According to Catholic Tradition: Was Jesus a Genius?

My goal is that they may be encouraged in heart and united in love, so that they may have the full riches of complete understanding, in order that they may know the mystery of God, namely, Christ, in whom are hidden all the treasures of wisdom and knowledge. (Colossians 2:2-3)

If Christ possesses all wisdom and knowledge, I guess that includes brain surgery.

In the Socratic method, the interchange between teacher and student probes reality and reveals new truths. That interaction is essential. The student's act of asking questions propels the teacher to new understanding, for himself and for his pupils.

Jesus did not need the Socratic method.

29 Then Jesus’ disciples said, “Now you are speaking clearly and without figures of speech. 30 Now we can see that you know all things and that you do not even need to have anyone ask you questions. This makes us believe that you came from God.” (John 16:29-30)

The above is an affirmation that Jesus had attained perfect knowledge by the time of the Last Supper.

(Disclaimer: this answer assumes a Trinitarian perspective.)

What do you mean by "genius"?

Jesus is God. God "hid" certain knowledge from "himself" (i.e. His incarnation as Christ) during said incarnation, but aside from those exceptions, Jesus was (still) omniscient. There are a few examples where He knew of events occurring far away, and at least one where he was aware of a person's thoughts.

Jesus is the Author of Life (see Genesis 1-2, John 1). Asking if the entity that made humans (and everything else in all of Creation) has "at least a 21st century education of the world and of science", or enough knowledge to perform brain surgery, is rather silly.

Anyway, at least when it comes to brain surgery, I doubt He would bother; he performed many healing miracles and even three resurrections (counting Himself). I can't imagine why, if He desired to heal someone, He wouldn't just do so. Similarly, He is recorded as creating bread, fish and wine miraculously. It stands to reason that He can create any artifact He wishes, whether by natural means (i.e. using tools) or supernatural.

That all said... consider Luke 2:41-52:

⁴⁸ [Jesus' parents] found [twelve-year-old Jesus] in the temple, sitting among the teachers, listening to them and asking them questions. ⁴⁷ And all who heard him were amazed at his understanding and his answers.

At minimum, the Bible teaches that Jesus possessed a noteworthy degree of wisdom, which might match one possible definition of "genius".

Yes.

Being God, Christ had divine knowledge, knowing Himself perfectly. Having a human nature, he also had infused and acquired knowledge.

Explaining "Whether Christ had any knowledge besides the Divine?" (Summa Theologica III q. 9 a. 1), St. Thomas Aquinas writes (co.):

the Son of God assumed an entire human nature, i.e. not only a body, but also a soul, and not only a sensitive, but also a rational soul. And therefore it behooved Him to have created knowledge, for three reasons.

1. on account of the soul's perfection. […]
2. because, […] Christ would have had an intellective soul to no purpose if He had not understood by it; and this pertains to created knowledge.
3. because some created knowledge pertains to the nature of the human soul, viz. that whereby we naturally know first principles; since we are here taking knowledge for any cognition of the human intellect. Now nothing natural was wanting to Christ, since He took the whole human nature, as stated above (q. 5). And hence the Sixth Council [*Third Council of Constantinople, Act. 4] condemned the opinion of those who denied that in Christ there are two knowledges or wisdoms.

Now, did "the soul of Christ" "know all things in the Word" (Summa Theologica III q. 10 a. 2)? St. Thomas answers (co.):

When it is inquired whether Christ knows all things in the Word, "all things" may be taken in two ways:

1. properly, to stand for all that in any way whatsoever is, will be, or was done, said, or thought, by whomsoever and at any time. And in this way it must be said that the soul of Christ knows all things in the Word. For every created intellect knows in the Word, not all simply, but so many more things the more perfectly it sees the Word. […]
2. "all things" may be taken widely, as extending not merely to such things as are in act at some time, but even to such things as are in potentiality, and never have been nor ever will be reduced to actuality.
   • Now some of these are in the Divine power alone, and not all of these does the soul of Christ know in the Word. For this would be to comprehend all that God could do, which would be to comprehend the Divine power, and, consequently, the Divine Essence. For every power is known from the knowledge of all it can do.
   • Some, however, are not only in the power of God, but also in the power of the creature; and all of these the soul of Christ knows in the Word; for it comprehends in the Word the essence of every creature, and, consequently, its power and virtue, and all things that are in the power of the creature.

Thus, Christ's human soul knows all what creatures can do,* but it does not understand all what God can possibly (but has not and will not) do.

^{*This includes what human creatures have done creating "21st century education of the world and of science" and "brain surgery".}

Christ even had wonder, in his empiric (experiential) knowledge, "in order to teach us to wonder at what He Himself wondered at." (Summa Theologica III q. 15 a. 8 co.).

Trinitarians will say Jesus was 'fully human' - as such, the question is applicable and can be rephrased as 'in his human nature' or some such thing.

What Jesus says and does conveys significant intelligence. He was clearly very familiar with the Jewish scriptures, and innovated theologically (some examples are given here). He was clearly precocious in this area, as in Luke 2:46-47.

"46 Finally, after three days they found Him in the temple courts, sitting among the teachers, listening to them and asking them questions. 47 And all who heard Him were astounded at His understanding and His answers."

He probably could read and write, which would be an unusual accomplishment for his time given his background as a carpenter's son. He engaged in high-level debate or discussion with Jewish scribes (an example, see Mark 12) - the intelligentsia of the time - apparently leaving them incapable of a good response at times.

Given this, I think it's reasonable to conclude Jesus was highly intelligent.