If you want to slice a ripe tomato cleanly, you need a sharp knife. Or a serrated blade. What is the mechanical property of tomatoes or material property of tomato skin that makes them resistant to slicing?
Think about how easy it is to run a dull knife across your skin without hurting yourself whereas a razor blade can cut you with almost no effort whatsoever. Think about how difficult it would be to cleanly cut a very ripe grape, or a very light and fluffy cake, with a very dull blade.
It’s not a tomato thing - materials that have lots of give will compress beneath a dull blade and rupture around it rather than being cleanly cut.
The reason tomatoes have a very bad reputation is that they’re soft and round and tend to also be slick, which makes them terribly dangerous for cutting with a dull blade. Dull blades can still slash the shit out of you if you handle them poorly.
The skin is somewhat tough but more to the point the underlying tomato architecture is squishy and slidey so if you try to press down to make your cut you get a mess on your hands (and cutting board).
I have an Old Hickory knife that’s sharp enough to slice even soft mushy tomatoes into paper-thin slices. That’s what you want: a knife that thinks it’s a razor blade.
Or as my brother-in-law said about hus roommate: his knife was so sharp, his tomato would last a month.
Penn Jillette of Penn & Teller has mentioned on numerous occasions (his podcast, and on Fool Us just last week) a story about Johnny Thompson, their late collaborator and mentor. Thompson was apparently a walking encyclopedia of magic and practiced for hours daily into his old age. When asked the most difficult trick he had ever learned, he would say it was cutting tomatoes.
He had had a job selling knife sets at carnivals, and part of the spiel was a demo showing how amazingly sharp the knives were by cutting incredibly thin tomato slices. Thompson said the trick to it had little to do with the knife sharpness or quality (they were low cost knives) - it was all in the technique, and it was very difficult to master.
I don’t know how true this is, but Penn seems to believe it.
I don’t know if there’s any truth to that, but I do know for sure that a sharp knife is necessary, especially if you’re aiming for very thin slices. I often hone my Henckels chef’s knife before slicing tomatoes. The “technique” as far as I’m concerned is in the ability to cut consistently thin slices, rather than slices that are too thick or fragments that fall apart. A good sharp knife is, as the saying goes, a necessary but not sufficient condition!
Yes, well put!!
In my experience, cheap knives usually start off just as sharp as quality knives-- The difference is that they don’t stay sharp.
Yep, and as long as you’re willing to sharpen it, just about any cheap knife will do.
Heck, this guy makes all kinds of knives out of crazy materials (and his videos are crazy entertaining, IMHO). He also sharpens them to kind of unbelievable grits. They all cut very well, probably better than my own steel knives. But then again, I don’t sharpen mine to 10K/30K, etc.
But yeah, his bismuth knife was never gonna last.
Any sharpened edge is at the microscopic level a jagged mountainscape. More saw than a cleaving edge. Really good edges have a very even profile and even serrations. Poor sharpened edges can a hopeless mess, including turned over burrs, and broken off peaks, and little consistency. Even finishing sharpening with a strop leaves the microscopic detail as a jagged edge.
To cut a tomato you need the teeth/peaks of the edge to cut the skin and not dig deep enough to catch in the skin and pull on it. A really good edge makes this easier because the peaks are much smaller and the evenness of their distribution makes the entire action more predictable.
So, with a poor edge, success requires that the edge only brush the skin with enough force to allow a few peaks to lightly penetrate the skin and make very shallow cuts. As the knife progresses the cut can deepen. But even the tiniest bit of extra pressure, and the knife will catch and pull the skin. I can well imagine that the skill needed to make a poor edge look good cutting a tomato whilst also doing so at what appears to be a normal cutting pace would be a real trick to master. Start with a fast very light touch and deepen the cut at a very measured rate. Not trivial.
I suspect serrated knives can a void the tearing action because they impose a succession of heavier and lighter pressure on each point of contact, and the lightening of pressure releases the catching of the skin, so it is less likely to tear. Laser cut knives, with a succession of a sharp teeth cut not just on the bottom edge, but cut on the side of the teeth, and even when the skin catches, there is cutting motion that can cut through the caught section of skin. This probably helps conventional serrated blades to some extent as well, as they have some element of lateral cutting edge.
In the end, any cutting of things into chunks benefits from more longitudinal motion and less pressure. As the usual maxim goes, let the tool do the work.
Time to hijack to one of my favouritest fun facts. Forget your sharpened knives and your laser-cut knives, what you really want is an obsidian blade for your tomatoes.
Producing a pressure-flaked obsidian blade creates an edge that tapers into single molecules. Electron microscope pics of a medical scalpel blade show, as @Francis_Vaughan says, a mini-Switzerland, while the obsidian blade is still too clean and diffuse to photograph sharply.
Obsidian blades are now used in things like eye surgery because of their sharpness, and presumably will be in the finest kitchens in the world once this fact gets out.
To quote from Pratchett’s Reaper Man: “Death (Bill Door) sharpens a scythe blade. First on a grindstone, then on an oilstone, then on a steel. It was too blunt. Miss Flitworth supplied, from her rag bag, satin, then silk, finest white silk, never worn (from her wedding dress). It was still blunt. Then it was sharpened on cobweb. Then on the breeze at dawn.”
And then, finally, it was fit to become …
… a quality Japanese sushi/sashimi knife! 
I’ve never owned or even used one of those things, but I’ve read about them and seen them in use. Man, those single-edged things that will rust if you even look at them the wrong way are incredible – and not cheap. It takes money to buy one – unless you consider a minimum of $500 for a knife to be cheap – and care and knowledge to maintain one.
I stress that my only knowledge in this area is my ability to open my pie-hole and pop sushi into it, and watch the preparation proceedings. But I understand that the best of these knives are really remarkable. I’m sure they could slice tomatoes real good! 
There was a poster a while back who asked me a lot of questions about diamond blades. Yes, you can buy single-crystal diamond blades for ophthalmic surgery (also applications like histology, etc.) Note that they require maintenance (it is supposedly hard to clean debris off a diamond scalpel) and for normal surgery disposable steel blades are used: you make a single cut and throw the blade away; don’t try to re-use them. Then again, besides diamond and glass (obsidian), you can get blades with zirconium nitride and other coatings, so we really need to hear from a surgeon what the current best practices are.
For kitchen use (including tomatoes, I suppose) I knew someone who had a zirconia knife.
I’ve seen those, appeared to be carbon steel.
While they have an extremely sharp edge, wouldn’t they be too fat to be effective for slicing tomatoes?
I could swear I have seen pictures of old glass fruit knives
Yes, but not many modern ones. They were produced from the 20s to the 40s before the advent of relatively inexpensive stainless steel knives were available.
again, high price is not a prerquisite for sharpness… I can get my $13.00 Opinel “Carbone” to ridiculously sharp levels … and they keep it like that for a couple of hours of kitchen work.
Good tomatoe trick (when you are stuck with a blunt knive) - poke the skin with the tip of the knive where you want to make the cut, and once the skin is “compromised”, it’s way easier to slice along the slash.
… and let’s not forget “cutting by laser” …
nods
Here’s mine, $18.75:
[NOTE: image horizontally compressed here, not sure why; looks normal if you click through]
You have to work on it with a whetstone to get it there for the first time. It comes with a mediocre-sharp surface and some people actually use it that way. But invest some time and patience and you can get that carbon steel blade sharp enough to take into the OR and dissect blood vessels. After that, periodic resharpenings don’t take anywhere near as long.
This is carbon steel, not stainless steel; if you immerse it in water or leave it out after cutting, it can rust or tarnish.
I have no doubt that those high-priced Henckels and Wusthoffs can be brought to and kept to an amazingly sharp edge, but most owners don’t, and stainless steel is a lot harder to sharpen, so even those who make the attempt are usually toting around comparatively dull knives.