Does science ever prove anything for certain?

What is the difference between proof and evidence?

A mathematical proof is a chain of logic. It starts from agreed rules and shows, step by step, that a statement must follow from them. Take Fermat’s Last Theorem. It says that no positive whole numbers x, y and z can make x cubed plus y cubed equal z cubed, and the same goes for every higher power. Pierre de Fermat stated it in the 1600s. Andrew Wiles finished the job in a paper published in 1995, with help from Richard Taylor. The Norwegian Academy of Science and Letters gave him the 2016 Abel Prize for what it called his “stunning proof.”

Science cannot work this way, because its claims are about nature, not about rules we chose. The Stanford Encyclopedia of Philosophy sums up a point the philosopher Karl Popper built on: experience can never logically verify a universal law, but one genuine counterexample can refute it. One example it gives is the law of conservation of energy, which amounts to saying that no perpetual-motion machine can exist. Every machine that fails fits the law. One that truly worked would break it.

So science deals in evidence and degrees of confidence. Understanding Science, a project of the University of California Museum of Paleontology, says real, absolute proof “is not particularly scientific.” Science accepts or rejects ideas based on the evidence, and any idea could be overturned if the evidence called for it. Our editorial standards put it this way: “Proof belongs to mathematics and logic. Science works with evidence, tests and probabilities, and even strong theories can be refined.”

What do hypothesis, theory and law mean?

In everyday talk, “theory” often means a hunch. In science it means something much stronger. The National Academies describe a scientific theory as a comprehensive explanation of some part of nature, supported by a vast body of evidence. The idea that the Earth goes around the Sun, cell theory, the idea that matter is made of atoms, and plate tectonics are all theories in this sense.

A hypothesis is a tentative explanation that can be tested, and the Academies add that it must be stated so that it could be rejected. A scientific law is usually a compact description of a pattern in data, a statement of what we expect to happen. Understanding Science gives the ideal gas law as an example. It links the pressure, volume and temperature of a gas, yet real gases do not follow it exactly. Laws can have exceptions too.

Hypotheses do not grow up into theories, and theories do not graduate into laws. Understanding Science compares them to apples, oranges and kumquats: they differ in how much they cover, not in how well they are supported. So calling evolution “just a theory” misreads the word. The National Academies call evolution both a theory and a fact, and note that many religious groups see no conflict between evolution and faith.

How do scientists test an idea?

Falsifiability, and its limits

Popper argued that a scientific idea must be able to clash with possible observations. He prized “risky” predictions, ones that could conceivably have turned out false. One example that impressed him was Einstein’s theory of gravity, which predicted that light passing a massive body would bend. Arthur Eddington’s observations in 1919 bore it out. Popper contrasted this with theories that could explain any outcome at all, which in his view made them untestable.

Philosophers later found its limits. In the 1800s, the planet Uranus did not move quite as Newton’s physics predicted. Assuming Newton was right, Adams and Le Verrier, working separately, proposed an unseen planet and calculated where it should be. Galle, at the Berlin observatory, found Neptune right there. Popper’s former student Imre Lakatos later asked: what if Galle had found nothing? Scientists would not have abandoned Newton. They could have blamed something else, such as the Earth’s air blurring the telescope’s view. Big theories come wrapped in extra assumptions, and a failed prediction can land on those instead. The Stanford Encyclopedia reports that Popper himself finally accepted that falsifiability alone cannot separate science from non-science.

Sigma: how surprising is a result?

To tell a real signal from random noise, physicists use sigma (σ), a way of saying how unlikely a result would be if only noise were at work. The Particle Data Group’s statistics review notes that in particle physics an effect often qualifies as a discovery at five sigma. That matches a probability of 2.87 in 10 million, or about 1 in 3.5 million, that noise alone would give a result at least that strong.

On July 4, 2012, the ATLAS and CMS experiments at CERN each reported a new particle at about that level. CERN still called the results preliminary and described a particle “consistent with” the long-sought Higgs boson. ATLAS’s later published paper reported 5.9 sigma, about a 1.7-in-a-billion chance that background noise alone would fluctuate that high.

Sigma is not the whole story. The same review says belief in a new effect also depends on how plausible it is and on trust in the model behind the numbers. The National Academies give an example. Under the assumptions in the report, suppose a hypothesis starts with only a 1 percent chance of being right, and a study reports a result at the p ≤ 0.01 level. Then only about one in eight such conclusions would be correct. With a 25 percent starting chance, more than four in five would be. This is one reason extraordinary claims need extraordinary evidence.

Replication: can others get the same result?

The National Academies separate two checks. Reproducibility means getting consistent results from the same data and code. Replicability means a new study, with its own data, reaching consistent results. In 1989 two electrochemists, Martin Fleischmann and Stanley Pons, claimed room-temperature “cold fusion.” Dozens of laboratories tried to replicate it over the next several months, and a consensus soon formed that they had erred.

In 2015 the Open Science Collaboration repeated 100 studies from three psychology journals. Of the originals, 97% had statistically significant results. Of the repeats, 36% did, and the effects were about half as large. The Academies note that not every failure to replicate is a mistake; some are a normal part of studying complex systems.

What is the strongest objection?

The strongest objection goes like this: if science never proves anything, why trust it more than any opinion? The answer is that “not proved” is not the same as “not known.”

Understanding Science points out that accepted ideas are reliable because many lines of evidence support them and their predictions keep coming true. Openness to change keeps that reliability honest. Until 1938, paleontologists accepted that coelacanths, an ancient kind of fish, had died out about 80 million years ago. Then a live one turned up off the coast of South Africa, and the idea was revised.

The theory of gravity shows the same pattern. The National Academies note that it has been backed by many observations on Earth, and that general relativity expanded it in the early 1900s. The Academies write that new knowledge that displaces or reframes older knowledge “should not be interpreted as a weakness in science.” A method that can admit mistakes can also fix them.

What do people often get wrong?

• “Scientists keep changing their minds, so nothing is reliable.” Understanding Science notes that news coverage tends to highlight disagreements, and that fast change at the cutting edge is normal and healthy. Ideas backed by many lines of evidence are unlikely to change.
• “Five sigma means 100 percent sure.” It means noise alone would rarely produce such a result. Hidden errors and other explanations still have to be ruled out, which is why independent teams check.
• “One study proves it.” A single study is a starting point. Confidence grows when other teams replicate it with their own data.
• “If science can’t prove it, anything goes.” Evidence comes in degrees. A claim with strong evidence and a claim with none are not equal just because neither is proved.

How can you check this yourself?

• Swap the verb. When a headline says “scientists prove,” read it as “scientists found evidence.” Then ask how strong the evidence is.
• Look for the uncertainty. Error bars show how precise a measurement is, and a p-value or sigma number shows how often noise alone would give such a result.
• Look for replication. Has an independent team, with its own data, found the same thing?
• Ask what would count against the idea. If no possible result could, it is not being tested.
• Check the label. Our answers use six evidence labels, from Established to Beyond science.
• Build the habits. See common thinking traps, how to tell good science from bad, and, for the process in history, how the expanding universe was proposed and tested.

Science does not deal in proof. It deals in evidence, and the best of that evidence is very strong.