Arbitrary classifying things as "paleo" or "not paleo" does not do anyone any good. I think that rather than do so, it might be more prudent to classify different foods as "beneficial," "without impact," or "harmful." Particular classifications will vary from person to person and even then, it is important to ascertain how often one is okay with eating foods that fall under the latter two categories.
With that said, buckwheat is no where near as harmful as wheat dough wrapped around industrial chicken 'product' and fried in corn oil, but it's still nowhere near as nutritious as say, a potato for instance.
Check out Chris Kresser's info./recipe regarding sourdough buckwheat pancakes: http://chriskresser.com/heavenly-sourdough-buckwheat-pancakes
Most folks will say not paleo, but mostly because folks don't regard it as nutrient dense. Personally, the obsession with maximizing nutrient density in every bite is a bit silly and not a good reason to DQ it from being paleo.
It's not something to base one's diet upon, but occasional consumption could fit a personal paleo framework.
OK Wiki says - buckwheat is related to sorrel, knotweed, and rhubarb.
Buckwheat contains a glucoside called rutin, a phytochemical that strengthens capillary walls. One clinical study showed mixed results in the treatment of chronic venous insufficiency. Dried buckwheat leaves were manufactured in Europe under the brand name "Fagorutin" for use as a tisane. It also contains galloylated propelargonidins and procyanidins. Buckwheat contains D-chiro-inositol, a component of the secondary messenger pathway for insulin signal transduction found to be deficient in Type II diabetes and polycystic ovary syndrome. It is being studied for use in treating Type II diabetes.  Research on D-chiro-inositol and PCOS has shown promising results.
Also check out http://www.healthaliciousness.com/buckwheat.php for the nutricional breakdown.
Looks ok to me!
I put it in the same category as white rice, it is not as harmful as grains that contain gluten, doesn't have a lot of anti-nutrients, but also doesn't have many good nutrients, and is basically an empty starch. I think it is something you could have every now and then but I wouldn't have it more than once every week or two.
When I went to my friend's house there was nothing I could eat except this "holy crap" ("skinny b" version) cereal, which was just organic chia, hempseed and buckwheat. I've seen variations of this "cereal" in health food stores (always containing buckwheat and chia) and it would be comforting to know that the only thing concerning about buckwheat is the carbohydrate (which I don't watch personally).
I've lived in Russia for a while, and toasted buckwheat kernels are boiled and eaten as a side dish, like potato or pasta. Buckwheat has a lot of good stuff in it, and the carbs are complex, so if eaten sparingly it should not cause an insulin spike. It is very nutritious, but it makes me feel bloated and gassy, so its not in my diet anymore.
I thought buckwheat was related to rhubarb?
Paleo or not I don't know, but it plays havoc with my digestive system so I don't bother with it! I guess its back to that n=1 thing, if you have no trouble with it its fine for you :)
Buckwheat is definitely a part of my paleo recipes. Check out my paleo plan http://apaleodiet.info/category/paleo-diet-archive/
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