activities: namely, you should take it seriously (but perhaps not terribly seriously) and apply good judgement about making and formulating conjectures. (But I am not sure there is even controversy about it.)
I think you are known for being not very hesitant to make a conjecture, Gil. I think I even heard conjectures from you that contradicted each other 😉
Dear Karim, yes yes this is correct of course (and gently put). Personally, the problem is that I can also see the joy of making reckless unmotivated and weird conjectures.
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