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An assumption is a thing that is accepted as true or as certain to happen, without proof.

A conjecture is to form an opinion or supposition about (something) on the basis of incomplete information.

What is the different between the two?

  • Where are those citations from? – tchrist Jun 30 '14 at 15:58
  • They come from the Google Dictionary. Oddly enough it doesn't have a CITE option?! When you are in Google Docs, you can go to Tools > Define and it opens a sideboard with a dictionary in it. – randomblink Jun 30 '14 at 20:18
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You can make assumptions about whether or not certain things are true or false.

You can form a conjecture that holds true for the evidence at hand, but which has limitations with regard to some unknown facts.

A conjecture is closer to a hypothesis than it is to an assumption. You could also build a conjecture/hypothesis base upon previous assumptions (result,of course, may vary).

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Perhaps how these words are used the mathematics context would help:

  1. Assumptions. We take them as granted. We never try to prove an assumption is correct or false.
  2. Conjectures. Sometimes they can also play the roles of assumptions (we assume they are true in order to derive logical conclusions from them) and in these case they are often referred as hypothesis. However (the expectation) is that at some point (with more information/knowledge), one will be able to either proof that a conjecture is true or that it is false.
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  • 1
    +1 for saying that there is a difference of purpose. A conjecture has, as part of its purpose, to be a trial balloon, with the expectation/hope that more information will improve, prove, or disprove that guess. – Drew Jun 30 '14 at 17:43
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The major difference is that a conjecture is explicitly formed. People wouldn't sit around and think up assumptions but they would try to explicitly form a conjecture based on whatever information they had available to them.

You can spot this in the definition you quoted:

A conjecture is to form an opinion or supposition about (something) on the basis of incomplete information.

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