Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
Every great idea emerges out of a process of trial-and-error experimentation.
Survival in the demand economy depends on and requires experimentation, risk taking, and trial and error.
You still want to be thoughtful about what you do, no doubt, but you have to learn through trial-and-error experimentation as well.
science progresses by trial and error, and when it is forbidden to admit error there can be no progress.
Music is really all about experimentation and lots of trial and error. It's just mind-numbingly boring until you hit on something that works well.
Through a process of trial and error and experimentation, I discovered the simplest method - using only black - produced work with the strongest visual impact installed.
'Victory Lap,' even the title. It's the accumulation of trial and error; that's what I represent; trial and error.
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
If you ask most smart or successful people where they learned their craft, they will not talk to you about their time in school. It's always a mentor, a particularly transformative job, or a period of experimentation or trial and error.
Science advances by trial and error. When mistakes are made, the peer-review publication process usually roots them out. Cuccinelli's version of the scientific process would be "make an error and go to trial." Einstein did not arrive at E=mc2 in his first attempt. If he were working in the state of Virginia under Cuccinelli today, he could be jailed for his initial mistakes and perhaps never achieve that landmark equation.
Sometimes, we find what we want by also finding out what you don't want. All of that is trial and error. Once you're in that pit, the trial and error is important. It's up to us; we've got to keep moving forward.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
The brain has a good error rate. But, the point is, you can function with that error rate. Animals do a lot of guesswork.
You don't learn from a situation where you do something well. You enjoy it and you give yourself credit, but you don't really learn from that. You learn from trial and error, trial and error, all the time.