Much needs to be done in mathematics and mathematical education:

1. The Gibbs-Heaviside vector algebra has a cross-product which is not associative and without an inverse. Hence, the standard definition of vector space forms an additive group, but allows only multiplication by a scalar -- no multiplicative group. However, in multivector theory, by contrast, products are associative and all vectors have inverses, as have all non-projective multtivectors. Hence, an extended vector space with additive and multiplicative group can be considered.
2. A Mathematical Handbook (PL) needs to be developed to aid teachers.
3. A Syntactic Dictionary (PL) needs development to aid teachers, students, and self-teaching adults.
4. The whole of the arithmetic, algebra, geometry, analysis of complex numbers can be recast in the language of multivectors, without any explicit reference to i = -1. This task needs to be carried out to provide alternative learning for those who might benefit from it.
5. Develop means for interactive derivation of multivector theory (say, in JavaScript), so that students can "discover it for themselves".
6. In particular, recasting "the theory of a complex variable" in multivector language allows extensions into higher dimensions^[31] not possible in the conventional Language. Not only would this provide advances in learning but perhaps advances in mathematical physics.
7. The subject of o-probability (PL) needs to be developed in mathematics, statistics, and in applications (especially in biology and evolutionary theory, where observations are predominantly of order/degree, but the proabilities are only in type/kind).
8. Two consequences of frinteger theory (PL) are that (1) innumerable events for probability measure are being ignored; (2) innumerable queries in database applications are being ignored. Correction is needed.
9. The "lessons" of point sets (PL) in mathematics and the sciences need to be developed.
10. Investigate the possibility that every algorithm can be recast in antitonic language.
11. Investigate the possibility that all of mathematics can be described in bypass language.
12. Investigate the possibility that every process is FuTesatefu.
13. Investigate the possibility of SaTefutesa processes.
14. Develop generative arithmetic in the vector-multivector format and develop a few textbooks thereof ONLINE.
15. Develop means for interactive derivation of generative arithmetic (say, in JavaScript), so that students can "discover it for themselves".
16. Investigate applications of the fidance measure to business and other administrative processes.
17. Investigate applications of the asserbility measure.
18. Investigate applications of digital fuzzy logic.
19. Investigate applications of intrinsic arithmetic.
20. Just as the discrete binomial proability distribution gives rise to the continuous normal distribution function. Investigate similar extension of the partorial probability distribution.
21. Investigate the derivation of Euclidean geometry from reflection and its consequences in mathematics and mathematical physics.
22. Investigate possibility of deriving and developing bracket theory from alternating sum in elementary numerical algebra.