Lignum Vitae. Bulnesia arborea. Tiga.

Strongest and hardest are to different things. It has a lot to do with the shape of the cells, orientation of the cells and makeup of the cell walls in the tree. Woods that are tough and will flex instead of break are often not as hard as woods that will break and not flex. If you want strongest, as in toughest, high tensile strength, not likely to break, then you want oak. That is probably the toughest thing you will find in a lumber yard. Ash and hickory have a very high tensile strength and are fairly light weight, which is why they were used for buggy shafts, wagon tongues and wheel spokes. If you have a young, green horse who is likely to try to turn around in the shafts, you want something that will bend and not snap and stab the colt in the side. You aren't likely to find them in your average lumberyard. If you go to a salvage lumberyard, where they sell elements from demolished houses and barns, you may still be able to find a piece of chestnut, which is tougher and more rot resistent. If you want tough as in rot resistant for outdoor use, you want locust, which makes strong rot resistant fence posts. Cedar and cypress are also known for rot resistance. There is a great old book by Eric Sloane called A Reverence for Wood which explains why different woods were used for different purposes back when wood was used for everything. If you want hardest, as in least likely to ding, you want Maple, which is used for butcher blocks precisely because it is so hard that knives usually won't cut into them. However, maple is very prone to rot.