The word "nut" in botanical terms has a fairly precise definition: A nut is the compound ovary of a plant. It is both the seed (or perhaps two conjoined seeds) and the fruit. Technically it can't be anything that splits, has a big fruit around it, or comes clustered together with other seeds. Every nut is a seed, but not every seed is a nut.
Some examples might help: Walnuts, filberts (hazelnuts), pecans, and chestnuts are all genuine nuts. They grow from a flower as basically stand-alone objects.
In contrast, famous "nuts" that are not technically nuts in the botanical sense, although they are seeds, include Brazil nuts (they are seeds that come in a cluster with other Brazil nuts in something called a "capsule"). Horse-chestnuts also come in capsules and don't count as genuine nuts. Technically almonds aren't nuts since they are the seeds of "drupes" -- fleshy fruits with a hard pit that encloses the actual seed. Peach pits and cherry pits are also not nuts. Pistachios are out for the same reason as are coconuts. Cashews come from a seed that hangs from the bottom of a rather large fruit and technically also do not count as nuts. Pine nuts are seeds and not nuts.
Finally, peanuts are legumes, with the seeds in pods like peas and beans. Interestingly, peanuts grow underground and are sometimes called "ground nuts." The "ground" part of the name is right, but the "nut" part is technically incorrect.
Of course, context is all when one thinks about definitions, and for culinary purposes, all of the above can be thought of as "nuts." (If you have allergies to peanuts, you might not be allergic to a walnut, but the same factories often process both, so be careful!)
Dr. Knowledge is written by physicists Stephen Reucroft and John Swain, both of Northeastern University. E-mail questions to firstname.lastname@example.org or write Dr. Knowledge, c/o The Boston Globe, PO Box 55819, Boston, MA 02205-5819. Include your initials and hometown.