Knowledge is generated through critical and creative thinking. Creative thought is something new or original created with value. Critical thinking is a type of thinking that questions assumptions and validates or invalidates a current belief or something said to have previously been true. Knowledge is created through the culmination of generally accepted assumptions and creativity. How do you separate general assumptions and creativity? These two types of thinking can easily be separated with regards to concrete or realistic ideas versus abstract or original ideas, however to generate new and acceptable knowledge critical and creative thinking must interact together. Questioning long-held beliefs by creating new, unorthodox ideas will expose the most beneficial knowledge to the world. Mathematics can be concrete and use reason as a way of knowing. These are concepts learned through repetitive procedures. Critical thinking is a type of reasoning that uses logic that will never deviate. The first mathematics concepts taught in schools are believed to be concrete with fixed steps and formulas for solving problems. Just think about the steps previously taught and accept them as true. Concepts can only be accepted as true by using the abilities to process and generate information and beliefs. However, using skills as an “exercise” without meaning or understanding is not critical thinking. The area of ​​a right triangle is always assumed to be half the base times the height. Reasoning can be used through drawing a grid to prove that this formula is true. Therefore, mathematics uses critical thinking as a modality of skills known to guide behavior based on intellectual engagement… half of the paper… generated over time through technological developments, scientific advances, and advances in mathematics and art. Architecture and engineering incorporate mathematics and the arts through designing buildings or constructing bridges using creative and critical thinking. Another example is computer graphics related to the incorporation of mathematics and art. This knowledge is generated over time through technological developments, pushing new limits and expanding old ideas. Both critical thinking and creative thinking are necessary to generate new knowledge. Works Cited http://it.toolbox.com/blogs/enterprise-solutions/using-creative-problem-solving-11491 http://depmath.ulbsibiu.ro/educamath/ em/vol1nr1/marcut/marcut.pdfhttp:/ /forumonpublicpolicy.com/spring2010.vol2010/spring2010archive/karakas.pdfhttp://des.emory.edu/mfp/efficacynotgiveup.html