These Sample Programs provide guidelines to major in mathematics at Bryn Mawr from a few different perspectives. Certainly, in every case, there is substantial flexibility to tailor a course of study to fit an individual’s personal preferences and needs. This selection is by no means a complete picture of every alternative. A student can choose from a variety of options to fashion a program that suits her desires. Almost anything is possible in our mathematics department!
Please note that the annual Course Guide indicates exactly which course meets which Divisional Requirement by the use of Roman numerals I, II, and III. In all departments, many courses are offered every semester while some courses are offered only one of the two semesters each year, or even every other year. These factors must be taken into consideration in any long term planning. The illustrations available here can be ideal starting points to create your own perfect fouryear curriculum!
All programs of study MUST be designed with the advice of a Major Advisor.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I 
Math 102: Calculus II Foreign Language Distribution Requirement Free Elective 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra 
Junior Year 
Math 301: Real Analysis I Math 303: Abstract Algebra I Free Elective Free Elective 
Math 302 or Math 304 
Senior Year 
Math 398: Senior Conference Free Elective 
Math Elective (200 or 300 level) 
Note: If considering graduate study, enroll in as many 300level math electives as possible.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Major Advisor.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 102: Calculus II Emily Balch Seminar

Math 203: Linear Algebra 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 206: Transition to Higher Math (as math elective) Math Elective (200 or 300 level) Distribution Requirement Free Elective 
Junior Year 
Math 301: Real Analysis I Math 303: Abstract Algebra I Free Elective Free Elective 
Math 302 or Math 304 Math Elective (200 or 300 level) Free Elective Free Elective 
Senior Year 
Math 398: Senior Conference Free Elective Free Elective Free Elective 
Math Elective (200 or 300 level) 
Note: A student following this program should consider doing research and/or Honors in the senior year. Discuss this possibility with a Major Advisor early in the junior year. If considering graduate study, enroll in as many 300level math electives as possible.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Major Advisor.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 201: Multivariable Calculus Bmily Balch Seminar Foreign Language Distribution Requiremet 
Math 203: Linear Algebra Distribution Requirement 
Sophomore Year 
Math 301: Real Analysis I Distribution Requirement

Math 302 or Math 304 Distribution Requirement Free Elective Free Elective 
Junior Year 
Math Elective (200 or 300 level) Free Elective Free Elective Free Elective 
Math Elective (200 or 300 level) Free Elective Free Elective Free Elective 
Senior Year 
Math 398: Senior Conference Free Elective Free Elective Free Elective 
Math Elective (200 or 300 level) 
Note: A student following this program should consider doing research and/or Honors in the senior year. Discuss this possibility with a Major Advisor early in the junior year. If considering graduate study, enroll in as many 300level math electives as possible.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Major Advisor.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra 
Sophomore Year 
Math 301: Real Analysis I 
Math 302: Real Analysis II Math 304: Abstract Algebra II Distribution Requirement Free Elective 
Junior Year 
Graduate Math Course* Free Elective** Free Elective Free Elective 
Graduate Math Course* Free Elective** Free Elective Free Elective 
Senior Year 
Graduate Math Course* Math 398: Senior Conference Free Elective 
Graduate Math Course* Free Elective Free Elective 
Note: This plan assumes 4 transfer credits (such as AP, IB) toward the BMC degree.
*Two Graduate Math courses may be advanced 300level Math courses with additional work. Up to two graduate courses may be taken for both AB and MA credit. **It is highly recommended that a Math elective be chosen.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Major Advisor.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I Emily Balch Seminar Foreign Language Distribution Requirement 
Math 102: Calculus II 
Sophomore Year 
Math 201: Multivariable Calculus Free Elective 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Distribution Requirement Free Elective 
Junior Year 
Math 303 or Math 301 Math Elective (200 or 300 level) Free Elective Free Elective 
SEMESTER AWAY (Free Electives) 
Senior Year 
Math 301 or Math 303 Math 398: Senior Conference Math Elective (200 or 300 level) Free Elective 
Math 302 or Math 304 
NOTE: Meeting with a Mathematics Major Advisor as early as possible can increase the options available.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Major Advisor.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 102: Calculus II Emily Balch Seminar Foreign Language Distribution Requirement 
Math 203: Linear Algebra 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 206: Transition to Higher Math (as math elective)
Math Elective (200 or 300 level) Distribution Requirement Free Elective 
Junior Year 
Math 303 or Math 301 Math Elective (200 or 300 level) Free Elective Free Elective 
SEMESTER AWAY (Free Electives) 
Senior Year 
Math 301 or Math 303 Math 398: Senior Conference Free Elective Free Elective 
Math 302 or Math 304 
NOTE: Meeting with a Mathematics Major Advisor as early as possible can increase the options available.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
YOU MUST MEET WITH MAJOR ADVISORS IN BOTH DEPARTMENTS.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 102: Calculus II Phys 121: Modeling the Physical World: Foundations & Frontiers Emily Balch Seminar Foreign Language 
Math 203: Linear Algebra 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 206: Transition to Higher Math (as math elective) Free Elective 
Junior Year 
Math 301: Real Analysis I 
Math 302 or Math 304 Math Elective (200 or 300 level) Phys 305 or 331 Free Elective 
Senior Year 
Math 398: Senior Conference Physics Elective (300 level) Physics 398: Senior Seminar I Free Elective 
Math Elective (200 or 300 level) 
Some suggested courses to fulfill remaining Math Electives are Math 311 (Partial Differential Equations), Math 312 (Topology) and Math 322 (Functions of Complex Variables), because these courses relate best to the field of Physics.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Mathematics Major Advisor and a Health Professions Advisor. Students should also refer to the Health Professions web site at: www.brynmawr.edu/healthpro.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I 
Math 102: Calculus II 
Sophomore Year 
Math 201: Multivariable Calculus Distribution Requirement 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Chem 104: General Chemistry II Distribution Requirement 
Junior Year 
Math 301: Real Analysis I

Math 302 or Math 304 Free Elective 
Senior Year 
Math 398: Senior Conference Math Elective (200 or 300 level) Physics 101: Intro. Physics I Free Elective 
Math Elective (200 or 300 level) 
Note: This plan allows the student to have a “glide year” after graduation, before entering medical school. It is entirely possible to design a program of study that permits the student to enter medical school immediately upon graduation from Bryn Mawr. See a Health Professions Advisor for details.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
Programs of study MUST be designed with the advice of a Major Advisor in Mathematics and with another advisor from the Education Program.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I Emily Balch Seminar Foreign Language Distribution Requirement 
Math 102: Calculus II 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Distribution Requirement Free Elective 
Junior Year 
Math 301: Real Analysis I Ed 210 or 275 (at BMC or HVD) 
Math 302 or Math 304 Math Elective (200 or 300 level) Math Elective (200 or 300 level) Free Elective 
Senior Year 
Math 398: Senior Conference Ed 301: Curriculum/Pedagogy Sem. 
Ed 302: Practice Teaching Seminar 
Suggested math electives: Probability: BMC 205 or HC 218; Discrete Math: BMC 231; Geometry: BMC 221 or HC 205b. Meeting with a math major advisor as early as possible can increase the available options.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
YOU MUST MEET WITH MAJOR ADVISORS IN BOTH DEPARTMENTS.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I CMSC 110: Intro. to Computer Science Emily Balch Seminar Foreign Language 
Math 102: Calculus II Distribution Requirement Foreign Language 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math Elective (200 or 300 level) CMSC 206: Data Structures Distribution Requirement 
Junior Year 
Math 301: Real Analysis I Free Elective 
Math 302 or Math 304 Math Elective (200 or 300 level) Computer Science Elective Free Elective 
Senior Year 
Math 398: Senior Conference Computer Science Elective Free Elective Free Elective 
Math Elective (200 or 300 level) 
Note: Computer Science electives must include any two of CMSC 240, 245, 246, 340, 345.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
YOU MUST MEET WITH MAJOR ADVISORS IN BOTH DEPARTMENTS.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I CMSC 110: Intro. Computer Science Emily Balch Seminar Foreign Language 
Math 102: Calculus II Distribution Requirement 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Computer Science Elective Distribution Requirement 
Junior Year 
Math 301 or Math 303 
Math 302 or Math 304 
Senior Year 
Math 303 or Math 301 
Math Elective (200 or 300 level) 
Note: The following Computer Science courses double count for the major in Mathematics and the major in Computer Science:
CMSC 231 (Discrete Mathematics), CMSC 340 (Analysis of Algorithms), and
CMSC 345 (Theory of Computation).
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
YOU MUST MEET WITH MAJOR ADVISORS IN BOTH DEPARTMENTS.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I Geology 101: How the Earth Works Emily Balch Seminar Foreign Language 
Math 102: Calculus II Distribution Requirement 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Chem 104, Physics 102, or Physics 122 Distribution Requirement 
Junior Year 
Math 301 or Math 303 
Math 302 or Math 304 Geology 204: Structural Geology Free Elective Free Elective 
Senior Year 
Math 303 or Math 301 Math 398: Senior Conference Math Elective (200 or 300 level) Geology Elective (300 level) 
Math Elective (200 or 300 level) 
Note: CMSC 110 (Introduction to Computer Science) is strongly recommended.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
YOU MUST MEET WITH MAJOR ADVISORS IN BOTH DEPARTMENTS.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I Chem 103: General Chemistry I Emily Balch Seminar Foreign Language 
Math 102: Calculus II Distribution Requirement 
Sophomore Year 
Math 201: Multivariable Calculus Distribution Requirement 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Chem 212: Organic Chemistry II Physics 122 or 102 
Junior Year 
Math 301 or Math 303 
Math 302 or Math 304 Chem 231: Inorganic Chemistry Chem 252: Research Methodology II 
Senior Year 
Math 301 or Math 303 Math Elective (200 or 300 level) Math 398: Senior Conference Chemistry Elective (300 level) 
Math Elective (200 or 300 level) 
Suggested Math Electives: Math 210, Math 251 or Math 351, Math 312.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I Soc 102: Society, Culture and the Individual Emily Balch Seminar Foreign Language 
Math 102: Calculus II 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Sociology 265: Research Design and Statistical Analysis Distribution Requirement 
Junior Year 
Math 301: Real Analysis I 
Math 302 or Math 304 Math Elective (200 or 300 level) Sociology 303: Junior Conference (DisciplineBased Intensive Writing) Sociology Elective* 
Senior Year 
Math 398: Senior Conference Sociology 398: Senior Conference Math Elective (200 or 300 level) Sociology Elective* 
Math Elective (200 or 300 level) 
* Of the 5 Sociology Electives, at least 1 must be at the 300level, and 1 may be at the 100level.
Note: Two of the math courses count as allied work for the Sociology Major. To design your program, you must meet with a Math Major Advisor and with Mary Osirim in the Sociology Department.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I Emily Balch Seminar Foreign Language Distribution Requirement 
Math 102: Calculus II 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) English 250: Methods of Literary Study Free Elective 
Junior Year 
Math 301: Real Analysis I 
Math 302 or Math 304 Math Elective (200 or 300 level) English Elective (200 level) * English Elective (300 level) * 
Senior Year 
Math 398: Senior Conference English 398: Senior Seminar Math Elective (200 or 300 level) English Elective* 
Math Elective (200 or 300 level) 
*Of the 8 English Electives, at least 3 must be at the 300level (not counting English 398 or 399). You need to take two 200level classes before taking English 250. English 250 should be completed either in the spring semester of sophomore year or the fall semester of junior year.
Note: You must meet regularly with advisors in both departments and gain approval to double major.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.
All programs of study MUST be designed with the advice of a Mathematics Major Advisor and the Bryn Mawr Director of the Environmental Studies Program, Professor Victor Donnay (vdonnay@brynmawr.edu).
Note: In each sample program, distribution requirements and electives can be interchanged among the various semesters to accommodate the student's desires.
Fall Semester 
Spring Semester 

Freshman Year 
Math 101: Calculus I EnvS 101: Introduction to Environmental Studies Emily Balch Seminar Foreign Language 
Math 102: Calculus II Foreign Language Distribution Requirement 
Sophomore Year 
Math 201: Multivariable Calculus 
Math 203: Linear Algebra Math 206: Transition to Higher Math (as math elective) Environmental Studies Elective* Distribution Requirement 
Junior Year 
Math 301: Real Analysis I Free Elective 
Math 302 or Math 304 Math Elective (200 or 300 level) Free Elective Free Elective 
Senior Year 
Math 398: Senior Conference Math Elective (200 or 300 level) Free Elective Free Elective 
Math Elective (200 or 300 level) 
*The Environmental Studies minor requires four electives beyond the introductory EnvS 101 and the capstone EnvS 397, any of which can be used to satisfy distribution requirements. Two of these must be chosen from the approved list in the natural sciences, math and engineering (many of which satisfy SI), and two from the approved list in the humanities and social sciences (many of which satisfy CI, CC or IP).
Note: Math 210 Differential Equations is strongly suggested as a Math Elective.
All programs must satisfy the Bryn Mawr College Distribution Requirement
One semester course in each of the following four "Approaches to Inquiry"
Critical Interpretation (CI)  critically interpreting works, such as texts, objects, artistic creations and performances, through a process of close reading.
CrossCultural Analysis (CC)  analyzing the variety of societal systems and patterns of behavior across space.
Inquiry into the Past (IP)  inquiring into the development and transformation of human experience over time.
Scientific Investigation (SI)  understanding the natural world by testing hypotheses against observational evidence.