As far as my current experience goes there seems to be two types of intelligence at play: cognitive intelligence and silent intelligence. Cognitive intelligence seems largely at odds with silent intelligence. Cognitive intelligence is governed by unconscious forces but sometimes it can manifest itself consciously - rarely actually. With continued practice cognitive intelligence is brought into line with silent intelligence. Silent intelligence is far superior to any kind of meagre thought. It grows beautiful flowers and spins swirly galaxies and a bunch of other cool stuff. Aligning ourselves with such an intelligence must indeed be beneficial to our own unconscious intelligence. Practice affects our intelligence by subduing unconscious behaviours so that more conscious behaviours can take form.

Accelerate the advancement of science? Yes, perhaps with far less stupidity. 

This is doubtful. There is likely no direct connection between intelligence and mediation. People typically claim other changes from having a meditation practice but not more smarts.

I'm studying it right now, but I don't see IQ being correlated to Mindfulness. It's also debatable which intelligence people are talking about. Most of the studies in The Mindful Brain show that executive functions that control impulses become stronger and thicker. Being able to control impulses is a form of intelligence that is very important, but it won't make you pass a test. It may help your exam results in that you can control emotional dyregulation and do the best you can on an exam. Daniel Kahneman's Thinking Fast and Slow shows that practice and preparation are more important for self-efficacy, because when you habituate knowledge it can be applied more quickly. Nothing replaces consistent study. As long as you have an average IQ, with effort, you can be very intelligent and impactful in your life.

I have noticed that all the people I've ever met personally who were seriously invested in meditation clearly seemed to possess what would normally be considered above average intelligence. No real dummies on retreats, regardless of background. Is it that you need to be pretty smart to begin with in order to "get" meditation? Even vipassana retreats conducted in prison, IIRC, have been voluntary, so they may select for smarter prisoners. As for meditation increasing intelligence, for all it's worth it seems that the longer I daily maditate on the breath, the greater the decrease in my critical thinking, and learning capacity - I become very forgetful and increasingly unable to correlate information and draw conclusions. So I, at least, feel like mindfulness of the breath actually could potentially significantly dampen at least some of the aspects of cognition that make one appear "smart". I do become more open-minded, but it rather seems like an increase in gullibility when I'm not in that state. Like sometimes I'd believe almost anything.

One area where I know my intelligence was affected was when I first got into equanimity. There were some extra forgetful periods and a foggy brain. It was temporary, but if you're not used to it, it can be a little scary. I remember some other meditators on this site complaining about the same thing, but again it was temporary. I do remember Shinzen Young saying you might gain a couple of IQ points, but that doesn't seem like much

EDIT:

I found quote here from Shinzen:

https://www.shinzen.org/wp-content/uploads/2016/12/art_emptying-mind.pdf
Of course this means only reducing distractions from your thinking. I'm sure time pressure and certain situations where people are worried about rejection in jobs or worried about their grades can affect people, even if they have a good meditation practice. School counselors often have to deal with students having suicidal ideation because so much of their future school choices rides on their grades. Another area of concern is using meditation to avoid. When people have habitual stressful thinking, it takes years to reduce stress and meditation helps partially in the practice and partially because you've let go of responsibilities that are burning you out. This may be necessary in the beginning, but one has to face those responsibilities when returning from a retreat. 

It's an important question because many meditators are professionals and they hope to get worldly results from the practice.

Ultimately there will always be a certain about of growth pain. Daniel Kahneman talks about pupil dialation when people are tested with math problems. There's a certain amount of effort with rewiring no matter what. The effort and pain only go down when the problems become known and repetitive. What fires together, wires together, so the brain improves with practice, the same as always. Daniel Ingram found a spiritual example of this:

https://www.integrateddaniel.info/retreats/

Realize that learning and growth always involves suffering.

I did notice this mental block around doing math almost completely disappear after one particular opening early in practice but that seems more of a inhibition being discarded due to insight rather than an increase in intelligence. These inhibitions were reinforced by childhood stories: "I suck at math. I hated my math teachers. I was always better at essays...etc."

I do "feel" more intelligent than before taking on insight work but I'd wager that most of that is just confidence being freed up from the grips of self-conscious mental habits.

I agree with Shinzen in Richard's post. It seems that there's a greater efficiency and confidence to the mind that may make one experience increased mental power.       

Probably the most important thing I can say about meditation and intelligence is that you can go too far on it. As Britton said about side effects, you can decondition important signals (including traffic signals), and that there has to be a balance. Some stress is actually healthy, but we have to pick and choose more carefully. You want to let go of ruminating about things that distract, and cognitive therapy helps to zone in on inflexible thoughts that aren't realistic. That means to relax the body and thoughts and return to your activities. There are a couple of things I learned so far about high performance learning that you need to condition MORE of to develop intelligence:

1. Anders Ericsson pointed out that engaging with a skill really well (even if slow at first) is necessary. After you've staked out what a high quality procedure or skill is, then do enormous practice. This way you are not practicing mediocre skills. There are lots of studies of Deliberate Practice, especially with Spelling Bee's you an look up.

2. In conditioning psychology class there was a practice I learned, that sounds a lot like Thinking Introversion, where you create clear definitions of what you want to learn. One of the ways to do this is to create true and false testing questions. You define a concept you want to learn and use as many examples of the concept and non-examples to test yourself. In the textbook they said that doctors use this. This way you are able to recognize when something is or isn't when you encounter phenomenon. A lot of mistakes in work involve not recognizing what you are seeing, and therefore not being prepared for it. The more thorough your IS's and IS NOT's in your practice, the more thorough you understand a topic. You can use a diamond example. "What I'm seeing is this side of the diamond and it's also not the other side." When you know a subject really well you'll know because whatever is thrown at you, you know what to do, and if you've been practicing #1, then you'll do it really well.

So #1 involves a lot of effort because of the practice and #2 involves a lot of cognitive processing to understand a subject. All these drain a certain amount of energy, but if you have less worrying thoughts that interrupt it, or low self-esteem issues about what you are capable of, these practices will be engaged with more and you'll learn faster because you're not spending time worrying about psychological baggage. If you have psychological baggage, you can still do the above practices and get good results, like most non-meditators, but it's less efficient.