There is a disturbing trend in the world today in which common society and the scientific community are growing apart, not just in beliefs and knowledge but in even the language used to communicate. This problem has gotten so bad, that there are now courses and textbooks being offered to scientists on how to give public lectures, write popular books, and perhaps most disturbingly on how to properly testify in courts as an expert witness. The language of science and technology is precise, and regrettably the language of society is not.

And so as a small contribution to solving this ongoing issue, I have listed a few common terms which have different meanings for the two groups:

Conjecture: In common language, the word 'conjecture' means random speculation with no evidence or proof at all. It is equivalent to a guess, and nothing more. However to a mathematician, a conjecture is often a very strong theorem that lacks one minor detail or has one very exotic exemption. Many conjectures in number theory have been proven true for every integer less than several trillion, but cannot be called a theorem because it is possible that an even larger number will violate it. In a sense, even the statement that the sun will rise tomorrow is only a conjecture, because although it has risen every morning for the last five billion years there is no (strictly mathematical) proof that it will do so again. And so to a mathematician, a conjecture is often more proven than what most people would call a known fact.

Error: One of the more common misunderstandings between scientists and non-scientists is through the term “Error”. In common speech, it means a mistake. Something is wrong. The results are incorrect. But in science it is almost the opposite meaning – every measurement of any precision will include an error. In scientific terms, error and uncertainty are both used to describe how precise a measurement is. If you measure a distance to within 1cm, the error is plus or minus 0.5cm because that is smaller than you have measured. If the same distance is measured to within 1mm, the error is plus or minus 0.5mm. There are parameters in particle physics that are measured to one part in a billion, and yet they are still said to contain an error (basically it is plus or minus half a part in a billion in that example). And unfortunately, this misunderstanding apparently often arises in court cases.

Theory: This is the worst of all. To the layman, theory means something speculative and unknown. It is just a proposal with no substance. To a mathematician, it is the most definite fact there can be. Nothing is more precise and more definite than a theorem (In mathematical terms, a collection of theorems comprises a theory, such as in Number Theory or Graph Theory). Physicists and chemists are almost as precise, with a theory referring to a collection of equations and proofs and experimental confirmation. For these communities, a theory can be anything from an initial proposal that obeys all existing laws of physics and conforms to experimental data but makes no new confirmed predictions(ie superstring theory) to a collection of equations proven to be true by countless independent experiments (ie Newton's theory, Maxwell's theory, the theories of relativity).

Uncertainty: Another common misunderstanding is in the term uncertainty. In common society, uncertainty means a lack of knowledge. It means that other people might know it, but the speaker does not. In science though uncertainty has a much different meaning. In science, every piece of data and every measurement has a limit on it. A length might be measured as 1 cm, 1.0cm, or 1.000cm and although they appear the same, to a scientist they are different measurements. To a scientist 1cm means the “true value” is between 0.5cm and 1.5cm, while 1.000cm means the “true value” is known to be between 0.9995cm and 1.0005cm, which is a more precise number. To a scientist, it is that range of possible values that is called uncertainty, and the term is used even for data measured to twenty or thirty decimal places.

These are the terms that seem to get misinterpreted and misunderstood with the greatest frequency. I am certain that there are many others, so there may be a second edition of this list post at some time in the future. For the present, I hold to the hope that entries such as this one can begin to bridge the linguistic gap between scientists and laymen.