How can antimatter exist at all? What amount of math had to be done until someone realized they can create it?
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There is actually a natural process that creates antimatter: Radioactive Beta Decay.
It comes in 2 types which involve a proton turning into a neutron or vice versa. To keep all of the energies balanced the nucleus will “throw out” this extra charge in the form of an electron or positron (antimatter electron).
If a positron is created, it is immediately annihilated with regular matter (electron) into 2 pure energy gamma rays. This amount of energy is based on the mass, which is always the same for electrons or positrons. So by measuring that specific gamma ray, we know an annihilation happened and what mass the antimatter particle was (which takes a surprisingly small amount of math IIRC, though at a pretty late stage in the development of physics).
Actually capturing antimatter is a whole different deal that I can’t even begin to confidently explain or even fathom, really. I do know that smashing atoms together with insane energy will release all sorts of weird particles, many being antimatter.
If we have the capability to measure particles that small in the first place, detecting their antimatter counterparts is actually very easy.
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