(I think that you have gotten some excellent answers from others, and am not trying to contend for "accepted answer". I thought some added information might be helpful.)
Identification can be important in planning to provide for gifted children's needs. First, you may have an inaccurate sense of your child's abilities. The term "genius" is subject to a wide array of interpretations; many use it in a quite restrictive way, with the idea that only a select few individuals (Einsteins, Mozarts etc.) are geniuses. Many people also have a vague notion that only prodigies are deserving of the label "genius". Instead of thinking about whether your child is a genius or not (as he may be by some measures), it might be useful as a first step to figure out just how gifted he may be-- because profoundly gifted people may have vastly different needs from highly gifted, who are often highly different needs-wise from moderately gifted, who themselves are still different enough from average to have difficulty in a standard classroom.
(For what it's worth, your son is likely to be at least highly gifted if he is doing algebra and trigonometry at age 7, although the term "algebra" has undergone somewhat of an expansion in recent years; I recall one woman reporting proudly that her first grader was doing algebra, when it turned out to be simple variable replacement sort of stuff. My son who is 7 is currently working through geometry and algebra courses simultaneously, and has been tested as "profoundly gifted", again for what it's worth. Achievement is not the same as ability, of course.)
Have you considered testing? While testing may raise uncomfortable feelings of not wanting to pin down a child with numbers (I feel this way myself, especially as I largely subscribe to Joseph Renzulli's three-ring model of giftedness and also know that sometimes people don't perform at their best on tests), testing is likely to tell you a great deal about your child that will be useful in planning for him, as well as simply understanding him. Testing can also be useful in gaining access to programs.
In considering whether to test, first I would assess what gifted programs you may be able to access for your son; see if they have any specific criteria (not all programs accept all tests). If money is an issue, explore options such as the possibility of free testing through your local school, or for cheap through the psychology department at a local university. However, be aware that the best results are often achieved by seeking out a professional familiar with testing gifted children; for example, local schools often do a subpar job, depressing results, because of issues including lack of expertise and bias. If you do test, make sure to get a full written report and not just a list of scores, and make sure that all tests are administered which may be required to get access to programs or services (testing with subsets of full tests from the WISC-IV, SB-V, and DAS-II is not uncommon). If your son tests highly enough (as he well might) and you are in the U.S., I would consider applying to the Davidson Young Scholars program, since it can provide much-needed planning help, as well as access to nationwide gifted programs and tuition assistance.
Educational strategies available for serving the gifted vary widely, and deciding on an appropriate approach depends on considerations of the child's social and emotional needs as well as academic needs. While a moderately gifted or "bright" student may be able to get by with a few extra accommodations, such as unrestricted higher-level reading during class time and math enrichment to do while the rest of the class catches up, at some point a gifted child's ability to learn quickly and deeply may require further intervention.
A gifted child can experience difficulties because not only do they often learn in different ways, but their pace can be vastly different, often letting highly gifted children learn many times faster than normal and with good integration and recall. That implies that some sort of acceleration is needed or else these children's intellectual growth-- or, even worse, desire to learn-- will be stunted.
Acceleration strategies which may be used to allow gifted children to learn at a proper pace include early admission, grade acceleration, subject acceleration, continuous progress, self-paced instruction, combined classes, curriculum compacting, and telescoping curriculum. Two of the most common include grade acceleration (skipping or double promotion) and subject acceleration. Both may be highly beneficial if correctly implemented; I recommend reading A Nation Deceived for a fairly comprehensive overview of research on the subject.
Note that for highly gifted children a skip/subject acceleration or two will often not be enough; all such measures may do is briefly level-set a child at a roughly appropriate subject-matter level, but problems of pacing and depth of material may remain. Expect therefore that even if you decide to skip, it's often going to be only a temporary fix.
The IOWA Acceleration Scale is a helpful aid in deciding whether acceleration is appropriate, and in fact is used by many school districts in deciding whether a grade skip may be appropriate in a specific case. Note that if a child does not desire a skip, it is never recommended.
Homeschooling is certainly a good option, and in some cases may be the only realistic one (e.g. where there is a vast mismatch between the local school options and a child's needs, which sometimes happens when a school is inflexible). You should also consider engaging with the school to see what services they may offer, but be aware that advocacy for a highly gifted child in a backwards school system may take years and still yield little benefit. Become informed on your state's support for gifted education; some states have gifted education mandates, which may provide for mandatory free testing, gifted IEPs for identified students, and the like. If your school is not ideal, look around for others in the area, including charter schools and private schools, many of which offer scholarships if money is an issue.
Another option which works for many is afterschooling, i.e. supplementation of schoolwork with enrichment of some sort after school or on weekends. I have found this to be most helpful for allowing my son's interests to grow in areas not served by the school. However, it cannot perfectly address a mismatch in an academic area such as math, without modification of schooling during the day. Why should a child learning algebra and reading adult-level fiction sit through entire class periods where he is "taught" things learned years before, and restricted from spending his time more productively? In the case of my son, we currently do brief math lessons at home three days a week after school, and send work to school for him to do during math time, as double acceleration in math was insufficient, and the school balked at sending him to the middle school for math at his current age. The current arrangement at least lets him use his time more productively.
Mentorship can be a great option, and it can be used as a supplement to other forms of instruction. Your son may not yet be at a level of achievement where it would be very helpful.
A few tips:
Ask your son what he'd like the most, what his ideal schooling situation would be.
Consider that for children where the academic mismatch is severe, acceleration may be the best option despite being suboptimal socially. That is, you cannot let worries about ruining his childhood prevent you from serving his urgent academic needs. Yes, it's true that for a skipped child classmates will generally drive earlier, be more mature physically, etc. Those factors are important to consider, but so is the evidence that acceleration is generally positive (see, e.g. "A Nation Deceived") and may even be necessary to maximize growth potential for certain fields. The best of all worlds, of course, would be to find a schooling situation with other highly gifted youth, but those are rare.
The right teacher can make a world of difference. Don't be afraid to advocate for a particular teacher in an upcoming year, if you think that he or she will make a difference. Be alert for bias on the part of teachers; tread lightly with assertions of giftedness or gifted needs until you feel a new one out. Teachers like to feel that they have noticed gifted traits for themselves, and you have to be aware of perceptions that you may be one of those parents ("My Johnny is just so special").
If you determine that a teacher or school is not doing right by your son, don't sit around and wait for things to change. They won't.
If you engage in advocacy with the school, politely leave a paper/email trail of all interactions. Find out about the law pertaining to gifted education in your area. If your school tries any funny business such as inaccurately stating what's been agreed to, consider using your FERPA right (in the U.S., obviously) to amend your son's education file. Be politely persistent.
Don't allow a school to delegate to next year's teacher how to implement gifted services for your child, leaving undecided exactly what will be done. Most teachers have little to no experience or training with highly gifted children, and this will only result in a massive delay.
Teachers will often be open to minor enrichment with a minimum of hassle if it means little or no work for them. For example, in some classrooms, especially in the younger years, it's common to see restrictions on reading: a child may be forced to pick from books aimed at young children during reading time, or may be restricted to a young-reader's section during library trips. Politely ask for any such restrictions to be lifted, offering to send material from home and mentioning what your child is up to at home; teachers are often unaware, especially with a child that likes to "fly under the radar".
If your school offers mixed-grade classrooms, those can be a great way to try out a "soft skip". For example, maybe your son goes into a grade 3-4 mixed classroom, where he is given a lot of the material that the fourth graders get, and you and the teacher can assess how well he'd do socially if promoted to fifth the following year.
Scouting, sports, and similar activities are great for encouraging appropriate physical and emotional development. They can go a long way in helping an accelerated child (or any gifted child) feel normal in his own skin.
Your child may have special emotional needs, not just academic ones. Perfectionism is a common issue; some gifted children may feel like impostors. Try to make sure that no matter what happens, your child feels that academic supports are just giving him what's normal for him.
If you can, try to find other gifted people in the area. At your son's age, he may find these through robotics or other clubs, through social groups for gifted people, etc.
Since your son is highly interested in math, consider using the Art of Problem Solving resources, including the free Alcumus. These are designed to stimulate highly gifted students by challenging them to discover new principles through tough problems. I could go on at length recommending math-related enrichment, but for now will just mention Ed Zaccaro, Martin Gardner, The Moscow Puzzles, and Raymond Smullyan.
Your son is also at a good age for learning computer programming, which would help him develop problem solving and modular thinking skills. If he's interested you may want to check out Scratch, Python, Java (Eclipse is a good free IDE), Lego Mindstorms, Arduino, etc.
Some sites that may be useful:
About Gifted Children
Center for Talent Development
Center for Talented Youth
Critical Thinking Co.
Davidson Institute for Talent Development
National Association for Gifted Children
Supporting Emotional Needs of the Gifted
The following are currently the most active forums related to gifted children and education:
Accelerated Learner Board @ The Well-Trained Mind
Gifted Issues @ Davidson Institute for Talent Development
Parenting the Gifted Child @ mothering.com