# What are examples of theories in recent history of science and mathematics that were hold pretty long but turned out non-true?

The atomic theory was already present in ancient Greece. In the nineteenth century it was disputed only to return with a vengeance later on.
Likewise the geocentric view was replaced by the helio centric one, to be replaced by Einstein's view which stated that both are equally valid.
Are there examples of theories that suffered the same faith? Or only the first part? I'm interested mainly in theories that were introduced from the time the present view had it's main predecessors ready, say from the time of Maxwell. Later FR and QM were introduced but within these confines for sure non-realities were upheld.

I ask because I am very conspicious about the Higgs mechanism. It was introduced in the context of the unification of the weak and electromagnetic force. It gives mass to the vector bodons governing the weak force and leaves the photon massles. Four massless particles are thought to exist before the spontaneous symmetry breaking of the Higgs field. And this field has some very weird properties. Its value is zero for non-zero field variables! This is reflected in the Mexican hat potential. The theory introduces ghost particles on top of that. If that doesn't make one frown... Nevertheless it is considered an integral (integrating) psrt of the standard model.In the future, this theory will be seen as another kind of phlogiston, for sure.

The theory can be replaced by a more fundamental though. There are equal amounts of matter and antimatter (only an asymmetric distribution) in that theory and only two elementary particles (you can't have less). There is no need for some magic mechanism and the weak force is just a residue one.

So. It would be comforting to know if the Higgs mechanism (not the particle) could turn out to be not true.

I mention the Higgs mechanism because it's a present day phlogiston and contrary to phlogiston unprovable.

• Like geocentrism, phlogiston and ether? How recent and how pretty long? The atomic theory that "returned with a vengeance" was very far removed from the Greek atoms with hooks. But Einstein's cosmological constant did make a comeback as dark energy. So did black holes. String theory didn't turn out either way yet, but the initial enthusiasm has waned. Even more so with magnetic monopoles and proton decay. Aug 6, 2021 at 12:59
• @Conifold As a matter of fact, proton decay is pretty easy envisioned in the theory I refer ti. I mean the era, say, of the last 150 years. Aug 6, 2021 at 13:02
• Please focus the question more, as it is remains unclear. I would also suggest to either expand on whatever you meant with the no Higgs mechanism or reduce that part. Aug 6, 2021 at 13:02
• @Mauricio I think the Higgs mechanism is a perfect example of present day phlogiston. Aug 6, 2021 at 13:03
• An example from mathematics is that it was generally believed that the logarithmic integral was always greater than the prime counting function until Littlewood proved that $\text{li}(x) - \pi(x)$ changed signs infinitely often. The first change occurs for $x$ approximately $10^{316}$.
– nwr
Aug 6, 2021 at 20:03

Massless neutrinos. Mostly certainly thought as massless since the 50s (even if some like scientists like Pontecorvo were against it since the beginning). Many people were even describing neutrino physics using Weyl equation (the equation for massless fermions). Neutrinos were definetely proved to be not massless in 1998 with Super Kamiokande.

• That's a very good example! The Higgs coupling was first supposed to be zero. It turned out to be very small though. Aug 6, 2021 at 18:13
• @DescheleSchilder No, this is a bad example. It was not that everyone thought that neutrino were massless with some wierdoes like Pontecorve holding minority view. It was simply thought that neutrino masses can be neglected which means that they may be massless but also may have small masses. You can find the discussions of the possible neutrino masses in pre-1998 textbooks, e.g. in 1982 Cheng & Li (of course also in Peskin & Schroeder and Weinberg shortly before the discovery)
– OON
Aug 12, 2021 at 4:46
• @DescheleSchilder Also we don't know Higgs couplings for neutrinos yet and don't know anything about their mass generation mechanism.
– OON
Aug 12, 2021 at 4:47
• @OON I get your point. We are living in more skeptical and empirical driven era, the possibility of massive neutrinos was discussed before any confirmation of the solar neutrinos problem. Yet I would argue that it is the case with more modern theories due to the nature of current science. Probably there were a few critics to phlogiston/caloric theories too, but the field of physics was much smaller. Aug 12, 2021 at 8:54

The Cosmological constant, according to Wikipedia with refs there in:

From the 1930s until the late 1990s, most physicists assumed the cosmological constant to be equal to zero.

In the 1990's

"astrophysicists carried out measurements on distant supernovae and showed that the speed of galaxies recession in relation to the Milky Way increases over time. The universe is in accelerated expansion, which requires having a strictly positive Λ.

• Maybe the steady state universe theory could have a mention here too. Aug 7, 2021 at 8:14
• Again this is also not very good example of the sort "There is this possible parameter which we can neglect, could be zero but also could be simply small"
– OON
Aug 12, 2021 at 4:49

The fine structure constant $$\alpha$$ which was believed to be $$\sim \frac{1}{137}$$ (and was taught this way in most physics courses till very recently) is now believed to vary with time. See https://en.wikipedia.org/wiki/Fine-structure_constant#Potential_Time-Variation

• Believed by whom? That Wikipedia article that you mentions says “So far, most experimental data is consistent with $\alpha$ being constant.” Sep 19, 2021 at 7:15
• Believed by all physicists. You should read the full article. For example, "Using the Keck telescopes and a data set of 128 quasars at redshifts 0.5 < z < 3, Webb et al. found that their spectra were consistent with a slight increase in α over the last 10–12 billion years. Specifically, they found that..." Sep 19, 2021 at 7:45
• "Believed by all physicists"? Highly doubtful statement. Dirac, for example, considered that alpha may not be constant. There have always been long debates if the "constants" are indeed constant and I doubt any physicist will rule this out totally, although the experimental evidence is that if they do vary, then the variations are too small or slow to detect with our present technology with enough certainty. But their constancy is not a dogma or belief. Feb 5 at 21:16

An example from mathematics is that it was generally believed that the logarithmic integral was always greater than the prime counting function until Littlewood proved that $$\operatorname{li}(x)−\pi(x)$$ changed signs infinitely often. The first change occurs for $$x$$ approximately $$10^{316}$$.

Thanks to @Nick who answered in a comment. That was before I included math. It's an example which shows that quite the opposite can be true of what was thought. It shows the hugeness of infinity. I wonder how it could be actually has been seen that for such a huge number it's untrue.

The steady-state universe was a model still believed to be viable in the fifties. Hoyle thought it to be true. But it isn't.

• I think the steady state theory was neither widely accepted nor accepted for a lengthy period of time. Aug 10, 2021 at 20:48
• @DrChuck I think it has even fans these days. A varying speed of light could create matter constantly. Aug 10, 2021 at 20:54