What would it even mean for science and religion to be compatible?
Science acquires knowledge by examining the evidence presented to us by our senses. The meaning of evidence in this context is expressed very clearly in the following example, given by artificial intelligence researcher Eliezer Yudkowsky:
Walking along the street, your shoelaces come untied. Shortly thereafter, for some odd reason, you start believing your shoelaces are untied. Light leaves the Sun and strikes your shoelaces and bounces off; some photons enter the pupils of your eyes and strike your retina; the energy of the photons triggers neural impulses; the neural impulses are transmitted to the visual-processing areas of the brain; and there the optical information is processed and reconstructed into a 3D model that is recognized as an untied shoelace. There is a sequence of events, a chain of cause and effect, within the world and your brain, by which you end up believing what you believe. The final outcome of the process is a state of mind, which mirrors the state of your actual shoelaces.
What is evidence? It is an event entangled, by links of cause and effect, with whatever you want to know about. If the target of your inquiry is your shoelaces, for example, then the light entering your pupils is evidence entangled with your shoelaces.
Because it requires this sort of evidence-entanglement, science only makes claims that can be tested empirically. If a certain statement of fact isn’t causally linked to anything we can directly experience, then science won’t make any claims about it.
Historically, the Jewish religion hasn’t held its claims to the standard of being entangled with observable evidence. Some of its claims, like the creation of the world 6000 years ago, can be confirmed or rejected by such evidence, while others, like the existence of God, cannot be addressed by similar methods.
People who want science and the Jewish religion to coexist usually speak in terms of two separate spheres. In the empirical sphere, they either acknowledge that science has disproved some claims made by the Jewish religion or they find sources to suggest that the Jewish religion never actually took those claims very seriously. Jews have been suggesting that reason can challenge tradition in some areas since ancient times; the medieval rabbis Rambam and Saadia Gaon both made statements to that effect.
When people want to reconcile science and the Jewish religion, they’re suggesting that they can simultaneously accept the non-empirical claims of Judaism and the empirical claims of science. They want to believe in the Jewish conception of God while simultaneously accepting scientific models that explain the natural world, like evolution and the Big Bang theory. This belief system works pretty well upon a superficial examination. It contains no obvious contradictions.
But it’s not fair to call that belief system a reconciliation of science and Judaism. Truly accepting science means more than just accepting the specific findings that scientists come up with. It also means accepting the underlying process that scientists use to form beliefs- the systematic evaluation of beliefs based on evidence. It’s clearly impossible to use this method to form beliefs regarding God.
It’s pretty clear that faithful Jews wouldn’t consider their belief in God to be scientific. There isn’t any evidence (in the sense described above of direct causal entanglement) supporting such a belief. Nobody has ever used the scientific process to demonstrate a causal link between God and anything in the natural world.
So these people must be evaluating their belief in God based on other criteria. Some of them want the sense of community that religion brings, or the comfort that comes from believing that there’s something powerful and meaningful beyond them. Others come up with arguments that seem to prove the existence of a higher power, but the whole point of science is that you don’t just get to do that! You hold beliefs because they’re linked to evidence- not just because they make you feel all warm and fuzzy inside, and not even because they feel like they make sense inside of your head.
Sorry, Jews. You still have to choose. Believing in God is great, but we can’t keep claiming that it’s compatible with science.